Questions & answers 2003

Go to the collection 2001 , 2004 . 2005 . 2007 .

The following questions have been put foreward by the participants of the second 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 1.1.3: If a full explanation of a model requires mass fluxes besides energy fluxes, and if the first fluxes are better comparable, better testable and easier to describe, why use energy fluxes as a basis for an ecological model?

Answ: Mass fluxes are not always better testable, whether mass fluxes are easier to measure depends on the size of the organism. Furthermore, there are many masses (compound-specific) and just one energy. For mass fluxes you will have to decide what compounds you want to include and each compound requires its own methods to measure. Work with generalized compounds is only possible if its composition does not change. Energy fluxes (that is fluxes of free energy) can be used as one variable in time, as a sort of summary of the chemical story (of different compounds).

Quest 1.2: When can one be confident with a model? This is a recurrent question for me and also for many. It seems that danger with many energetic models is that either one tends to be obsessed with minor details and lose a big picture or one focuses just on a big picture and ignore many important factors. However, it is often difficult to assess what are important details that we must take into account and what are not. There are many assumptions: some are good assumptions that are supported with many observations and others are ad hoc assumptions. How can one be confident with resulting models? Is there any criterion? How can one be assured that consistency between a model and observations is because of including important factors in the model and not just mere coincidence?

Answ:Unfortunately there is no easy answer, since there is a limitation in our way of thinking and there always is a trade-off between simplicity and reality. A model is then a tool to structure our thinking, although complex models hardly help in further understanding the problem. One way is to start with formulating your assumptions based on current thinking (and keep them "simple") and derive a model and experimentally test the outcome. Then accept some deviations, but this is on a subjective judgement. If the experimental data and model predictions differ too much, you need to replace some assumptions. But beware of subtle inconsistencies in assumptions. E.g. certain assumptions can have (hidden) implications that violate other assumptions and problems may arise when assumptions interact. The indirect testing of assumptions via the output of a model also complicates matters. See the first chapter in Basic Methods in Theoretical Biology.

Quest 1.2: Perhaps because of my background in statistics, where we too often regard systems as black boxes, I take for granted that theories simply cannot explain things beyond a certain level; in other words, at a certain point a theory has to accept some of its elements as unexplainable, even if such elements work in the manner predicted by the theory. On the other hand, I think I understand Bas when he explains the `irrelevance' of allometric relationships (they are not only unable to explain what is going on, as they lack consistency as a whole), and accordingly agree that there is a lot that can and should be understood. I would not equate the 'difficulty' expressed in my first sentence with the need for making assumptions for 'practical reasons', though the two are clearly related. It seems to me that the assumption about metabolic rates being equally affected by temperature, for example, points to a real 'difficulty'. My question is whether there is a level beyond which DEB theory could be seen as a form of allometry.

Answ: This is not a simple question! A mechanistic explanation at one level of organisation usually requires descriptions on another (lower) level. There is no strict distinction between mechanistic and descriptive, it is a matter of degree. Allometry runs into problems as it is purely descriptive: it is not possible to explain a certain relationship (also because of the dimensional problems).

Quest 1.2.3: If dimensionless variables become intensive variables, that cannot be added in a meaningful way, why use them, if not to understand the behaviour of the system, in an abstract and initial stage?

Answ: Intensive variables can be added (in a meaningful way), but only in a indirect way, via extensive variables. You have to be careful with the use of dimensionless variables. Dimensions are context dependent and subtle differences in dimensions can be important; the weight of algae per weight of water is not necessarily dimensionless.

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Chapter 2: Basic concepts

Quest 2.1: DEB claims to be a modelling framework for all living organisms. However, I can imagine that larger animals like mammals are more difficult to model than smaller ones like bacteria. What are the main differences between two such animals with respect to modelling in general and DEB in particular?

Answ: The answer to this question mainly depends on what you like to investigate. This will largely determine the amount of detail and the level of organization. Levels of organization vary from small (molecules or even smaller particles) to large (like populations or larger systems), but this does not mean that the lower level you choose, the easier it will be to model. Every level has below and above it another level, and you will always need to simplify. One thing that might play a role however, is this general rule: the bigger you are, the less homogeneous is your environment; big organisms (such as cows) usually live in a two dimensional world, while small organisms (such as bacteria) usually live in a three dimensional world.

Quest 2.1.1: What is the essential difference between supply and demand systems? Chapter 3 follows the fate of food and ends with production processes. This would be natural for supply systems but not for demand systems. What would be natural for demand systems?

Answ: For demand systems we could start with specifying growth and reproduction, as controlled by internal processes such as hormone levels, followed by the specification of organisms' needs in terms of food intake by variations in satiation, and how food intake controls satiation and hormone levels. Typical demand systems can handle less variation in food levels than typical supply systems; real organisms have properties of both extremes.

Quest 2.3: How can you measure the amount of reserves of an organism?

Answ: You can only measure the amount of reserves indirectly.

Quest 2.3.1: Strong homeostasis assumption seems very straightforward to understand. It basically states that chemical composition of reserve or structure does not change as an individual grows (I think). However, the weak homeostasis assumption seems more difficult to understand. This seems to assume that ratio between structure and reserve remains constant because the homeostasis assumption is applied to the whole organisms and because of the strong homeostasis assumption. Or can the weak homeostasis assumption holds without the strong homeostasis assumption? According to the text, the weak homeostasis holds if food density does not change and reserves are at equilibrium. It seems to me that if the reserves are at equilibrium and the strong homeostasis assumption holds, then the weak homeostasis is no longer an assumption; it is the consequence of the equilibrium and strong homeostasis assumptions. I am also not sure whether reserves can be at equilibrium when food density changes. Can the weak homeostasis assumption only be applied to organisms that show determinate growth? I would also like to know cases when the weak homeostasis assumption does not hold if any (i.e. chemical composition changes under the equilibrium state) and how this assumption is supported with observations.

