Questions & answers 2001

Go to the collection 2003, 2004. 2005. 2007.

The following questions have been put foreward by the participants of the first tele-course on DEB. The answers were formulated by the reporters, after discussions among participants, both via internet and in weekly reporter meetings. The questions refer to the given section numbers of the DEB book 2000.

Go to chapters 1, 2, 3, 4, 5, 7, 8, 9, 10

Chapter 1: Energetics and models

Quest 1.1.1: In section 1.1.1 our author says that the growth curves are astonishingly similar, but he doesn't say precisely what is similar about them. They don't look particularly similar. The Von Bertalanffy equation evidently "fits" all of the curves. Is fitting this function to growth data any less of a "meaningless empirical regression" than fitting allometric functions to body size? (especially as we have some indication that the curve also fits the data when the basic assumptions are violated).

Answ: The growth pattern of a yeast cell and a bird fit the same general curve (the Von Bertalanffy curve in this case); the differences in morphology only relate differences in parameter values. Of course, this is not a proof that they are actually similar (indeed the goodness of fit is a poor argument), but it motivates a search to find a theory explaining the similarity. Could it be that the underlying principles are similar? The Von Bertalanffy curve is specifically interesting as it follows from theory (and it doesn't have the dimensional problems of an allometric relationship).

Quest 1.1.1: What are the rules for the decomposition of mass into storage and structural component? For example, we "measure" a fat score and a muscle score on birds (tits in our case) to assess their body condition. There seems to be evidence that parent birds "lose" muscle during the nestling feeding period, so muscle serves partly as an energy storage, while it is basically a structural tissue.

Answ: The answer to this question is fundamental to the DEB theory. Any compound is not a priori divided into a reserve and a structural component. The determination is done by experiment. The change in the concentration of the compound is observed at different growth rates. This change then indicates to what extent the compound can be considered as structure or reserve. It is important to note that reserve tissue is not inert, but is immediately available for use, and is used all the time.

Quest 1.2.1: Page {10} last paragraph. In the book it is stated that it is very hard to model processes on large spatial and small time scale and vice-versa. We think that time scale is set by life expectancy. And if you take some radioactive particles, it is a very small spatial scale but a large time scale. So the question is: Is time scale better linked to life expectancy than to spatial scale?

Answ: Time scale should be coupled to life expectancy in the evolutionary studies, when individuals are the main objects. For example, if we are studying mutation rate then generation is the main unit. We are here dealing with ENERGY processes, however, where the units are molecules, enzymes and energy. Their age and time is the same both in short and long lived organisms. Besides, the idea of the author about the time scale, I guess was more linked to different levels of processes - molecules, cells, populations, ecosystems. So it is not the same question as comparing individuals with different life expectancies (for example comparing bacteria and elephant). How would you define the life expectancy of an ecosystem or the molecule?

Detailed knowledge on molecular theory does not necessary leads to solving problems in ecology. However, often the problems are linked. For example knowledge on the technic on the cylinders of cars is of little help to solve traffic jams.

Quest 1.2.1: When I read the DEB book's Chapter 1, I find that I basically agree with the author's point of view. Theories are, in fact, always idealizations. I too reject the idea that it is useful to think of a theory as "falsifiable".

However, the idea of falsification was advanced by Karl Popper to distinguish science from pseudo-science (astrology, Freudian psychotherapy). Popper argued that pseudo-science always had ex-post facto explanations for things, whereas science could predict things in advance. A theory that predicted something that did not come true would be falsified. Thus, falsification marked the demarcation between science and nonscience.

Thus, I pose the question: If we accept the author's point of view, how are we to distinguish between science and non-science?)

Answ: We discussed this point to some extent. There is however no real answer to it (as in most philosophical issues). The author's point is that goodness of fit is not a particularly good way to accept or discard a theory (often, the deviations from data are more interesting to improve a theory!). A theory should be judged on the basis of its usefulness. Usefulness is a temporary thing: a theory may be useful until new evidence is presented. A theory is a good one when it can be applied within a certain context and helps to trace new relationships between quantities (as long as it serves it purpose in a scientific field, its Ok). Of course, usefulness is a gradual scale and the degree of usefulness depends on elements like predictability (does the theory predict something that can be measured), description of mechanisms (does the theory describe why this prediction is accurate) and possibilities to manipulate the system (can we manipulate the system to verify the mechanisms).

Quest 1.2.3: What is the practical use of scaling a system when this results in compound parameters? Even if this allows you to identify these compound parameters by regression on a data set, how do you interpret these compound parameters in a biological sense?

Answ: Scaling can reduce the number of parameters. For a prediction with a model it is not required to know the values of all parameters. If you can find identifiable compound parameters, this may be sufficient to predict model behaviour in other situations. Scaling can help in studying the behaviour of a model system and can be compared to choosing the units of graphs.

Quest 1.2.4: Section 1.2.4 is dealing with statistics and testing of models. As far as I understand the whole chapter is about estimating parameter values from a data set. I thought that a solid way of verifying a mechanistic model is the following procedure: First determine the parameters values in an experimental set-up or from literature. Then perform an experiment to analyze the relation between the dependent and independent variables. Check whether the model can really predict the dependent variable within this experimental setting. A satisfying prediction of the dependent variable can be considered as a basis to change parameter values, in order to make predictions beyond the experimental conditions. I know that this kind of studies are performed within compartment analysis, and I always considered it as very robust. This procedure is not mentioned in this chapter. I was wondering why.

Answ: This is indeed an elegant approach. So far, it has not been done often within the context of quantifying energy fluxes. It is a huge amount of work. However, such a study is running at the moment. One remark about parameters. Note that parameters are in fact composed of several parameters (or equations). The individual values of the elements within these composed parameters are impossible to deduce from the data set that is analyzed. For example: a growth rate can be determined from a time vs length plot. But in reality this rate is very complex, and the end result of various processes. However, the research question determines how detailed the model should be.

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Chapter 2: Basic concepts

Quest 2.1.1: The following is stated in section 2.1.1:
`Any systems model relates inputs to a system with outputs of that system, as a function of its state. Although many formulations suggest that the output is the result of the state of the system and its input, this directional causality is in fact a matter of subjective interpretation. The input might well result from the state and the output; input, state and output change simultaneously, without an objective causality.'
Do you agree or disagree with the author? Do the statements hold in a mathematical or in a biological context, or in both?

Answ: There was quite some discussion about this topic in the first meeting of the reporters. A short answer is not possible. I will give some points in the discussion:
- There are input-driven and output-driven systems. This already shows that output is not always "caused" by the system and its input.
- Causality is a nasty concept in science. In "linear" systems , e.g. A -> B -> C, we can say that changes in A cause changes in C, but in circular systems, e.g A -> B -> C -> A etc., causality is not clear or even absent.

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Chapter 3: Energy acquisition and use

Quest 3.1.2: Activity is coupled directly or indirectly to feeding and/or to reproduction and thus the costs should be incorporated in feeding costs and/or reproduction costs. This might lead to problems as stated in the book {72}: one has to choose between a general, non-specific, model strategy in which some phenomena have to be neglected, or a species-dependent strategy. (The latter indeed is not the aim of this book.) However, neglecting up to 15% of the daily energy expenditure might give an uncomfortable feeling and seems conflicting with the claim of mechanistic modeling. What do you think about this?

Answ: The DEB-model is a general model for a general individual organism. Organisms show all kind of species-specific activities. If you want to apply the model to a specific species the various activities must be classified under one of the energy powers. Many activities are not continuous in time. Their contribution to the energy budget will be averaged over time. One should always keep in mind that the aim of DEB theory is to give a general framework.

Quest 3.1.2: Section 3.1.2, {73} middle of the page: It seems odd that the different transport methods in order of increasing energy costs per km is swimming < flying < running. Flying seems most "inefficient", as staying in the same place already requires an amount of wing flapping (soaring birds like the albatross excluded). Is this apparent contradiction a result of expressing energy consumption as oxygen use per surface area (instead of "work" on mass basis)? At the same volume, flying birds or mammals are usually lighter than similar sized running organisms.

Answ: These are just reported measurements. These energy costs are still small compared to the entire energy budget.

Quest 3.1.3: Holling II type response is discussed in this chapter, and Holling I at {236}. But I did not find discussions on Type III response (with acceleration stage). Is it discussed somewhere in DEB or it is not relevant here?

Answ: Holling type III is not an alternative for type I and II. Type III is about food preference with a choice of diet, not a varying amount of food available. It therefore considers a different process. Interaction of substrates in assimilation is discussed in section 5.1.

Quest 3.3: {81} section 3.3: The author takes the assimilation efficiency from food to be independent of the feeding rate. This does not seem to be generally valid: assimilation efficiencies in earthworms (plug-flow feeders) are (linearly) related to feeding rates. More feeding implies shorter residence time (as volume is approximately constant) and thus less time for digestion. Woodlice (terrestrial isopods) seem to have a "strategy" of most-efficient residence times: in times of food shortage, the retention time is long to obtain as much as possible from the limited food; in times of excess, retention time is short (and assimilation efficiency low) as this is probably the most energy-efficient way.