Answ:The definition of strong homeostasis is correct. Weak homeostasis cannot hold without strong homeostasis but strong homeostasis can hold without weak homeostasis for the whole organism. The DEB model does not state any a priori assumptions for chemical composition of reserve or structure. If the organism goes through the life cycle at constant food density such that biomass (structure and reserve) does not change in composition, this indirectly gives constraints on reserve kinetics. Reserves cannot be at equilibrium when food density changes. An example where weak homeostasis does not hold would be mussels (Mytilus edulis) that funnel energy (resources) that are allocated to reproduction into a buffer, and at a certain point in time empty that buffer 'at once' and transfer it to eggs. Some organisms do that several times in one year, others at much longer intervals. Thus there is a systematic change of body composition during a year, where complexity comes from the buffer with destination reproduction. Deterministic versus indeterministic growth of species is discussed in chapter 8.

Quest 2.3.4: Why the aqueous fraction of an organism is important in relation to the kinetics of toxicants

Answ: Many toxins are stored in lipids, which play a role as reserve. In time of starvation, these lipids and toxins are released and then play an active part of metabolism via the aqueous fraction of an organism.

Quest 2.4: Why does DEB deal with mass and energy fluxes instead of concentrations, especially as fluxes are more difficult to measure than concentrations?

Answ: DEB theory deals with both concentrations and fluxes. However it only makes sense to use concentrations when the environment is homogeneous. When it is not, it is better to use absolute amounts or densities. Densities, like concentrations, are ratios of two amounts of mass, but now they do not need to be homogeneously mixed. In some cases, for example in a bacterial cell, the use of of concentrations is problematic because the volume is very small and does therefore not behave as a homogeneous environment. You can read more about this in the paper on 'Quantitative aspects of metabolic organization: a discussion of concepts' .

Quest 2.6: Regarding temperature the author argues that a change in temperature is simply a translation in time, since all metabolic rates are equally affected by temperature (Figure 2.17) while later on he claims that the rates of photon interception and water solubility are not (p. 58). This seems to be a contradiction. Given that not all rates change in the same way with temperature, the claim that changing temperature is but an aceleration of biological reactions no longer holds.

Answ: As a first approximation, all rates depend on temperature in the same manner. As the question shows, this assumption is not valid for all rates, but may serve as a simple approximation for many biological rates (as illustrated in Figure 2.17). When all the rates depend on temperature in the same way, the net result of a change in temperature is simply an accelleration. However, when some rates depend in a different manner on temperature, the situation is much more complex and the approximation does not hold.

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Chapter 3: Energy acquisition and use

Quest 3: I've a feeling that for the application and validation of the DEB model, we must do a complete experimentation of the organism we want to study! For example, I am studying on mussel, Mytilus galloprovincialis. I saw many models about Mytilus edulis. Could I use parameter values of M. edulis in my model or should I consider them to be different? How far similarity go?

Answ: Correction for differences in temperature and body size (see Chapter 8) gives a very good first guess for the parameter values for M. galloprovincialis, given the known parameter values of M. edulis. You have to realize, however, that parameters are model-specific. Although the parameter "specific costs for growth" might occur in two different models, this does not mean that their values are necessarily identical. E.G. most alternatives of the DEB model do not delineate reserves, which means that these costs include reserves in those models, while it refers to the costs for structure in the DEB model (excluding reserves).

Quest 3: Is it possible to apply the DEB model if I have got the growth's kinetics (value of weight) of my organism during one year, or should I follow the different state variables?

Answ: This depends on what you want and what prior knowledge you have available. If you has guesses for parameter values from data in the literature, or from other species, for instance, you can use the measurements on weights to reconstruct food intake, for instance (see e.g. section 7.1.4 at {223}). It will be difficult, however, to use these data (where both temperature and food density and quality varied over time) to estimate parameter values. This can best be done under controlled experimental conditions.

Quest 3.1.1: Under low mixing environment when the organisms depletes its substrate it is said that the functional response changes from hyperbolic to bilinear. How is this response affected by the size of the area the substrate is able to diffuse? Is there any intermediate response?

Answ: The situation of low mixing environments is discussed in section 7.2 at {235}. The functional response is defined as the feeding rate at a given substrate or prey density. If this density changes in time, for instance when the area is small and the number of prey decrease in time, the functional respoinse will also change in time. For intermediate mixing levels, intermediate responses are possible.

Quest 3.1.1: In the textbook, kappa and assimilation efficiency are assumed to be independent of volume. I think there are arguments to support these assumptions, however, I don't understand them. Can anybody explain them in plain English?

Answ: Kappa can be function of structure but not reserves, given the assumptions for reserve dynamics. The assumption that it (usually) also independent of structure is the simplest one. Constant kappa and assimilation efficiency results the in von Bertalanffy growth at constant food density. This growth pattern fits data very well; variations of these parameter values in time (e.g. coupled to the amount of structure) would result in deviations from the von Bertalanffy growth curve.

Quest 3.1.1, {66}: On {66} (paragraph 3.1) it says that the three main factors that determine feeding intake rates are body size, food availability and temperature. I think that the presence of competitors (conspecifics, predators) also determines feeding rates in the sense that competitors may displace animals from (rich) preferred feeding sites to less profitable feeding sites. Does DEB theory take this into account, cq should DEB theory take this into account or does DEB theory incorporate this in the factor 'food availability'?

Answ: The basic DEB model specifies food intake given a certain food density. Another model should specify how individuals interact, for instance by feeding on the same resource, and how they migrate in a spatially heterogenous environment. Chapter 9 on population dynamics will discuss the consequences of the simplest choices for such assumptions. They can be replaced by other assumptions without changing the basic DEB theory.

Quest 3.1.2, {73}: The energy required..... and just proportional to distance. The energy required for walking and running is found to be proportional to velocity, and that means that the energy costs for walking and running is independent of (speed=velocity). We thought energy required is the energy that it will cost to take that action (in this case run). So, if (energy required = energy cost of action) and if (speed = velocity) the sentence is somewhat contradictory! We thought the parameter 'energy required' has a time component (as in energy required per time unit). If the velocity is proportional to the energy required, the factor 'time' is of no importance, and therefore the energy costs are proportional to distance. Maybe the author should say that "power" (energy/s) is proportional to speed, instead of "energy required", to avoid miscommunication?

Answ: The main point of these phrases is that it requires the same amount of energy to get from A to B, independent of whether you are running or walking. Running requires more energy per time, but takes less time. However, it might be worth considering to rephrase this part of the text a bit to avoid confusion.