Answ: This assumption is made for simplicity's sake (to keep the number of parameters small) and follows from the argument that a certain amount of digestion time is required for optimal digestion. This sets an upper bound to the ingestion rate. For specific organisms and/or specific situations you may need to adapt the model (the model in Chapter 3 is a general one on which can be and will be expanded to describe particular species, if digestion efficiencies are depending sensitively on feeding rates). The coupling of low feeding rates and long gut residence times is automatic in the DEB model. It is important to discriminate between digestion efficiency, and the size of the assimilation flux. Optimazation considerations of feeding behaviour should include the fate of the assimilates.

Quest 3.4: At one point around {86}, the author notes, in connection with the partitionability assumption of the DEB model, that "The only information cells have is the energy content of the blood and body size." This is not obvious as all cells have hormonal information from the blood and many cells have neural sources of input. A cell also has information about how many times it has divided, in the form of telomere length.

Answ: This is a difference between theory and empirical practice. The cell does not have any other information "in the model"! Of course hormones regulate all kinds of processes, what what regulates the hormones? Hormones are just the mechanics: you can't grow any faster than the amount of energy available for growth. In the model, the growth is linked causally to the energy available; in practice, hormones are the mechanics that make this link possible. The reduction of telomeres at cell division is restricted to some tissues in mammals, and not a general phenomenon.

Quest 3.4: Reserve dynamics: The book states that "the dynamics of the reserves follows from three requirements: the reserve dynamics should be partitionable, the reserve density at steady state should not depend on structural body mass, and the use of reserves should not directly relate the food availability. " None of these requirements is self-evident, are they reasonable, and what is the empirical foundation for them? Partitionability questions also have a direct bearing on the kappa-rule. The author states that the partitionability requirement implies or leads to the idea that kappa cannot depend on reserve density. Why not?

Answ: First you have to distinguish between the mechanistic design of the system and the empirical testing. You start from assumptions, develop a mechanistic model and then compare it to data. If the fit is poor, you shouldn't change the model directly but go back to the assumptions, change them and derive a new model.

The partitionability is a logical requirement if you want one model for all organisms, where species with a single reserve evolved gradually from species with more reserves. The requirement is implicit in the concept of reserves being a generalised compound, where lipids and non-lipids, for instance, have to follow the same kind of kinetics in order to avoid changes in the chemical composition of the reserves. This requirement makes no assumptions for mechanisms, however. The second requirement (constant reserve density at steady-state) is the weak homeostasis assumption. The third requirement (use of reserves is uncoupled from food availability) follows from the choice that reserve and structure are the state variables of the system; the use of reserves must be a function of the state variables only. It is a choice to uncouple the external and internal environment by using the reserves as buffer. This makes that the system reacts smoothly to irratic changes in the environment, without making assumptions on allocation of energy fluxes.

Kappa cannot depend on the reserve density as a consequence of the partitionability requirement. The derivation is given in the book.

Quest 3.4: The partitionability of reserve dynamics implies that kappa cannot depend on reserve density. The author also deduces that kappa is independent of the amount of structure as well using the argument that energy allocation is an intensive process. Thus kappa does not depend on the state of the organism. Some organisms in variable and unpredictable food environments may choose to allocate more (or less) to reproduction vs. growth. Does a kappa-rule animal have this choice? Can kappa depend on age? Is kappa an intensive parameter (size independent) because it relates molecular processes (energy density dependent) and not to the physical design of the organism?

Answ: Although kappa is constant, the energy flux allocated to growth + somatic maintenance is not. The flux itself does depend on amounts of structure and reserves. So we have to differentiate between relative and absolute allocation. If kappa would depend on feeding conditions, so on reserve density, then reserves dynamics would no longer be partitionable. The argumentation that kappa also does not depent on the amount of structure is of a weaker type. If we would take it to be a function of the amount of structure, the resulting model will be more complex, but this would not affect the structure of the DEB theory. The case studies in the coming chapters deal with this subject more extensively (cf chapter 8 compares determinate and indeterminate growth).

Quest 3.5: Is the value of kappa in the reserve dynamics of the DEB theory fixed for a species or is it possible to vary by individual? In other words the value of kappa is fixed within an individual (requirement of the DEB theory), but can differ between members of the same sex. This might allow individuals of the same sex to follow different reproductive strategies. Is this correct?

Answ: Basically the kappa-rule should be applied to individual organism. Within the life cycle of one individual organisms it is fixed. It can differ between individuals of the two sexes, and even within sexes. Inter-species differences will be discussed in Chapter 8. Some environmental factors can effect the value of kappa, however; so if these factors vary, kappa can vary as well.

Quest 3.5: On {87} the kappa-rule is explained. Maintenance and growth compete directly, while development and reproduction compete with growth plus maintenance. It is also stated that the kappa-rule explains why different sexes show similar growth patterns, despite the fact that females invest more in reproduction than males: the kappa-rule implies that growth control is the same for males and females. But if I understand this allocation story well, then males must invest more in maintenance, or maybe in development. Both options seem unrealistic to me... Can anyone comment on this?

Answ: From the kappa-rule follows that if males and females are keeping up in size, males would allocate less to development and reproduction, and males and females have the same digestion efficiency and specific somatic maintenance costs, males will eat less. Another option is that males eat the same, allocate less to development and reproduction, but have higher specific somatic maintance costs (e.g. activity costs).

Quest 3.5: Concerning the kappa-rule, {87} in the third paragraph, it is explained how the regulation might work. Concentration of active carriers may depend on age, size and environment. I do not see how this goes along with the second paragraph's statement that a fixed proportion of energy is spent on growth and maintenance (through the entire life-time?). At first sight paragraph 4 states more what one would say: that when conditions become poorer the kappa-value is changed accordingly. Or is "fixed" only meant for situations that do not change during life-time?

Answ: The concentration of active carriers depends on size and environment. This does not contradict with the statement that a fixed proportion of energy-reserves is spent on growth and maintenance (kappa-rule). Reserve expenditure itself is a consequence of a first order process. The higher the reserve density, the more reserves are used for all kinds of processes. This expenditure is the catabolic flux. It is a fixed part of this particular flux which is spent on somatic maintenance and growth. Emergency situations (prolonged starvation) can cause deviation from "normal" kinetics.

Quest 3.5: {89}: When organisms are exposed to chemical toxicants and environmental stress (radiation also included), these agents may sometimes affect kappa-value. If the substrate level is the same and kappa-value is shifted to a certain direction, growth rate (increase of size per food intake) will shift with the switch of kappa-value. Is this true?

Answ: Ideally "kappa" is a constant during the lifetime of an organism. However, some kind of stress may affect its value. If this happens, the growth rate will indeed change along with it. Development and or reproduction is affected as well.

Quest 3.7: We discussed a lot about steady state conditions in our group. Just to sum up:

Some remarks:

What are examples of organisms in steady state and what is the relevance for modeling and model testing?

Answ: Time averaging could lead to steady state if times scales allow averaging. For example if we are interested in the behaviour over a year, then it might be reasonable to average over a day and not count every hour. Then averaging over a day gets rid of light/night cycles for example. But we should average over time scales only if they are much smaller than the time scale of interest.

One may need to distinguish between steady state as a mathematical tool and steady state as a biological reality. Even if steady-state never quite exists in biological reality, the concept of steady-state could be a useful mathematical tool for, say, extending or analyzing the model. Another example would be to use steady state to solve for unknown values of parameters in a differential equation.

However, one should keep in mind that the "tool" is not allowed to "deviate" far from reality. It should approach the real world "well enough" for applying the model.

Some variables can settle at a particular value (for instance the amount of structural mass), while other variables continue to change (such as the cumulated damage that is inherent to ageing). The D of DEB stresses to point that the full system is never in staedy state at the level of the individual.

The absence or presence of steady states depends on the level of organisation at which you observe. A population of individuals can be in steady state, while the individuals themselves are not; the individuals follow a life cycle, while population descriptors, such as the frequency distribution of individual states (such as age and body size distributions) remain (eventually) constant under particular environmental conditions.

Quest 3.7: Does the theory help us predict and control growth of an animal? Specifically, I propose two hypothetical scenarios and ask the author if the DEB theory helps me. Scenario A: Predicting the growth curve, under ad libitum feeding ("all-you-can-eat") conditions. Suppose that I had a juvenile captive zebra in my garage, eating a known amount of hay. Does the DEB theory help me predict how fast the zebra will put on weight? What else, other than hay, do I have to measure in order to predict the juvenile zebra's growth. Scenario B. Predicting the growth curve, under restricted feeding conditions. Suppose that I restrict the hay that the juvenile zebra receives, while it is living in my garage. Suppose further that I know what the growth curve will be for a juvenile zebra under ad libitum feeding conditions. Does the DEB theory help me predict how fast the juvenile zebra will put on weight? What else, if anything, do I need to know, in order to predict the zebra's growth.

Answ: Yes, DEB is able to make such predictions (this is the core of the theory) but you have to know the parameter values! The question only considers weights (of hay and the animal) so you don't need to know parameters with energy in it (only compound parameters in which energy falls out). For the prediction of growth under ad libitum food conditions, only three parameters are required (initial weight, asymptotic weight and the von Bertalanffy growth rate under the appropriate environmental conditions; if you decrease the temperature in the garage for instance, the zebra must allocate more to heating, which affects growth); the prediction of growth under (dynamic) food restrictions requires more parameter values. There are 11 basic parameters in total (a.o. kappa, max. surface-specific assimilation rate, volume-specific maintenance), from which zebra's full response can be deduced (including repiration, reproduction etc). For just weights less parameters are required. Parameters tend to covary among species in predictable ways, which may be used to guess values for zebra's, knowing values for other species.