Quest 3.1.3, {74}: On {74} (2nd paragraph) its states that 'F' (filtering rate) depends on mean particle density only, and not on particle density at a particular moment. Why? And is this also a way to correct for prey depletion?

Answ: Variablility of particles is assumed to be irrelevant on the larger time scale thus small scale variability in food density is averaged out.

Quest 3.1.3, {74}: In expression : JX = 1/ (tp + tb) = 1/ tc, at {74}, where we understand that JX is the mean mass flux and tc is the busy period which is characteristic of the SU. We can't see how the physical dimensions match there.

Answ: The flux JX has the dimension `per time', because we follow C-moles, while all t* have dimesion `time'.

Quest 3.1.3, {74}: I have a problem with JX = 1/ ((1/ JXm) + (1/ FX)) = JXm X/(JXm/ F + X). How do we get from the left side to the right side, and what about the dimensions?

Answ: The dimensions of JX and JXm are `per time', of X is `mass per volume' and of F is `volume per mass per time'. You go from the left to the right by multiplication of numerator and denominator with JXm X.

Quest 3.1.3, {74}: On p.74 the saturation coefficient or M.M. constant is parameterized assuming a sum of a building period and a handling period. The author clearly assumes this differentiation to be realistic and important. Later on, in the next page, he states that (under special conditions [see text]) there is no need to know the exact number of intermediate steps to relate the production to the original substrate density. Can we not consider the previous parameterization of the saturation coefficient as one of this intermediate steps? If so, why not assume a constant value for it? What makes this distinction more important than other intermediate processes?

Answ: The strategy of the author has been to simplify the world as much as possible, as a start, to make it easier to understand. Subsequently more complex situations are studied for which the model still holds, sometimes axactly, sometimes as an approximation.

Quest 3.1.2, {75}: The feeding rate is said to be proportional to the surface area. This doesn't seem to express the 'learning capacity' some species have meaning that as they get old they catch their prey more easily. Or, maybe, knowledge depends on surface area because surface increases with age? Although this factor is of little importance for high feeding rates.

Answ: Learning is problematic to incorporate in a deterministic model if the organism feeds on a relatively small number of prey items. Such a situation calls for stochastic modelling. Still, it would be possible for "soup-feeders", but it will become complex in varying environments with more than one food type. The DEB strategy is: what are the simplest broad patterns among all species? If necessary, species-specific model elements can be built into the model to understand particular phenomena as variations on the simplest common scheme.

Quest 3.4: "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 to the food availability." Why are these assumptions made and how do they produce the equation on {83} before the eqn (3.7).

Answ: The assumptions are made to specify reserve dynamics. Assumption 1 is of importance to understand how (eukaryotic) metabolism evolved (see the paper on symbiogenesis). Assumption 2, on weak homeostasis, is of importance to partition weight in two components in an indirect way; if you would refrain from weak homeostasis, great difficulties arise to quantify structure and reserve. Assumption 3 is of importance to incorporate smoothness in behaviour, and to allow e.g. maintenance to proceed when food is absent temporarily. The comments give a derivation of the formula on {83}

Quest 3.4, {83,84}: The most difficult part of the chapter is, to my impression, the one on the reserve dynamics. This gave rise to the following questions:

  1. The first requirement for reserve dynamics is the partitionability of reserves {83}. Does this mean that regardless of the composition of the resource, the assimilation flux is added up to a reserve pool that has a constant composition?
  2. From the figure on {84}, it seems that a kappa-fraction of the reserves adds up the structural growth. How does this comply with the strong homeostasis assumption?

Answ: Assimilation is the process that converts food into reserve; such a conversion involves a conversion efficiency that depends on the quality of the food. If we have two substitutable types of food and one type of reserve, we can add the incoming fluxes of reserves, because they have the same composition. Chapter 5 discusses situations of complementary food types and several reserves. The diagram has its limitations; it only illustrates the flux that is allocated to growth, but we here need a conversion efficiency again to quantify the flux of structure that arrives in the pool `structure'.

Quest 3.6: It seems that the volume-related maintenance cost is assumed to be proportional to the sum of structure and reserve. Does this assumption require weak homeostasis assumption?

Answ: Volume-related maintenance costs are NOT proportional to the sum of structure and reserve, but proportional to structure only. This explains why the weight-specific maintenance costs decline with size among species (see chapter 8).

Quest 7.3.1: On {95} it says (last paragraph) that the requirement that food density is constant for a Von Bertalanffy curve can be relaxed if food is abundant, as long as food intake is higher than 80% of the maximum possible food intake (which relates to properties of the hyperbolic functional reponse). Three questions:

  1. Can this requirement of constant food density in a similar way be relaxed for V0- and V1-morphs (p. 108)?
  2. In case growth functions are of other forms than Von Bert., {258}, (how) can the assumption of constant food density be relaxed?
  3. In case of mild starvation (p. 223), food intake can be assumed to be lower than 80% of the maximum possible food intake. In the derivations from growth (dV/dt) to the specific growth rate (r') and subsequent predicted growth curves ({95}, {108}) the assumption is made that if food density is constant long enough energy density tends to [E]=f[Em]. How can you model growth in case of mild starvation if the assumption of constant food density is violated?

Answ: Yes it also applies for V0 and V1 morphs, because is only depends on the shape of the functional response curve. Their growth curves, and that of other non-isomorphs, at constant or abundant food differ from the Von Bert. curve. If food density changes, you will need the full DEB model, and can result in almost any growth curve, as Fig. 7.6 b illustrates at {227}. Here a spline function is fitted to the growth data, and the DEB theory is used to reconstruct food intake.

Quest 3.8: Fig. 3.21 on {111} shows for five different food levels the size of Daphnia magna at the moment of egg deposition. These data show that the volume (Vp) at the first appearance of eggs in the brood pouch of daphnids seems to be independent of food density, and that age at maturity is accelerated under high-growth conditions. Troy Day & Locke Rowe (2002; Am. Nat. 159(4): 338-350)) predict with a general model that (not assuming von Bertalanffy growth, but power function growth) age at maturity is predicted to increase with growth conditions (opposite to patterns found in nature). If they incorporate a developmental threshold, this reverses the predictions and shows that age at maturity decreases with growth conditions. They claim that these thresholds provide one potential explantation for the observation that age at maturity decreases with growth condition. I wonder if the DEB model provides an explanation for why the juvenile/adult transition only occurs at a fixed structural volume and if the DEB model provides an explanation for the (common) observation that age at maturity is accelerated under high-growth conditions?