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Chapter 4: Uptake and use of essential compounds

Quest 4.1: I was wondering how the flux of essential trace elements should be incorporated in the DEB model. Depletion of such elements can result in serious 'health' problems. To make it more complicated: also a surplus of these elements can lead to serious problems. A famous example is copper. No wonder that their uptake and allocation is usually regulated. So far, I have not read anything about this. Does anyone have any ideas?

Answ: There are two ways to incorporate the flux of essential trace elements in the DEB model. First, one can model it as a fixed proportion of reserves and of structure and link it to food uptake. Second, it is possible to quantify a special flux, which allows more freedom for the content of trace elements/compounds in biomass. This is discussed in chapter 6.

Quest 4.4.3: Page {139}, line 1 states `Since age is not a state variable'. Some random thoughts about this statement. If age is not a state variable than the theory of DEB implies among others that:
1) The duration of the so-called sensitive period during the process of song imprinting in birds can be manipulated by food;
2) Transitions between life stages and the duration of processes within a life stage are independent of biological clocks. The above mentioned makes sense or is completely nonsense?

Answ: General: A lot of processes seem to be linked to age. Under normal conditions (of enough food) there is a one-to-one relationship between age and structural length, so length-driven processes and age-driven processes are hard to distinguish. See also {20} of the DEB-book (State Variables). Indeed, a lot of behaviours can be manipulated by food, and the theory does imply that imprinting periods can be manipulated by food. Durations of life stages are frequently shown to depent on food supply.

Quest 4.4.3, {140}: If you consider (cell) death as a discrete event, does this mean that death in this context occurs after having reached a certain threshold value for the damaged DNA concentration?

We like to add one remark:
On {145} the evolutionary role of free radicals is discussed. Although I understand the intentions of the author, I would suggest another way of formulating. The point is that it is written as if evolutionary forces act at the species level. Even the term "...the species can exploit free radicals for adaptation..." is used. As far as I know selection pressure acts at the individual level, and there is nothing like "beneficial for the species". So the free radicals, if no cell death occurs, cause mutations that might change traits of individuals. If environmental conditions change in such a way that these traits become beneficial, they might become dominant in the population. I agree that this change of formulation is a bit niggling, but the whole book is formulated very accurately. Also, there has been a lot of confusion within evolutionary studies because of formulations in terms of "beneficial for the species".

Answ: The remarks about species versus individuals are absolutely correct; species are abstract categories of similar individuals that can exchange genetic code. Cell death is quantified by the hazard rate, which is not a deterministic process, but inherently stochastic.

Quest 4.4: At the bottom of {135}: "The expression for dissipating power is consistent with the observation that respiration rate increases with reserve density while reserves themselves do not use oxygen." If reserves do not use oxygen (which I think is a defensible assumption), why do reserves increase respiration? What exactly is dissipating power?

Answ: If reserve density is high, the use of reserves (for growth and/or reproduction/maturity) is also high and, as an indirect result, respiration is high (maintenance and growth overhead are oxydation processes of reserves). Dissipation processes are the collection of processes that are not associated with assimilation and net synthesis.

Quest 4.6: What is the role of lactation in the DEB theory? {148} says: " milk of female mammals is an example of a product that is coupled to maintenance, ..." The energy that goes into making milk would be coupled to a dissipative power, since maintenance is part of dissipation, {124}. However, why is lactation considered part of maintenance instead of part of reproduction?

Answ: You've got 3 organising fluxes (assimilation, dissipation, growth). From the DEB model, through the assumptions in Table 3.3, it follows that all products can be written as weighted sum of these powers. Lactation is not linked to growth as a mammalian mother usually doesn't grow anymore so it is a sum of dissipation and assimilation. The latter is for instance important in mice (they stop milk production when facing starvation) but probably not in other mammals. So the logical choice is to consider milk as mainly dissipation. Dissipation is the energy flow not coupled to food intake or growth, so not related to biomass synthesis. Reproduction allocation itself is also linked to assimilation, dissipation and growth, if combined with reserve synthesis (as explained in the book).

Quest 4.8: Reading the chapter on water balance I was surprised that no osmotic costs are mentioned. The water can penetrate the organism or be lost if the aquatic organism lives not in the iso-osmotic environment. And, as far as I know, these osmotic regulation costs might be very high. Actually this defines the distribution of organism of different salinity tolerance.

Answ: The DEB theory delineates volume and surface area coupled maintenance costs. Osmosis appears as surface area relates maintenance costs. In chapter 2, {91}, there is an example for endothermic animals. The length of the endothermic animals is shorter than expected without the overhead costs of losing heath, because they had to lose some energy towards the heating process. The same can be said when you substitute heating by osmosis. In fresh water, the fish will be smaller, because they have to put some energy in osmo-regulation.

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Chapter 5: Multivariate DEB models

Quest 5.1: Tetrahymena, a heterotrophic protozoa, can grow on E. coli and on a peptone solution. The growth rate of Tetrahymena with E. coli plus peptone is higher than on peptone alone. These food sources are widely different and are taken up via very different mechanisms. How can the theory be used to describe growth of Tetrahymena on peptone and E. coli simultaneously?

Answ: This can be done with theory for SU kinetics for parallelly processed substitutable substrates. Bernd Brandt (here in Amsterdam) just submitted a manuscript on co-metabolism, which has a SU-based model formulation that allows for mixtures between substitutable and complementary compounds. We then have 3 conversions: yAC A -> C yBC B -> C y'AC A + y'BC B -> C For appropriate choices of yAC, yBC, y'AC and y'BC, complex interaction patterns are possible, both for the appearance of C (reserves of Tetrahymena) and the disappearance of A (E. coli) and B (peptone).

Quest 5.1: Why are many equations (e.g.: 5.1, 5.5) in chapter 5 developed for V1-morphs?

Answ: The surface area is proportional to volume in V1-morphs, so that both exchange and internal processes can be linked easily without including shape correction factors. This results in a population dynamics that is unstructured (total structure and total reserves), rather than structured (where we need to follow all individuals in the population). This gives an attractive simplicity at the population level for V1-morphs. It can be treated as an useful approximation for dividers (which reset their volume after an increase by a factor two), even in the case where they change differently in shape during growth.

Quest 5.1.1: Another question about reserves is from {162}: "If the prey has a reproductive buffer it is possible that assimilative power exceeds pAm". But in the previous chapter on {129} it was said that two buffers are added to one buffer. Why then they are treated separately in the prey?

Answ: The reproduction and reserve buffer cannot be summed up in the dynamics of energy budgets, because of the differences in the dynamics of the buffers and in destination of the buffers. They must be added in the macro-chemical reaction equation to see that the sum of the allocations to the reproduction and reserve buffer is a weighted sum of assimilation maintenance and growth, while the allocation to reproduction itself is not such a sum.

Quest 5.1.3: How does the described DEB approach relate to the body of knowledge that already exists on photosynthesis?

Answ: The first thing one has to realise is that models for photosynthesis (on a molecular scale) frequently deal with process rates that are quite different from the growth rate of the individual (plant or alga). DEB tries to capture the essence of photosynthesis and to describe this on a time scale that is relevant to individuals. Many detailed models for photosynthesis ignore potential problems with links to other physiological processes, by assuming constant enzyme concentrations for instance. Nitrogen limitation can easily lead to problems in the synthesis of these enzymes, however.

Quest 5.1.3: The uptake of nutrients and processing them into a form of reserves requires energy, but this is not in the equations. Where is this cost being paid from?

Answ: These overheads are taken into account in the form of conversion coefficients (yield coefficients); the higher the overhead costs, the lower the conversion coefficient from substrate(s) to reserve(s).

Quest 5.1.3: The section "Photosynthesis sensu lato" is hard to follow. Specifically, where do the (1 + 1/z ...) terms in the nominators of equation 5.10 and 5.12 come from? Furthermore, what does the flux jCH,A precisely represent? The synthesizing unit "CB-cy" (cytochromes b and c?) generates this flux, which is one of the input fluxes for the synthesizing unit that forms generalized reserves. However, "CB-cy" also generates jEC,A (carbohydrate reserves). Is "CB-cy" a 2 product SU? Or is jEC,A the C rejection flux of the synthesizing unit producing generalized reserves? In addition, how does Fig 5.2 relate to Fig 5.6? Fig 5.2 does not include N reserves, but 5.6 does. How general are the results in Section 5.1.3?

Answ: The abbreviation "CB-cy" stands for the Calvin-Benson cycle, see {164}; it plays the role of a two substrate, single product SU. The flux jEC, A is the specific flux of EC (which is the carbon-reserve, think of starch and/or lipids) in association with assimilation. Part of the synthesized carbohydrates, CH, are also used for the general reserves, E, and, therefore, not included in jEC, A, but in jE, A. The terms z are only introduced for rescaling purposes, to give the parameter jCH, Am for instance the interpretation of the maximum assimilation rate. The interpretation of partial fluxes should always relate to the overall process of formation of reserves for several types of substrate. This process has two aspects: appearance of reserves and disappearance of substrates. The flux to N-reserves is indeed not indicated in Fig 5.2. It should be included in between N-car and Synth, since some of the incoming assimilated N cannot always be processed by the synthesizing machinery (e.g. if carbohydrates are limiting). The results in 5.1.3 are believed to be general, but critical testing against experimental data still has to be done. It does not yet include some epi-phenomena, such as photo-inhibition; several other extensions are realistic as well, but complicate the theory further. The present formulation shows how light, carbon dioxide, oxygen, a nitrogen source, and water interact in photosynthesis at a time scale that is of relevance for growth.