Answ: The DEB model is a threshold model in this respect, although it is energy-based, rather size-based, in the first place. Only if maturity maintenance costs relate to somatic maintenance costs in a special way, it is sized-based as well. If not, you will notice that the size at maturation depends on food density, and this can be used to infer the maturity maintenance costs.

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Chapter 4: Uptake and use of essential compounds

Quest 4.1: Because of strong homeostasis, I can understand that the overhead in the conversion from E -> V is fixed by constants. How does this work for animals in environments with different food qualities?

Answ: Use of different substrates is the topic of chapter 5. Conversion efficiencies from food to reserve are food-specific; if several types of food are around, we have several conversion efficiencies, and we have to model how much eat eaten from all of them.

Quest 4.1: DEB considers C,H,N and O. Does this mean that other possible limiting factors (P in most fresh water environments and Fe in vast areas of the ocean) cannot be taken into account, or it is possible to embody these as well?

Answ: You can use the whole period table of elements if it is required for your understanding. Using one reserve with a fixed composition you can calculate any mineral flux. If several compounds can be limiting simlutaneously, however, you need to model these interactions in the assimilation and/or in using more reserves; see chapter 5.

Quest 4.2: I miss a clear definition of the powers. Is dissipating power the lump term for overhead costs in the conversion steps? Are these costs also necessary for stoichiometric reasons, because of the different compositions of reserve and structure?

Answ: The definition of dissipating power is (3.58) on {124}. The overheads of growth are NOT included, although the associated energy does dissipate. Overhead costs for growth related to differences in composition of structure relative to reserve. Some reserve molecules are oxydized to convert other reserve molecules to building blocks and drive the synthesis of these building blocks into structure molecules. A similar situation occurs in the conversion of food to reserves.

Quest 4.2: I have difficulty in disentangling the respiration, dissipating heat and nitrogenous waste. From energy balance point of view, there are two major components in a broad sense: (1) assimilation that is energy acquisition from food and (2) costs that are energy expenditure associated with maintenance, growth and reproduction. Since conversion of reserves to gamete and somatic growth does not occur with 100% efficiency, then we have a by-product: dissipating heat. What I am not clear is the dissipating heat. In other word, how can we measure it? Usually we can measure respiration rate (the use of oxygen or the production of carbon dioxide), which includes maintenance. Is the dissipating heat included in respiration? If so, the measured the use of oxygen must include dissipating both heat and maintenance.

Answ: The terminology is confusing here. Dissipating power is not the same as dissipating heat. The power is a specific power that is defined in the text. It excludes contributions from overheads of growth, reproduction and assimilation. The total dissipating heat, however, does have contributions from these processes.

Quest 4.3.4: We couldnīt understand how the change in composition of biomass for increasing growth rates can be used to obtain the composition of reserves and structural mass.

Answ: The DEB model specifies how the reserve density depends on the growth rate, while reserve and structure have a constant (but unkown) composition. The empirical data show how the composition of biomass depends on the growth rate. This information can be translated into the composition of reserve and structure (see the parameter values n** in the legends of Figure 4.2). The figure shows an example for the elemental composition only, but this can be done for any compound as well (cf rRNA in 7.5 at {244}).

Quest 4.3.4: About the Figure 4.2 on {134}: a) We couldnīt understand the variables neither "relative abundance" nor "yield of dry weight" along the vertical axes of the figures (we think that we might obtain "relative abundance of oxygen" (for example) in the weight of the individual making the quotient between the amount of oxygen present in its reserves and the amount of oxygen present in its structural mass, but we donīt know if this guess is right). b) We couldnīt understand the physical dimensions for the "yield of dry weight" and the "specific oxygen consumption rate" (or the "carbon dioxide production rate").

Answ: The abundance of an element, relative to carbon, is obtained by the ratio the measured number of moles of that element and of carbon in sample of biomass. The yield of dry weight is obtained by the ratio of the measured dry weight of biomass that leaves a chemostat at steady state during some period and the measured weight of substrate that is consumed during that period (difference of what goes in and what goes out). These values in grams are here converted to C-moles by multiplying the measured moles carbon per gram in biomass and in substrate. For chemically pure substrates, we don't have to measure it, it is known, but grams sometimes include cristalline (or other) water. The specific dioxygen consumption rate is obtained by the ratio of the measured dioxygen consumption during some period, and the measure biomass that is involved in the consumption. The latter is done by measuring the biomass in a sample of the chemostat (or in the outflux), can correct for the difference in the volume of the sample and that of the chemostat.

Quest 4.3.4: a) We couldnīt understand how the data on the elemental composition, yield of dry weight and specific oxygen and carbon dioxide fluxes lead to the relationship between the mineral fluxes and the three basic powers reflected in the matricial equation on {135}. b) What is the reason to assign a plus sign to the mineral fluxes in that equation?

Answ: The legends of Figure 4.2 shows which parameters are estimated from the data shown. The index + is included in (4.11) to remind us that we are dealing here with populations rather than individuals, but for V1-morphs that amounts to the same results. At {131} we derived that JM = - nM-1nOetaOp, where etaO is given in (4.5). We now substitute parameter values. The signs appear automatically; a negative sign means consumption, rather than production. The powers in p are always taken to be positive.

Quest 4.3: Were do the integer values in nM in eqn (4.2) at {130} come from? And are the nM and nO on {130} all species-specific, and hence need to be measured seperately for each species?

Answ: Integer values corresponds to the composition of CO2, H2O and O2. The body composition is species-specific, in principle, but the compositions of related species resemble each other very much. So it seems safe to use such data, if better data are not available.

Quest 4.3: In Figure 4.1 the flux to structural biomass has a small maximum just before birth (the first discontinuity), why is the increase not monotonous and what is the cause?

Answ: Observe that this is a flux not the absolute amount, the flux decreases as a result of depletion of reserves and an increase of meaintenance costs. The growth curves of embryo's, as presented in Figure 3.15 at {99}, first increase in steepness, and then decrease.

Quest 4.4: In C3-plants have an additional light-dependent respiration activity - referred to as photorespiration - that consumes oxygen and produces carbon dioxide. When the intracellular concentrations of O2 are high, one of the enzymes responsible for CO2 fixation in the C3 dark reactions - ribulose-biphosphate carboxylase - can also catalyze the oxidation of a Calvin cycle intermediate, initiating a series of reactions that produce CO2 and glycine as end products. Hence, when the splitting of water during the light reaction furnishes oxygen, photorespiration takes place, in addition to basal respiration.? I don't understand how this can fit in DEB model. Is respiration measured as a dissipative power.

Answ: Photorespiration will be discussed in chapter 5, at {166}. It modifies the assimilation flux, from light, CO2 and O2 to carbohydrates.

Quest 4.4.2: Older animals tend to eat less (e.g. shown for springtails), which means less energy income. However, the springtails do not decrease in size. So where does the energy for maintainance come from? Or can kappa change with age?

Answ: Indeed, some changes are required to accomodate this behaviour. Kappa, and all other parameters, may be linked to damage. Chapter 6 on toxicokinetics shows that parameter values can be linked to internal concentrations of toxicants; cumulated damage by free radicals plays a role similar to these internal concentrations. We also need such a construction to model the ceasing of reproduction in old individuals.

Quest 4.4.2: About DNA repair mechanisms: In the text, changed DNA accumulates proportional to the catabolic rate. This means DNA repair rate is also proportional to the catabolic rate. In other case, the author assumed the constant neutralization probability to changed DNA. Why is not DNA repair rate proportional to the changed DNA? or why is not damage reversible? Text book only treated aging process in ectotherms, but suggested a possibility of additional mechanisms to remove free radicals in endotherms. Why are the aging processes in ectotherms and endotherms different?

Answ: Damage repair is taken to be proportional to catabolic rate because this rate is supposed to quantify the metabolic activity. If it would be some function of DNA damage and if it represents an energy drain, it would modify the allocation patterns as described in Chapter 3. The problem with endotherms is that this model for aging does not describe the survival data well; some additional ageing-accelleration is needed. The basic ageing model predicts a curve, similar to a Weibull with shape parameter 3, but in Figure 4.7 it is closer to a shape of 7. A more complex ageing model has been developed that includes an additional acceleration step: damaged mitochondria produce free radicals.

Quest 4.4.2: In the paragraph preceding Eqn (4.22) at {141} it is said in words that d(Mw)/dt = kMQ, where Mw is the amount of wrong proteins, MQ is the amount of altered DNA and k is an arbitrary constant. That is, the accumulation of wrong proteins is a first order process of damaged DNA accumulation. But isn't there a turnover term missing? After all, proteins don't live forever, hence the expression should be of the form d(Mw)/dt = kMQ - zMw, where z is a turnover constant (k and z are probably specific for each type of cell and protein).

Answ: If z is not extremely small, we would have the situation where some individuals can become extremely old. This is perhaps less realistic, and makes the model more complex, especially in population dynamical applications. One way to quantify the complexity of a model at this level is in the amount of memory that is included. We here would like to have models that soon become independent from their initial conditions, which means that the founding cohort must dissappear soon.

Quest 4.4.3: In Q&A written by Bas, a new paper about aging model was introduced. I was so surprised and confused that the difference between the new aging model and an aging model in text book, (chapter 4, and chapter 7). What is important is not mathmetical forms of the two model (Gompertz and Weibull type model), but differences in their assumptions. In textbook, the author assumed damage inducing compounds(changed DNA) and accumulated damage (wrong protein), but the new paper suggested a new concept, 'oxydative damage' and its amplication and positive feedback loop. I think the authors changed the definitions of '(accumulated) damage', which is directly related to aging rate. Can both of the models be reasonable?

Answ: The book mentioned that survival data of endotherms don't fit the model in the book, although it works well for ectotherms. The new paper introduced the acceleration mechanism that has been failing. It now matched endotherm survival data, but we did not yet test it for the ectotherm data presented in the book. It has an extra parameter, so it is more complex. Both models have many similarities though, and damage is directly coupled to respiration in both models. That one has the Weibull and the other has the Gompertz model as special cases is strange coincidence. I presently think that both models are reasonable, but I hope to develop a preference for one of them (or a third one) in a theory that is both "beautiful" and realistic.

Quest 4.5: What is the source of the nitrogenous waste? Is it directly excreted from food passing through gut during ingestion process or from reserves during conversion process of reserves to growth and reproduction? If it is the latter, is there any relationship between the nitrogenous waste and dissipating heat?

Answ: Nitrogenous waste, like dissipating heat, has contributions from assimilation, maintenance and growth. The weight coeffcients, however, can differ. This also holds for dioxygen consumption and carbon dioxide production, and explains why dissipating heat is a linear combination of Nitrogenous waste production, carbon dioxide production and dioxygen consumption. This is basic to the method of indirect calorimetry.

Quest 4.8: What about the cactus? It stores water so the water uptake rate is not proportional to evaporation rate.

Answ: A model with one structure and one reserve does work well for organisms with a relatively simple metabolism, however, plants are more complicated. One storage is not always enough to model the plant and it can be necessary to add one or more reserves. For cactus in this case, it is necessary to add an explicit reserve for water. Including more reserves does complicate the model, as you can see on {181}. However, if water storage is important in the system it should be an explicit reserve. By including more reserves, you can remove constraints on the composition of biomass, but you pay for it by having a more complex model, which will be harder to apply in practical situations, and more difficult to extract useful conclusions from it.

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Chapter 5: Multivariate DEB models

Quest 5.0: To the build up of reserve A we can only have one nutrient limitation, for example, nutrient m, but for reserve B we can have limitation from nutrient n, because each reserve has a specific chemical composition. This is the reason why we have simultaneous nutrient limitation? Meaning that if we had only one reserve we would have limitation from just one nutrient?