Quest 5.2: We have had a long discussion about the general and special reserves and their utilization. As I am a biologist and not mathematician I am searching for some biological explanation for all the models - some examples from the reality. Here I put it rather straightforward, but please suggest some better explanation.

Reserves is everything was is assimilated from food and not yet dissipated or incorporated into structure. So reserves is not some measurable thing, but more the state of the organism. Taken as a simple example - the amount of general and universal compound it can produce (say glucose plus some amino acids). Then there are some special reserves delineated in the model. These special reserves could be understood as lipids, nitrogen reserves, etc.

There is a rejection and incorporation back into the reserves probability given. I can understand the rejection of reserve compound by SU only in this sence - the nutrients which come from the environment and cannot be incorporated into the structure due to stoichiometric reasons/lack of supplementary substrate can be rejected (just excreted as for example we do with the excess of vitamin C) or returned to the reserves with probability kappae (which I conceive as a real reserve - storage). And from these reserves material is taken only when it is needed and in the amount it can be used without rejection. Otherwise, it is difficult to imagine that any organism would take anything from its "real" reserves just to find out that there is not way to use it and reject.

To sum up - can anybody give some example from the reality about the rejection of the reserve compound. And what this incorporation probability kappae really mean? How to measure it?

Answ: At controlled conditions we know the ratio between structure and reserve. When we measure the chemical component and we use the known ratio, then we are able to make an indirect measurement for the amount of reserve. For more than 1 reserve the same can be done, it is only more work to do. So we can measure the amount of reserves indirectly. The idea is that things from the environment are always added to the reserves, the reserves are used at a certain rate, but some rejected reserves might return. This can result in a damming up of non-limiting reserves. The kinetics has been tested, {170-173}, but more more testing needs to be done.

Quest 5.2.3: On {172} the author states: "The balance equations ... apply only approximately to the data, because of measurements errors." In other words, the data are wrong. This presupposes that the model is 'right', or am I 'wrong'?

Answ: What actually is going on is the following: the data in Figure 5.5 are not consistent, because they are contrary to the mass balance. Because the model is based on the mass balance it is not strange if it does not fit the data. The model is `right' in the sense that it follows the mass balances, but this does not imply that the relationships between variables is realistically implemented. On the other hand, the statement in the book may seem blunt, but one should realise that experimental conditions are never ideal and biological variation is ubiquitous, so data are always scattered. Most scientist are inclined to overvalue their data.

Quest 5.2.3: From several of the examples given it is apparent that the testing of any given hypothesis in the DEB model needs the accurate measurement of several state variables. I do realise that there is an apparent improvement in the understanding of the processes taking place, maybe because in regulatory testing there is no such attempt at all. There two examples, from Figures 5.4 and 5.5, P and B12 were measured for several conditions or throughput rates. If we consider an extension of these kind of experiments to investigate the effects of xenobiotics on non-target organisms, we would be faced with testing that may involve higher costs than what such regulatory tests presently cost. Is the application of DEB to assess risk a likely alternative?

Answ: One should separate the testing of the theory against experimental data, and using the theory to understand experimental data. We need many different measurements in testing. However, we can make use of circumstantial evidence (from other data for instance) if the purpose is just using the theory (and fix particular parameter values). Some applications are simple, and require only few measurements to estimate parameter values; other applications are complex. The modification of toxicity by nutrients or energy substrates is hardly studied, and would involve rather advanced testing protocols; such advanced applications should only be considered after experience with simple applications.

Quest 5.2.4: I don't understand the argument on {172}, bottom of the page. "The density of limiting reserve increases with the growth rate, while the non-limiting reserve can decrease with the growth rate. ... can easily lead to the wrong conclusion that reserve densities decrease with the growth rate." Shouldn't this be the other way around: growth rate can increase when the density of the limiting reserve increases? Why should this lead me to wrongfully conclude that all densities decrease with growth rate?

Answ: In a 1-reserve model, a larger reserve density leads to increased growth. In a 2-reserve model, 1 reserve is usually determining the growth rate: more of the limiting reserve means increase in growth. The response of the non-limiting reserve depends on the fraction that is rejected. When rejection is small (as is common in microbiology) the non-limiting reserve tends to increase dramatically: decrease in growth, increase in reserve density. When rejection is large, however, then it is possible that a growth decrease is accompanied by a decrease in reserves. Spectacular reserve densities that captured the attention of research worker in algal growth usually represent non-limiting reserves, which feeds the popular belief that high reserve densities come with low growth rates.

Quest 5.2.6: Fig. 5.6 shows 3 types of reserves containing nitrogen, ammonia, nitrate and generalized reserves. It is argued that the ammonia reserves must be very small, since ammonia is toxic. There may be other important reasons, however. Ammonia would be an inefficient storage compound, as it is volatile and easily crosses membranes. It is thus easily lost. Moreover, most of this type of nitrogen may be in the form of ammonium. This molecule is charged and convenient polymers of it do not exist. Thus osmotic and energetic considerations imply that it is unsuitable as a significant storage compound. However, the same is true for nitrate. Therefore, one would think that nitrogen is mostly stored in the form of amino acids, but Fig 5.6 does not include a storage box specifically for organic nitrogen. Why not pooling the ammonia and nitrate assimilation fluxes in order to form 2 kinds of reserves, organic nitrogen reserves and generalized reserves?

Answ: Indeed, there are many reasons for why ammonia is not frequently stored to high levels. When you eat shark meat, however, you will notice that ammonia can sometimes accumulate. The reserve EN in Figure 5.6 should again be conceived as a generalized compound (which contains nitrogen in one form or another). No apriori assumptions are made (or required) for its chemical composition. The essential point is in the coupled uptake: can nitrogen (in the form of ammonia or nitrate) be taken up from the environment in absence of a carbon or energy source?

Quest 5.3.2 : The equations in the root & shoot section are derived under the assumption that the soil properties do not play a role, and thus that diffussion, etc. of nutrients, minerals is not limiting or that these are present in plenty amounts. Can this model also predict growth under conditions such as a lower water content in the soil? or conditions under which minerals would be only available at certain periods?

Answ: No, this is not true. Nutrients in the soil, as well as water can limit plant-growth in the presented model dynamically. DEBtool allows you to manipulate the chemical environment, as well as light. DEBtool does not (yet) allow you to assign time-functions to nutrient availability, although the model, as well as the basic routine (flux.m) allows this dynamics. Some important results are reported in 5.3, such as the reaction of the plant to changes in light and/or nutrients. (The plants partly compensates sub-optimal growth conditions, as a result of changes in allocation of resources to shoots versus roots (despite the fact that no assumptions about allocations are incorporated. These shifts just follow from the rules for nutrient exchange between root and shoot).

Quest 5.3.2: From the quizz: "Can a mother-foetus system be considered as a two-reserve, two-structure system? Correct answer(s): Yes, if translocation is large relative to foetal utilization. Feedback: Foetal assimilation can be zero; think of the model for plants, where shoot or root is still in the embryonic stage." I believe that the foetus, by definition, doesn't assimilate. I did not view roots as embryonic but as juvenile, as stated on bottom of {183}.

Answ: Foetal assimilation is indeed zero, root and shoot assimilation can be zero (during the seed stage) or positive (during the juvenile and adult stages). If translocation between foetus and mother is small, foetal development can be more complex than discussed at {103}. In plants, translocation can be limiting which requires an explicit description of this process in the model. This limitation of translocation can lead to accumulation of carbohydrates in roots or shoots or both; this divesity is realistic.

Quest 5.3.2: I understand the neccesity of and the realism gained in describing plants with several reserves. However, the number of parameters must have exploded since the simpler animal models. Have these models crossed the boundaries of testability; or in other words, is it still possible to test this models against data and obtain meaningful results or is this just a theoretical exercise (there is no comparison to "real data" for plants shown in this chapter)?

Answ: Testability of the plant model is indeed a serious problem. Point is that high quality data are scarce. If you have many parameters you need a lot of different types of data; not just a weight vs. time curve but also light intensity, nutrient levels, etc etc. If you don't have these elaborate data sets, the model can always be made to fit the data. Simultaneous measurements of different processes are needed to constrain the model and test its realism. Notice that other questions in this collection relate to the inclusion of even more environmental variables that affect photosynthesis and growth.

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Chapter 7: Case studies

Quest 7.1: It seems that when the going gets tough, an organism may choose to 'violate' one or more assumptions in order to prolong its life. The book presents one example in detail, i.e. deviation from the kappa rule in snails. There are other strategies, such as degrading structure (for fuel and reducing maintenance requirements), cutting on somatic maintenance and heating costs, and making the mobilization of reserves demand driven (so that all the reserves can be fully depleted while paying maintenance). However, one strategy is not mentioned, and this one seems to be of particular interest for the snail example: resorption of eggs or reproductive matter.

How can one distinguish between a snail that decides to use the energy allocated to reproduction for maintenance during periods of starvation and a snail that decides to stop allocating resources to reproduction when it cannot grow?

Answ: If a snail can use its reproduction buffer for maintenance, we need extra rules for the use of reserves which specify when to use what reserves; does it first use the standard reserves, and after depletion is starts to used the reserves allocated to reproduction, or does it use both reserves simultaneously? How exactly? One needs to specify this before the question can be answered. One approach to study the problem experimentally is to compare starvation behaviour between two individuals, one just before spawning, one just after (so with an empty reproduction buffer).