Answ: The definition of limitation of growth by a nutrient is that if we would increase the concentration of that nutrient a little bit, this would lead to a somewhat higher growth rate. If this would hold true for two or more nutrients, we have a case of simultaneous limitation of growth. This can be modelled in the DEB context in two different ways. Both nutrients may be required to make a particular reserve, or else, two reserves may be required to make structure. If, in the latter case, each reserve requires only a single nutrient, the organism can store the nutrients independently, with obvious consequences in variable environments.

Quest 5.2: Do multiple reserves in a model make it more difficult or more easy to fit the model to datapoints? Multiple reserves have more degrees of freedom, which might give more possibilities for fitting. On the other hand it is also imaginable that fitting several parameters simultaneously is more difficult. So which of these has the overhand?

Answ: This depends on the data. When you have poor data in combination with many parameters, you have a problem! Having more reserves allows you to deal with specific behaviour in your data. Many data points for just two variables will be of little help, we need data on more variables. In practice, fitting a more-reserves model requires data on more than one variable (as in Figure 5.5). As a rule of thump: the ratio between the numbers of parameters and the number of data sets should not exceed 3, and the number of data points per data set should be such that the relationship between the variables is well determined; if it has a wild morphology, you need more data.

Quest 5.2: You said that the model extends to more reseves without causing additional problems! This surprises me. I'm agree to say that the energetics of dividing organisms can be simplified, by combining somatic and developemental allocations, but, in my mind, more reserves introduce additional problems to account for simultaneous nutrient limitation!

Answ: When B.K. wrote that more reserves to not cause additional problems, he only had in mind that the theory on Synthesizing Units can handle an arbitrary number of variables. Since the DEB specifications for assimilation and growth uses this theory, the inclusion of additional variables is in a theoretical sense straightforeward. We certainly do run into all sorts of practical problems that come with the specification of all the interactions.

Quest 5.2.3: The model of multiple reserves seems to fit the data quite nicely (fig 5.5), but the shape of the line in the first figure is a bit strange. If you look at the data points, you could draw a completely different line through them, one that is more similar to the other lines in the same figure. Can you explain the dynamics behind this line? Does such a 'switch' in the line look realistic to you?

Answ: The switch in the upper curve in the left two graphs shows the transition from vitamine B12 to phosphate limitation. In fact, the switch is not sharp, but smooth (it is a property of synthesizing units, which do not have sharp switches). It is true that, if the other curves would not be there, the best fitting curve would look completely different. However, all curves are fitted simultaneously, and the data (don't look at the curve) in the lower left panel go up as well. The conservation law for mass implies that the data in the lower left and the upper left panels cannot go up both. The curves obey the conservation law for mass, and help to spot a problem with the data, in this case.

Quest 5.2.4: {172} first sentence of last paragraph: A change in density of reserves would imply a change in their composition. Since densities resemble concentrations, but the compounds are not necessarily well mixed at a molecular level, {41}, it seems to me that instead of density it should be concentration. Is this correct?

Answ: The composition of any reserve cannot change, because of the strong homeostasis assumption, that of biomass (so the combination of all reserves and structures) can change indeed. The section 7.6 at {246} on structural homeostasis gives some background to the difference between densities and concentration for reserves.

Quest 5.2.4: {172} last paragraph: Which is the way for to deduce the relationship between the density of limiting reserves and the non-limiting reserves with the growth rate?

Answ: Measure the composition of biomass under the various limiting conditions. If the concentration of some compound in the biomass increases for decreasing growth rates, it is probably relatively abundant in the non-limiting reserve. By fitting DEB predictions to measured data for different growth rates, you can extract the relative contents in the reserves and the structure for each compound, as well as the excreted fractions. The amount of work that is involved rapidly increases with the number of possibly limiting compounds.

Quest 5.2.6: ({176} 3rd sentence of 2nd paragraph) Why does the fact that ammonia reserves are quickly extinguishable mean that there is a double synthesis of the product of ammonia and carbohydrate? I think that in assimilation (prior to storage) ammonia doesn't have to be altered.

Answ: There are two steps: First, ammonia and carbohydrates can be used in synthesis of (general) reserves. Excess ammonia can be stored in a reserve, but if the turnover rate of that ammonia-reserve is very high, it is as if ammonia is directly used, in combination with other reserves, for the synthesis of structure. Notice that if the turnover rate of a reserve goes up, the (maximum) reserve capacity goes down; if the turnover rate is very high, it is as if the compound is not stored at all.

Quest 5.3: At {178}: "Vi/V+ stands for the relative length of the track followed by blood as it flows though tissue i". How can it be since Vi and V+ have the same units and therefore Vi/V+ is dimensionless?

Answ: The nail is in the word relative, in "relative length". The actual length of the track is proportional to the ratio and the proportionality factor should fix the dimensions.

Quest 5.3: At {178}: What is the reason to include the exponent i in the non-equality for V+ in the case of allometric growth? What is the meaning of this exponent?

Answ: Allometric models are empircally motivated: simple models that frequently fit data well. The exponent is usually obtained using linear regression on log-log transformed data. The exponent then appears as the slope, which (gnerally) differs for different body parts. This is implemented in the model by appending and index i.

Quest 5.3.2: At {193}, we read that "the shoot is adult if MVS > MVpS", but we could not find out what MVpS is.

Answ: MVS is the number of C-moles (M) of the structure (V) of the shoot (S); MVpS is the number of C-moles (M) of the structure (V) of the shoot (S) at puberty (so the transition from the juvenile to the adult stage). It is treated as a parameter value. In words: the shoot becomes adult if its structure exceeds a given value, whcih we call MVpS.

Quest 5.3.3: I have a question which has always puzzled me: What is the bioenergetic role of cutting the branches of fruit trees? Among other functions (as increasing the light exposure area or facilitating machinery use) there are two clearly bioenergetic functions in the cutting:

  1. Accelerate frutification - I believe this claim to be mpirically true.
  2. Augment yearly production - This claim I cannot corroborate because I never assisted to a controlled experiment but I take it as granted - otherwise farmers would not do it.
Technically, the part of the tree that is cut are the branches that are growing more straight up and that would lead to an increase in the size of the tree.

From a bioenergetic point of view, however, the cutting seems highly irrational. Regarding claim (1) maturation occurs after a certain investment has been made. If there is loss of structural volume, surface area and food acquisition decreases, hence reproduction should be retarded, not advanced! Unless if what declenches reproduction is not "a certain investment" but a ratio between maturation investment and structural biovolume.

Regarding claim (2) I see no clear explanation. One might be that light is not the critical "nutrient", hence reduction in surface area does not reduce that much the energy intake and the removal of structural biomass reduces the maintenance costs. However, the k-rule implies that in this scenario more energy is spent in regrowth, not in reproduction... the practice of cutting seems to imply a direct tradeoff between maintenance and reproduction investment. What if the maturation maintenance costs somehow for the fruit trees are dependent on the real biovolume and not on the maturation threshold volume? In any case, cutting would still be stupid because the reduction of aereal biovolume does reduce strongly the future growth of trees, i corresponds to precocious aging (this information is general, not specific to fruit trees). However, there is one ad hoc reason to explain cutting: it is the newborn branches that usually frutify, but this mechanism must be consistent with bioenergetics (in way that for the moment seems obscure to me).

Hence, I believe that claims (1) and (2) are completely open.

Answ: The plant model, specified at {181}, was constructed during the preparation of the second edition of the DEB book, and has not yet been tested against experimental data. It is coded in DEBtool to facilitate its evaluation and application. The code can be used to study the energetic consequences of cutting of branches (and/or roots) given nutrient, water and light levels. A full evaluation of such actions should include indirect effects, such as watering of soil and it effects on nutrient availability, etc. Such an application would be most welcome for the further development of the part of the theory.

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Chapter 7: Case studies

Quest 7.1.1: In this section feeding is described in terms of an alternating renewal process, the `off' periods being exponentially distributed with parameter lambda_0 and the `on' periods exponentially distributed with parameter lambda_1. Can we drop the exponentiality assumptions? If so, would it be of interest to investigate the problem theoretically?

Answ: This presented stachastic model for feeding is indeed the simplest of its class, and not necessarily realistic. Generalizations would be very welcome, including tests against experimental data.

Quest 7.1.1: I think that the value of the simulations shown in Fig. 7.1 is somewhat limited: they only show that the type of scatter usually observed in data can be reproduced by this particular model (and in my opinion this is the only conclusion that the simulation allows), but the variability in the data also comes from the variability in the parameters of the individuals. Do you agree that in order to say something more concrete about the plausibility of the model for feeding one would also have to specify (to some extent) the variability of the parameters?

Answ: This is fully correct. A general problem with including stochasticity in parameter values, as well as in behaviour is that the model very soon becomes comples and parameter-rich, which limits its applicability.

Quest 7.1.1: Do you think that the variance of the parameters in the population might be constant in time? If so, one might obtain the theoretical variance curves of e(t) and l(t) for a specific feeding model (or approximations thereof holding for a general class of models), and confront these with data. Do you think this would be useful? If so, do you think that one could determine the (main) parameters of the feeding process from a set of data? (Were this possible, I think it might help both the validation of the assumptions about the feeding process and the separation of the variability into different 'sources'.)

Quest 7.1.4: The emperor penguin feeds on plankton and has to face the meagre period between plankton peaks. In this case it is assumed that in this meagre period the penguin still feeds on plankton, so this results in low food intake in this period. What happens if the penguin could switch to an alternative food source which is abundant in this meagre period, but is less nutritious than the plankton? Will it be necessary to add an extra reserve in order to model this food uptake, since it differs significantly in its compound composition? Or is there a easier way to model this?

Answ: It is not necessary to add an extra reserve. In this case it is not possible to add a reserve to smooth out the differences in food availability (as e.g. in plants with daily fluctuating light and nutrient availability), because this is a long-term change. The different composition of the food causes a change in conversion efficiency, which will be lower for the less nutritious food source. Important in this matter is that the composition of the reserve does not change when the composition of the food changes. Therefore this can be modelled with one reserve. Depending on the metabolic system of the organism, it can deal with this low conversion efficiency either by increasing food uptake or in case of a maximum uptake rate, it will result in a smaller body size.

Answ: Quest 7.1.5: Isomorphic adults grow assymptotically to some constant size under constant environmental conditions, and might remain at that weight for quite some time. Differences in weight between individuals then reflect differences in parameter values, but quite a few parameters are involved in the DEB context. The variance of e(t) cannot be constant in time as long as l(t) is changing.

Quest 7.1.5: On {230}, the author assumed LD snails are dead at d/dt [E] = [pM], i.e, e = kappa l while MD snails are dead at [E] = 0. Why are the assumptions different between LD and MD snails?

Answ: This is because the reserve kinetcs is different in both cases, reserves of LD snails follows a first order kinetics, and that of MD snail is such that maintenance is paid only.

Quest 7.3.1: On {242}, if equation p(1,1) includes three basic powers kappa*pA, pD, pG at V = Vm, i.e. the population is growing at maximum rate. is pG not (kE- gkM)/(1+g), but k/g - kM = (kE- gkM)/g, isn't it?

Answ: Equation p(1,1) deals with the population growth rate of V1-morphs, although the latter is not stressed in the text. $Vm$ is the maximum structural volume of an individual. It will no longer grow if it has reached that value. If a population grows, we will have a variety of ages, and so of sizes, in the population. Not all individuals will have size that size, and probably, no one will. Eqn (3.38) at {108} shows that we have to dived by $1+g$, because new biomass consists of structure AND reserve.

Quest 7.3.1: On {243}, the author suggests the relationshion between YWX and growth rate (r) for V1-morphs. According to Yield factor on {315}, I think the equation is correct only when d/dt [E] = 0, and kappa = 1. What is correct?

Answ: The yield YWX of biomass on substrate is only defined at steady state, where we must have that d/dt [E] = 0, because of weak homeostasis. Think about an embryo that does grow, but does not feed, to realize that such a yield coefficient is defined for steady states only. The value for kappa is to some extend arbitrary for V1-morphs, because somatic and maturity maintenance can be combined, as well as growth and maturation. The value of kappa only affects the detailed interpretation of compound parameters (such as g).