Quest 7.1.4: {227}, The Emperor Penguin: does any combination of realistic parameter values for e(0), dV, .. and v result in the same shape of the food intake curve as displayed in Figure 7.6 or has additional information to be used? The first dale in the curve correlates highly with the change of parental care between female and male around 24 days!

Additional information: Williams T.D. The penguins. p158. Chick-rearing in Emperor Penguins: females return to colony around time of hatching, but if chick hatches before female returns it is fed by male with oesophageal secretion; chick can double is weight on this food. Chick brooded by male for up to 10 days following hatching; male then leaves for sea and female broods and feeds chick for 24 days, before being relieved by male for a further 7 days. Chicks start to spend time outside incubation pouch at about 1 month of age and form creches at 45-50 days. In the Emperor Penguin the frequency of feeding visits during the creche period increases as chick age increases because pack-ice recedes and distance to open water decreases; chicks receive 6-12 feeds from each parent. At the start of the breeding cycle, when sea-ice begins to form, the birds often have to walk 50-120 km over ice to reach their colony! Fledging takes place at ca. 150 days. The curve suggests that there is always at least one parent present.

I presume that the data in Fig. 7.6 are based on an individual chick, but that I do not exclude the possibility that that the data are based on culled birds keeping in mind the practice of some scientists of the D.P.S.S. Another point that struck us in figure 7.6 is the enormous fluctuation in food intake between 40 and 100 days, where the weight does not show much 'fluctuation'. What happens if the same cubic-spline approach is applied to the small adelie data? Will we see the same (but smaller) fluctuations as in the graph on the right? (Adelie Penguins: chicks brooded by both parents for 22 days following hatching; chicks then form small creches (10-20 birds), receiving feeds every 1-2 days from both parents, fledging at 50-60 days of age, clutch size normally two eggs)?

Answ: Apparently there is a lot of information that could be used to interpret the fluctuating food intake. In this particular dataset there are no clues about the food regime. It would be a nice experiment to monitor the feeding behaviour of the parents, and to examine the "response" of the chick. If the measurements were free of error, the feeding reconstruction could be perfect (given the DEB model), but stochastic error spoils such a reconstruction. This is why it is not done for the adelie penguin; the deviations from von Bertalanffy growth are really small; one could try, however. Small changes in growth of a large chick result in hugh changes in food intake, but much less so for small chicks. The parameters that are used for the reconstruction are obtained for other sources, and should be treated as rough estimates. This example just illustrates that all type of growth curves can result from the DEB model, not just the von Bertalanffy one, and that you can reverse the reasoning, with interesting potential applications.

Quest 7.1.5: We all struggled with the concept of maturity maintenance. Maturity maintenance seems to be a voluntary contribution, as we understand from the starvation variant of DEB describing MD snails. During periods of starvation an MD snail may fulfill part of the maturity maintenance bill, or it may shuffle the bill in a drawer and 'forget' about it.

What happens with the lucky MD snail that finds new patches of food after a period of severe starvation? Has it become an immature organism that has to pay its outstanding maturity maintenance bills before it can reproduce? Will it be forever a 'neuter'?

Answ: Interesting questions which still wait to be answered. We know of no systematic experimental work to guide the theoretical work.

Quest 7.1.5: Similar questions arise when other assumptions have been temporarily violated. Is restoration of the state of the pre-starvation animal a priority? Is restoration possible?

Answ: General empirical evidence points to a full recovery from mild starvation, and partial recovery from severe starvation. We know of no systematic experimental work on the issue to reveal the broad picture.

Quest 7.1.6: We wondered how we can measure the decrease in structural biomass after starvation. How to separate maintenance and structural reserves. (I have a deja vu feeling).

Answ: The DEB model has structure and reserves, not structural reserves. Maintenance is a process, amounts of structure and reserve are states. We could, in principle, quantify the amount of structure during starvation by measuring particular chemical compounds (some lipids for instance), for which we know the concentrations in structure and in reserve.

Quest 7.1.7: On {231} it is stated that maturity maintenance can be considered to be reducible maintenance costs. What does this mean from a physiological point of view? Because we think that once an organism is mature, it will not become a juvenile again (except for some worms maybe). So the costs remain. What is maintained by paying maturity maintenance costs. Reproduction? But aren't these costs covered by the energy reserve for reproduction?

Answ: Maturity maintenance is introduced to close mass balances when comparing the DEB model to empirical data (see for discussion AT {88}). We do not know the real physiological interpretation of these costs, but you can think of regulatory systems or maintaining concentration gradients. Reproduction is not paid by maturity maintenance costs; reproduction in adults corresponds with the increase in the state of maturity of juveniles.

Quest 7.1.9: Statement {232}: "...The second determinant is the temperature, which should be in the tolerance range for the species for a long enough period. If it drops below the lower limit, the species must adopt adequate avoidance behaviour (migration, dormancy) to survive."

Question: does the author not use an argument of Group Selection in the last sentence? An individual must adopt adequate avoidance behavior to survive, not a species?

Answ: Of course individuals are reacting and not species. It applies to all individuals, however, a species comprises.

Quest 7.2.1: What are inner and outer imaginary tunics (the example of 3D-annulus does not clarify much)? Can we give a biological interpretation to XK1 (mantle saturation coefficient)? And how should Xc be called? Should we give any meaning to Xc becoming negative?

Answ: The inner and outer imaginary tunics can be imagined as a sphere that is surrounded by a layer of stagnant water. The thickness of this stagnant water layer is dependent on the turbulence of the water. At low food densities, the organism can become dependent of the transport rate through this layer. So XK1 is a measure of the diffusion rate through this layer (actually, it is the food concentration at which half of the maximum food transport rate through this layer occurs). Substrate concentration Xc cannot become negative.

Quest 7.3: We discussed a lot about digestion efficiency in our group. Is it correct that the DEB model assumes that digestion is complete. We all know biological examples in which it is not. Some organisms require even more han 1 run to completely digest their food (runs through the intestines. In short: incomplete digestion may in some cases ensure higher energy assimilation than complete. Can you tell us something more about this?

Answ: These assumptions of the DEB theory are made for the sake of implicitly. "Fast"- eaters have a low gut residence time, which consequently might result in not-total digestion. The chemical composition of this is then a function of the digestion efficiency. This gives extra parameters. The DEB theory is constructed in a way, with the assumptions, that the chemical components are constant for food and feces; the gut residence time and the speed of eating are the variables. The existance of species which eat elephant dung (for instance) does not say that the elephant could take more nutrients out of the dung; dung-eaters have different enzymes and needs.

There is no theoretical argument that prevents the replacement of the digestion module by more detailed ones. All aspects of DEB should have a comparable level of detail, however, while the whole construct should still be applicable. This gives an upper bound for the number of parameters, that depends on the aim of the applicantion.

Quest 7.3: Figure 7.15 again emphasize the concordant change of rate of all the processes in the organism with the changing temperature. Maybe it is logical. But how to explain why some, say, cold-water animals cannot survive in the warmer temperature. The basic explanation often was that the respiration rate increase faster than feeding rate. Also, for the object of my interest, mysid crustaceans, gut residence time was shown to decrease faster than digestion at some threshold level, so the animals cannot manage to digest everything. According to DEB this should be wrong reasons?

Answ: The (simplest) DEB model states that all fluxes in an organism depend on temperature in the same way. So ratios of those fluxes do not depend on temperature; such ratios frequently have the interpretation of conversion efficiencies, which have a direct link to biochemistry. Feeding rates can vary of course, and depends on other species and processes under field conditions. These rates can depend in a different way on temperature, which can cause complex effects of temperature on the abundance of a species in a community.

Quest 7.3.1: can you explain why the dissipating heat tends to increase with the free energy of substrate, when different substrates are compared?

Answ: The max specific assimilation power, [pAm] and max. reserve capacity [Em] depends on the type of substrate. For micro-organisms you can test this easily with giving them another substrate. The dissipating heat can be written as a function of these parameters.

Quest 7.6: Structural homeostasis: a new state variable is introduced here, namely the amount of membranes Mc. Equations (7.12) through (7.14) show the new allocation rules that arise from this. I was wondering what happens with kappa: does this parameter change because of the new state variable, or does an extra allocation rule (e.g. kappac) have to be introduced.

Answ: Indeed, the idea is that a fixed fraction of the catabolic flux is allocated to membrane synthesis, which is at the expense of allocation to somatic maintenance and (the rest of) the structure. This part of the reasoning is similar to the discussion of organ growth in 5.3 on {177}. The section not only aims to explain weak homeostasis and the mechanism behind reserve dynamics, but also illustrates how sub-organismal modelling can be done in a DEB-consistent way.

Quest 7.7.1: As far as I can remember, lichens, {250-251}, are a form of symbiosis between an alga and a fungus. Knowing this, to what extent does DEB allow us to use a single parameter value for such growth forms that in fact exist of (at least) two species?

Answ: True; the section 9.1.2 on syntrophy shows that under mild contraints, the ratio of the biomasses of alga and fungus can become constant, and independent of substrate availability.

Quest 7.9.2: Subsection 7.1.9 end with the statement `This is typical for `demand' systems where regulation mechanisms set fluxes at predefined values with are obtained through adaptation. Within the DEB theory this means that the parameter values are under genetic control .... Subsection 7.9.2 first line states: `Growth curves suggest that some species, e.g. humans, change the partition coefficient kappa and the maximum surface-area-specific assimilation rate at puberty in situations of food abundance; see Fig. 7.29.

Question: do the above statements not contradict each other? Furthermore, why is in Fig. 7.29 not an extra curve presented of an individual not in a situation of food abundance? Growth curves of pupils in orphanages for instance?

Answ: From a theoretical perspective, it would be more attractive to keep all parameters fixed in all cases. This would lead to a more complex model, while this increase in complexity is only required for a small number of species. There is no reason why two parameters cannot change values, rather than just a single one. The reasons for the changes is not yet understood mechanistically. The example just illustrates how one can deal with such deviations in a DEB context, to guide research to the mechanisms of hormonal control.

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Chapter 8: Comparison of species

Quest 8.1: On {266} it is mentioned that fluctuations in reserve density that result from fluctuations in food density, may result into "dwarfing". But isn't it so that a large reserve can "protect" the organism against fluctuating food densities? A bigger reserve also allows a better regulation of metabolic activity. As a result, fluctuating food densities can also select for organisms with large reserves, which are usually bigger. On {273} (gut capacity), the large body size of giant carnivores is even explained by their ability to survive meagre periods.

Answ: To answer this question, 2 types of time scales have to be considered: 1. the evolutionary/geological time scale and 2. the time scale (within the life time) of an individual. For the first time scale, the trend is towards selection of smaller body size, because smaller organisms have smaller demands, so that the relative abundance of food increases. For the second time scale, optimisation goes towards increasing body size = increasing reserves, so that periods of starvation can be buffered.

Quest 8.1: I have one problem and one thing that irks me. The irky thing is in the arguments about primary parameters depending on maximum body size. The argument uses the method of elimination to get the parameters that depend on maximum body size. However, it lacks a biological or (bio)chemical justification.

My problem is that I don't see how the invariance property may explain dwarfing. The book states that organisms tend to evolve such that they experience a scaled food density close to 1, since that would imply a maximum of homeostasis with a minimum of regulatory systems. However, I thought that organisms have reserves to obtain this internal 'stability'.

Answ: The crux of the argument is that the reasoning follows from the assumptions listed in the table on {121}; so the biological or chemical justification concerns those assumptions only. The biological interpretations are only given to illustrate the reasoning, not to find a basis for new assumptions.

Indeed, reserves damp oscillations in ingestion rate, as experienced by metabolism, but if the oscillations are damped as well, the result is an even more constant condition for metabolism.

Quest 8.1: What are the basic differences between invariance property and primary scaling relationships models? Under what conditions they should be used?

Answ: The invariance property is a mathematical property of the DEB model, and does not involve any physical interpretation. The primary scaling relationships are derived on the basis of the physical interpretation of each primary parameter (being intensive or extensive). Except for the life stage parameters (size at birth and puberty), this leads to the same result.

Quest 8.1: We could not find solution to the contradiction:
1. fluctuating food densities (as it is in north) select for large body volume because of better survival over starvation and ability to have larger reserves, {274}.
2. fluctuating food densities select for small max ingestion rate because of smaller res density fluctuation and hence more easy regulation processes, {266}.

Then the observation that max ingestion rate increases with body volume seems to give a contradiction. Or the contradiction is in the first two assumptions.

Answ: This is not a contradiction, the explanation is in the amplitude of the fluctuations. Strongly fluctuating circumstances select for large body volumes when these oscillations are over relatively short periods. Think of meagre periods for food, or cold. When the organisms are big, the reserves will be big and allow the individual to survive the meagre periods. When food fluctuations are not deep and do not cause starvation (only reduced reserve densities), a reduction in max ingestion rate will result in a more constant reserve density, so an increase in homeostasis.

Apart from the amplitude, the time scale of fluctuations is important. When the period of a food cycle increases, an increase in body size can avoid problems during the meagre periods, but when the periods become too long, (very) small organisms are better adapted, by responding at the population level (short generation times, variation in population numbers).

Quest 8.2.1, {269}: The reasoning in the first complete paragraph runs as follows:
1. all cells are similar --> cells of equal size have equal maintenance costs.
2. maintenance of an individual is more or less the sum of the maintenance(s) of the cells --> volume-specific maintenance is independent of body size.

Does the author not implicitly assume that all cells are equally sized? And what does the conclusion mean? That [pM] is equal for all organisms?

Answ: We discussed a lot about the basic arguments of body size scaling. Yes, the author assumes that fequency distribution of cells sizes are (approximately) the same for small and large bodied species. Nerve cells of mice are comparable with nerve cells in elephants, etc. The specific maintenance costs [pM] can vary among species, but does not depend (in a systematic way) on maximum body size.

Quest 8.2.1: What are the ultimate factors, defining the maximum size of the organism and what is the mechanism of how they work? We have discussed pAm and kappa.
- If I understood correctly pAm is directly dependent on body size. Is there any scaling for pAm and volume, so that we can predict pAm and f from the volume? Is it only dividing by the factor z? How does it work ? (more carriers, more enzymes?).
- Kappa is not dependent on body size and is species-specific. It can be related to r and K strategies (?!). What is the mechanism for a different kappa? (as far as I remember again the number of carriers was mentioned in the previous chapters).

Answ: Maximum size is a function of what is going in and what is going out. We saw that the specific flux out is approximately constant among species. For instance a mouse requires the same amount of energy per cell than a whale. Consequently species differ primarily by the flux in.

The scaled functional response f primarily depends on food availability, not body size. All parameters are species-specific, but they tend to co-vary among species, which results in different maximum body sizes (among others). These trends can be predicted on the basis of the structure of the DEB theory. "r-selected" species in the ecological literature allocate a lot to reproduction and remain small, which corresponds to a small value of kappa.

Quest 8.2.2: How does gut residence time depend on size? Intuitively one would think that the absolute rate DOES depend on size. The book however states that residence time does NOT depend on size. If it does not - why should big animals be able to digest poor-food ? And still to that the contradictory example from the nature - poor food can be digested both by big and small animals, maybe partly because many of them use VERY SMALL symbionts for this (cows and termites).

Our practise was that gut residence time is longer than experiments show with small animals and it does not depend on ingestion rate! Summarized: How can gut residence time be independent of body size but nonetheless size accounts for better digestion due to longer time?

{240} states that "a shorter gut residence time in small individuals is exactly compensated by a higher enzyme concentration." Gut volume is proportional to body volume but gut residence time is related to gut length {83} (and thus a length measure). Ingestion rate according to Eq 3.2 at {75} is related to a squared length (and not a volume as on {273}).

Answ: Gut residence time DOES depend on size within a species. Gut length is dependent on food type across species. Think of a cow and a bacteria. The cow has to perform a large digestion time, because of the cellulose, which is very hard to digest; whilst some bacteria can deal with cellulose very easily. Moreover, the gut residence time is dependent on the gut length. You can even see it from the shape of the belly; the goat a large belly, the dog not, because of length of their guts.

Calder [146] indeed gives on {124} a table 5-8 that shows that gut capacity is about proportional to mass in birds and mammals. In retrospection, the text on gut capacity on {273} of the DEB book is a bit misleading. Large dinosaurs can only handle long gut residence times, not because of their large size, but because of their relatively large gut volume. Calder argues that gut length increases steeper with body size than gut diameter, from which follows that gut residence times should increase with body size. These morphological traits are beyond the scope of the DEB theory.

Quest 8.2.2: We found several strange values for body length in Table 8.2. Are those values wrong or do we misunderstand things? For instance:
Otters (Lutra lutra) female 178.1mm and male 197.1mm ref [885] refers to the otter in England. MacDonald & Barrett. Mammals of Britain & Europe: Otter: Head-body length: male 60-90cm; female 59-70cm; Tail-length: male 36-47cm; female 35-42cm
Southern Elephant Seals (Mirounga leonina): Ref. [133] male 1799mm and female 704.0mm The male is a juvenile of one-years old and the female probably would never have been born (Laws. Antarctic Seals: Newborn length 127cm).
The same hold for the Weddell Seal (Leptonychotes weddelli) 685.4mm (Laws. Antarctic Seals-Newborn 120cm).
The length values for the African Elephant seem to me also too small, etc, etc. Aptenodytes patagonicus 250.0 mm, so 25 cm. Those birds are about 1 meter tall! Puffinus puffinus 83.90mm, so 8.390cm. Elseviers Zeevogelgids: 31-38cm.
Rana sylvatica: 8.201 mm (!!). Rana tigrina: 12.79 mm. In Grizimeks Tierleben (length without tail)10-15cm. Triturus vulgaris 26 mm. Total length around 9 cm. T. cristatus: 40.40. Total lenth around 18cm.

Answ: Table 8.2: There is one mistake in the text: the data for Rana sylvatica are based on larvae (there should be an l in the first column, and the legend should explain that this means 'larvae' (cf Rana tigrina)).

But to understand the table, one should realise that Linfinity refers to a volumetric length. The volumetric length is the cube root of the volume, {24}. The original data were given as (fresh) weights. Assuming that the specific density equals 1 g/cm^3, the volumetric length is just the cube root of the weight. The Von Bertalanffy growth curve is fitted to the cube root of the weight data. The resulting Linfinity is given in the table.

To give an example: for otter (Lutra lutra) males Linfinity approximately equals 200 mm. That means that Vinfinity equals (200 mm)3 = 8 dm3. So the ultimate weight of a male otter should be 8 kg.

Quest 8.3.1: On r-strategy versus K-strategy (8.3.1), {290}: In the logistic growth, population increases by time exponentially, when population density is low. And when it grows to the capacity of the environment, it converges on the carrying capacity of K. r-selection may be active, when the food in the environment is small and unstable. And genotype that can diffuse and proliferate quickly takes an advantage to get the niche. While, K-selection may be active when the environment is matured. In this case, genotype that can tolerate the environmental stress (contact inhibition, accumulation of metabolic materials, etc) takes an advantage. Approximation that the factors in the environment for r-strategy is translated into the search for factors selecting for a small body size, and that for K-strategy is for large body size in DEB book. Body size may relate to the r-value, but is it related to K-selection ? Why ?

Answ: Time and spatial scales are coupled. Bacteria are small, grow fast, exhaust their supply soon, and then go through a long period of starvation, thinning (death) and/or resting stage. Their growth pattern in thus in the on/off mode, a short period "on", a long period "off". Elephants grow and reproduce slowly (at maximum rates), average their feeding activities over a large areas by migration; their population dynamics is usually such that their densities settle at the carrying capacity of the environment, which allows very slow reproduction, that just compensates the losses (by aging and accidents). These two examples illustrate a coupling of traits (feeding, growth, reproduction, generation time). Descriptions of r versus K strategies just aim the describe this coupling; the DEB-based body-size scaling relationships can be used to understand the coupling; Body size itself is just one aspect: co-variation of parameter values among species affect their body size AND other traits, such as reproduction and generation time.

The selection by environmental conditions for particular parameter values is another problem, which we try to understand in computer simulation studies, where rules are formulated for how the parameter values of the offspring depend on that of the mother. Selection is implicit in the competition mechanism, which results in "adaptive dynamics" for parameter values among individuals, and speciation. A little bit of this work is reported in Chapter 9.

Quest 8.3.2: Small versus large eggs. It is hearsay, I do not have that book of Stephen Jay Gould. I thought Gould on phylogenetic arguments made the case in a chapter in one of his books that you should not ask yourself why the kiwi produces such a big egg, but why did the kiwi shrink. Is his view consistent with the structure of the DEB model as outlined in subsection 8.3.2, {291}?

Answ: Egg size varies a lot between related species. The european cuckoo produces many, relatively small eggs, which are laid in nests of other birds, while their tropical relatives (anis) produces relatively large eggs and are not brood parasites. Reproduction strategy determines egg size here. It is hard to understand why the kiwi "forgot" to shrink its egg, while advanced evolutionary adaptation of relative egg size can be observed in other species.

Quest 8.4: Pages {299-300} speculate a bit about the plant-animal dichotomy, and mention the basic strategies of plants and animals. Where could we place organisms that have features of both lines of development, e.g. flagellates that have both phagocytosis (control of uptake by feeding on other organisms) and chloroplasts (control over light and nutrient uptake)? Or is this an example of a species that does not aim at specialisation, but at being as flexible/opportunistic as possible for a unicellular?

Answ: Indeed, myxotrophy is the basic life style of many non-specialized protoctists, from which plant and animal life styles developed as specializations.

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Chapter 9: Living together

Quest 9.1: Trophic interactions: There are 3 worked-out examples, namely 9.1.1 competition, 9.1.2 Syntrophy and 9.1.3 Symbiosis. What about 9.1.4 and 9.1.5? These seem to be discussed only in very general terms. Is a more detailed discussion of weak homeostasis not feasible for these interactions?

Answ: Predation is dealt with in more detail in the following sections on population dynamics. There has been little quantitative work on parasitism yet, so there is not much quantification to discuss here. Much work remains to be done.

Quest 9.1: The discussion of the first three interactions seems rather unbalanced. In 9.1.1 and 9.1.2 steady states are investigated. And the question is HOW AT STEADY STATE does the ratio of volume of the species vary depending on substrate. 9.1.3 is not derived but only simulated. And this simulation (Fig 9.1) is a simulation IN TIME. It shows that the ratio of structural masses is almost constant in time for ONE GIVEN substrate density. Stability in time was not tested in 9.1.1. or 9.1.2. Why are these different interactions not discussed in a comparable manner?

Chapter 9 starts with "The present aim is to discuss some constraints in these patterns to ensure weak homeostasis of structural masses ..." All the interactions are analysed in the light of weak homeostasis assumption. But why this is a starting point? Why we should base interaction studies on the assumption that composition of body (or the ratio of structural masses of different species) is the same?

Answ: Section 9.1 is more of an overview of the possible interactions, a complete analysis has not yet been performed for all interactions. It is true though that the start of 9.1 promises too much! The interest in constant ratios among populations is in the simplification of population dynamics at a higher level of organization. You don't want to deal with many species in community models; the model will be too complex to be useful. The problem is how to simplify in a way that is consistent and still allows you to walk up and down levels of organization. If weak homeostasis would apply, it is easier to lump species is a few functional units, and still apply mass and energy balance constraints.

Quest 9.1.1: I have only been reading untill 9.2.2, so maybe we will read about this more, but the author only mentioned briefly the phenomenon of competition. I think that this is a major aspect of population dynamics: it is very interesting to analyze the behaviour of populations when they have to compete for food, which happens all the time in nature. I assume that competition can be analyzed by simply adding x2 in the model, feeding on x0, together with x1 (to use paragraph 9.2.1 terminology). Then it should be possible to compare different parameter values: which traits are beneficial/competitive? I was wondering whether such a study has ever been performed within DEB.

Answ: This is indeed one of the key factors in population dynamics. Competition is most intense among con-specifics, because the have the same feeding strategy and nutritional requirements. Competition between species will be discussed later in the chapter, but more work has been done, than is reported in the book (see web site); much more work still needs to be done, however.

Quest 9.1.4: How would you deal with viruses? There is still a debate whether they are organisms or not. At least they seem to reproduce/copy themselves, and they can have considerable impact on species populations. A similar question could be asked for prions.

Answ: To model viruses, the same principle can be applied as to other parasites. Parasites are usually lacking metabolism (they have no maintenance costs but do reproduce). With regard to prions: we still do not know exactly about the mechanisms behind prion-related diseases (e.g. mad cow's disease and Kreutzfeld-Jacob, there may be viruses involved as well. Therefore, we should first know more about the exact mechanisms (qualitatively) before quantitative aspects can be further investigated.

Quest 9.2.1, {313}: Last paragraph: If the out-flowing food is fed back to the bio-reactor, the substrate and the biomass is coming back, I think. Is this still a chemostat? It is not obvious that this situation is covered by deleting only the last term is equation 9.7

Answ: It is no longer a chemostat `sensu stricto' but terminology is rather vague in process biotechnology. It is possible indeed to separate substrate and biomass, which means that in equation 9.7 only the last term has to be removed. Think, for instance, about sewage water purification, where biomass is allowed to settle in the effluent and is returned to the reactor.

Quest 9.2.2: On {324} it is stated that scatter is needed for stability of stable age/size distributions. Intuitively we would rather think the opposite. Can this requirement be explained in simple terms, or do we have to look it up in Diekmann et al (1984, 1985)?

On {325} (after 9.32), there is first an introduction on a mother cell that divides in two EQUALLY sized baby cells. Somehow, a few sentences later, the mother cell is suddenly being split up into two UNEQUALLY sized daughter cells Va and Vp.

Answ: If cells always divide at the same cell size into two equally sized baby cells and grow deterministically in a homogeneous environment, we have the mathematical problem that information about the size distribution of the founder population never gets lost and the population has an infinite memory. This is inconvenient, and biologically unrealistic. Two simple and realistic strategies can be followed to kill this memory: mother cells divide at slightly different sizes, or the baby cells have slightly different sizes (or both). Both approaches are discussed to solve the infinite-memory problem.

Quest 9.2.2: We found very interesting section 9.2 on population dynamics. The hypothesis that structured populations are more realistic representations of any population (to a certain extent because of spatial heterogeneity, seasonality, etc. as stated on {311}). If we understood correctly, this is meant as a mental exercise.

If we just take this further, away from a laboratory set up, e.g. in a real world situation, all the factors mentioned in the text as responsible for the not so realistic representation of a population model as spatial heterogeneity, seasonality, erratic weather, climatic changes, processes of adaptation and selection, subtle species interactions. It can be assumed that all these factors can be dumped into what we call natural variability external to and within the individuals forming this population.

Our question is, is there any (planned) development (if possible) within DEB towards estimating the influence or importance of these factors in the behaviour or response of one population species, may be of a small set of population species.

Answ: Within the department TB here in Amsterdam, we work on a number of population projects that include forms of stochasticity, and spatial heterogeneity; Our web site gives some info; We are looking for funds for a project on primary production at an ocean-basin scaled (e.g. the north Atlantic), in collaboration with a oceanographic group, where horizontal and vertical spatial structure dominates the signal. We also plan to work into the direction of adaptive dynamics (on an evolutionary time scale). A lot more can be done, and needs to be done, however.

Quest 9.2.2: On {330}, Fig. 9.12, it is stated that scatter in population responses tends to increase dramatically with body size. What is the rationale behind this statement. We have seen in previous chapters that size can be different for organisms of the same age, that they will grow at different rates could be attributed to external factors (see below). Would this have to do with the experimental conditions?

Related to this, on {335}, the observations made by van der Hoeven, it may be useful to describe what these external factors are, and it would have been interesting to know what/how were the fluctuations. Otherwise, the reader may assume that these external factors are not known.

Answ: The number of individuals usually decrease with body size in laboratory populations, and ciliates live on complex particulated food (bacteria that might clump) rather than homogeneously dissolved substrate on which bacteria live.

Nelly van der Hoeven analysed a considerable number of papers on population studies on daphnids in the lab. The initiation of reported oscillations sometimes coincided with changes in the medium, changes in light conditions, and changes in supplied food. Her paper [419] gives some details. The real course of the oscillations frequently remained speculative.

Quest 9.2.2: There seems to be information in the misfits of the figures 9.12/9.13. Can the author expand in these? In Figure 9.12, the "misfit" seems to have some specific information in the left panel. Growth rate is a bit steeper right from the start. Furthermore, the population seems to grow even at extremely small glucose levels. Does this mean that the maintenance costs of this species is extremely low? The species in the right panel has a more distinct cut-off at the x-axis.

Answ: Yes, maintenance seems to be very low in that species. When you see misfits you always have to ask whether they are reproducible and whether they are big enough to warrant a change of the model. In this case, the misfits are at low glucose concentration - low throughput rate, a situation which has a lot of experimental problems.

Quest 9.2.2: The author doesn't say much about Figure 9.13, only that the model closely matches the data. I don't know what we may expect from the model in these difficult cases, but is seems that there is some information in the misfit again: the model population increases sharply whereas the real population shows a kind of lag time. The subsequent decrease is sharp in the real population, but less so in the model one. The second peak comes earlier in the model than in the real population (may be a result of the lag?).

Answ: You have to note that no parameters have been fitted to the data and that this is a stochastic model. The fact that the model follows the big picture (rapid peak and the back to a rather constant level) is quite nice. Furthermore, the pre-treatment of the animals is unknown (e.g. whether they were well-fed or starved), which will influence the initial part of the model.

Quest 9.4: The effect of light is discussed as reaching a peak for the consumers and decomposers. An increase beyond the limiting value does not show an effect. We have observed that in outdoor aquatic microcosms, light has not a noticeable effect on the overall set of communities, interestingly enough. We have studied the effect of a herbicide compared with the effects of light prevention, run-off entries, and turbulent (mixing) conditions in the variability of phytoplankton and zooplankton. We observed effects on the communities due to turbulence (and of course herbicide) but none for run-off simulation or for light prevention (the latter one consisted of covering microcosms for 28 days at a PAR = 200 - 800 E/s*m2). Effects detected were defined as those that can "caught" by applying multivariate statistic e.g. PCA and PRC.

The question is if DEB could predict this at the community structure level. The effects commented in the book enlighten but at a more complex level they may be diluted. It may really depend on the light intensity levels for which Fig. 9.26 were generated.

Answ: Fig. 9.26 only reports potential behaviour of a community as functions of total C, N and light, based on "first principles". The parameter values have been chosen in a very provisional way. The behaviour should not be interpreted as accurate predictions. Turbulence would certainly be a factor of interest, but I would surprised when lack of light has no effect. The second law of thermodynamics is likely to apply to communities as well. The link of turbulence with DEB can be rather direct, as is illustrated in section 7.2 on diffusion limitation.

Quest 9.2: I find the population models of chapter 9 very theoretical and so far, hardly of any use for ecologists who want to explain why something occurs in the nature, and not why does the model behave like this. Please, correct me if I am wrong.

Answ: The models are indeed theoretical and cannot predict what really happens in the field. But, on the other hand, you cannot understand what happens in the field without using these models. First try to understand the simple things before you deal with the complex ones. Something the simple things turn out to be not that simple.

Quest 9.2: When population dynamics is discussed, how it is possible to account for semelparity and iteroparity. The semelparous animals, which also all reproduce at the same time and iteroparous and continuous reproduction? It is of course, clear that one have to account for mortality and stochasticity, predictability of environment and many other things to explain reproductive strategies. I was just wondering whether we can look at the evolution of reproductive strategies from the DEB perspective? Maybe it was already discussed?

Answ: DEB theory allows you to compare different reproductive strategies and see how they affect population growth under different circumstances. There is a partial discussion on {262} on suicide reproduction.

Quest 9.2: On the predation part, {310}, predators were assumed to be anyone, who eats others. So the cow is also predator? And Daphnia also (if algae or plants were assumed to be a prey?) What is a difference (if any) between real predators (III and upper levels of food chain) and herbivores as a predators?

Answ: It is bit semantic as there are many situations in between herbivory and predation. As example, Daphnia may graze on algae, but most algae are actually mixotrophs. When the algae are fed on glucose, the Daphnia are predators! This classification therefore says more about the ecologists than about the animals.

Quest 9.3.1: Cyclic predator-prey fluctuations are discussed in all the models, but hardly ever seen in nature. I guess more often we see more randomness in the population size fluctuations, both in predators and prey. Does it mean that in the nature the interactions are more "decoupled", because predator have more food resources than just one prey, and besides stochasticity plays very important role.

Answ; This depends on how you look at it. In the model, many parameters are kept constant that fluctuate in the real world. This is not true stochasticity as these things CAN be measured, in principle. Furthermore, scientist do not usually look long enough to be able to see these kinds of oscillations. You have to follow many generations to get rid of the memory of the system (the parameters of the founder population) and the environment must remain constant long enough. Figure on {343} is one of the few examples that hint at real oscillations.

Quest 9.3-4: Maybe the stupid question - but what does "canonical" mean? I have been doing canonical analysis of discriminance, which I understand as a matrix eigenvalue based solution, where eigenvalues describe between/within group variance of predefined groups. But I always feel bad, as I could not understand it fully and did not have anyone to discuss it. What does the CANONICAL communities or CANONICAL map of bifurcation mean?

Answ: Canonical is used here in the context of population models as the most simple form of community that still has non-trivial behaviour (see the glossary); so it has to include a producer, predator and decomposer. A canonical map is the most simple map that still has the bifurcation type under discussion.

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Chapter 10: Evaluation

Quest 10: This book has presented a consistent and apparently rather complete theory on dynamic energy budgets. However, we can imagine that there are still are parts of the theory that could be worked out with further detail. Could anyone indicate weak spots in the theory, i.e. things that may need further investigation/refinement?

Answ: There is plenty of room for a whole army of research workers in the different fields to develop the DEB theory further. The fields of population and community dynamics, and cellular metabolic organization are only initiated and urgently require further development. A more systematic analysis of experimental data is also urgently required, partly to test the realism of the theory, partly of obtain sets of reliable parameter values for a couple of species and study evolutionary trends; e.g. are specific maintenance costs larger for freshwater species, than comparable saltwater ones; Did high activity-high maintenance species evolve from low activity-low maintenance ones? do prey-predator systems co-evolve in terms of parameter values? So, are the parameters of the lion tuned to those of the zebra? Many of such questions still need to be studied. Then we have the practical applications. Participants' essays show some beautiful new fields of applications; the DEB information page lists some categories of potential applications, some of which are not even explored, let alone developed; e.g. medical applications such as diabetes.

Quest 10.2, {360}: Subsection Conservation laws
Optimal Foraging Theory (OFT) and Life History Theory (LHT). Statement:' "The DEB theory provides such a set of constraints (for LHT), which restricts optimization arguments to parameter values". Can the same argument not been made for OFT?

Answ: As far as I know, OFT is on behavioural issues, which has not always been modelled mechanistically in a way that involves parameters (algorithms only)

Quest 10.2, {360}: Subsection Generality
Statement: "Models that restrict the maximum body size of female animals by allocating an increasing amount of resources to reproduction, for instance, are problematic because of the existence of males, which do have a restricted maximum body size but are not able to allocate this way; sex determination is frequently affected by environmental factors. Size control should be implemented in a way that applies to both females and males". The message of the part `sex determination is frequently affected by environmental factors' is not clear to me. Does the author refers to situations that there is no genetic difference between males and females?

Answ: Sex is not always determined genetically. The book mentions a few examples; Some fish change sex during life, the sex of crocodiles is determined somewhere during embryonic development, the result depends sensitively on temperature; some observations suggest that sex in daphnids can be changed (just) after hatching.

Quest 10.3: The book refers in general to von Bertalanffy growth curves. What about the Richards, Gompertz and Brody curves? Do these curves possess some characteristic(s) which makes them unsuitable for a non-species specific theory?

Answ: Although the von Bert. curve results from DEB theory under special circumstances (isomorphy, constant food density), Ludwig von Bertalanffy had a totally different concept for growth in mind. Page {20} explains that Gompertz model is age-base, and why age is not a useful state variable to understand growth. Page {260} shows that Richards model is based on allometric functions (in a way that does not have dimensional problems), while section 1.2.3 explains why it is problematic to find a physical basis for allometric relationships. Body also deals with allometric functions.

Quest 10.3.1: Can static energy budgets (SEBs) have any purpose in the analysis of systems in steady state? What if the system is not in steady state?

Answ: In practice people sometimes do compile SEBs for transient situations. Notice that SEBs are not models, just balance sheets with numbers. The way they are compiled implies that you cannot quantify growth INVESTMENT in this way, only the amount on energy fixed in new tissue. Section 10.3.1 also discusses other differences with DEBs.

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