Quest 7.6: The author argued eqn (7.23) can be reduced from eqn (7.21) if [Em] << [EG] and g >> 1. Does the author consider g (and Vm) values for cell and individual are different? What is the bottom-line of these assumptions?

Answ: Parameter-values are specific for the individual; differences among parameter values of individuals belonging to the same species will be small; this will be discussed in Chapter 8. The aim of the assumptions has been to find a mechanism behind weak homeostasis and partionability of reserve kinetics. The conclusion is that such a mechanism has been found for part of the parameter space. Other mechanisms might exist as well.

Quest 7.6: What does a spatial micro-structure that is subjected to structural homeostasis mean? Logically, the first-order dynamics for reserve and weak homeostasis is appropriate assumptions if g >> 1. But what is important and is this assumption real?

Answ: Structural homeostasis can be a mechanism behind weak homeostasis and the partionability of reserve kinetics for large values of the energy investment ratio g. It need not be the only possible mechanism, and for small values of g we still need to find other mechanisms.

Quest 7.9.2: As long as food density remains constant, size-based models can always be converted into age-based ones. But if a period has a poor (but still constant) food density, can size-based models still be converted into age-based ones? Does in this case the size still follow the age?

Answ: As long as food density is constant you can convert size-based models into age-based models. However, when you include interactions between organisms in the model, this will cause differences in growth in environments even if food supply is constant (see e.g. the picture on page 21). And then you will be unable to convert size-base into age-based models. Size is a better variable to use, although in practice age is more often used as it is easy to measure and to model. Notice also that food density can hardly be constant for a long time, because populations will grow exponentially and exhaust food soon.

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Chapter 8: Comparison of species

Quest 8.0: DEB theory aims at describing the energetics of all species, however, there is an importance class of species, in population numbers and in habitat range, if not in species diversity, to which I saw no reference - these are domesticated species. In the DEB theory, the evolutionary changes introduced by domestication can be understand as adaptation (briefly discussed in chapters 7 and 8) and the exploitation of biological resources as product formation (briefly discussed in chapter 5). However, I believe there are many questions regarding domesticated species to which DEB could offer an answer (and that would probably be suitable to validate DEB in a wider context).

Answ: I can't agree more. Many high-quality data exist for such species, and application of DEB theory to the interpretation of these data could indeed lead to exciting results.

Quest 8.2: Until chapter 8 the DEB parameters are considered completely exogenous. However, in that chapter, it is argued that some parameters are intensive and others extensive, that is, some depend on size and other don't. Further ahead, it is argued that they can also be a function of temperature. In other point, it is argued that the functional response can adjust to low food density. Question: What are the DEB-parameters function of, in general? Are there "invariant meta-parameters" (i.e., parameters of which the DEB-parameters depend, valid for all species)?

Answ: All parameters are taken to be constant for an individual, in principle. Some do depend on temperature, as explained in 2.6, so if the temperature varies in time, rate parameter vary in concert. The aim of chapter 8 is to identify rules for the variation of parameters values among species, and find such invariances. This type of variation has nothing to do with variation in time during the life span of an individual; it might have something to do with that on an evolutionary time scale.

Quest 8.1: The introduction of the zoom factor as a stochastic variable coupling four energy parameters is not very clear for us.

Answ: Differences between individuals in a DEB context can only be set by differences in state variables and in parameters. Since the initial structure and damage are set to zero, the only state variable that can differ is the initial reserve. Such differences will only have minor effects. So the differences parameter values are important, but the process of setting the differences must be specified as well is we want to capture all processes that are relevant for energetics. We need to do that anyway to specify population dynamics (in chapter 9). The text suggests an attractive specification of such a process where the parameters of a daughter are taken from those of the mother, using a zoom factor that can slightly differs from one. This simple way of setting parameter values causes a co-variation of 4 primary DEB parameters, along the mosqui-to-elephant line, but applied within a species.

Quest 8.1: I have a paper that presents data of CO2 production and body weight of different benthic organisms ranging from small nematodes to big fishes. The authors fit two allometric regressions to these data, one for shallow warm water and one for deep cold water. How can I understand the differences in these lines based on DEB fits? What additional (apart from the CO2 flux and body weight) data would I like to have to explore this topic further or perhaps are even required for any interpretation?

Answ: Ideally, you should start specifying a scientific problem, rather than just asking "what can I do with given data". The DEB theory shows what controls CO2. Given assumptions on environmental temperature, you can try to use DEB theory to reconstruct food intake from these data, for instance. This is only feasible if some idealizations can be made.

Quest 8.2: I'm a little confused by the invariance property. I understood the definition presented on {266} 'two species with parameter sets that differ in a very special way behave identically with respect to energetics...' with 'very special way' including the restrictions presented in the same paragraph. When reading 8.2.1 I understood that primary scaling relations presented in the lower panel of table 8.1 where obtained for two species with Vm1/ Vm2 = z and that the upper panel was for the special case that obeyed the "invariance property". Therefore we could always apply the relations presented in the lower panel. But on {289} we can read "primary and secondary scaling relations follow directly from the invariance property". My question is : can primary scaling relationships be used for all cases or just between species that obey the restrictions implied by the "invariance property".

Answ: The invariance property is a mathematical property of the DEB model, and it has nothing to do with the physical interpretation of the (primary) parameters. The primary scaling relationships classify the parameters as intensive or extensive, using their physical interpretation. Then follows two observations: ratios of extensive parameters are intensive (so all extensive parameters depend on size in the same way), and the max spec. assimilation rate is proportial to volumetric length. The amazing result, however, is that this line of reasoning produces the same scaling relationships as the invariance property, apart from the stage-transition parameters. This points to deep mathematical nature of physical principles that I just partly understand myself.

Quest 8.2.1: Can the lower panel on table 8.1 be obtained just with Vm1/ Vm2 = z? How do we derive the relation between {JXm}1 and {JXm}2?

Answ: The lower panel of this table just summarizes all primary scaling relationships. The parameters for species 2 can be obtained from that of species 1, by multiplying the 6 extensive parameters with some common factor, while the 6 intensive parameter are the same. There are many ways to obtain the appropriate value of the factor with which we have to multiply; one way is to look at the ratio of the maximum lengths of the two species.

Quest 8.2.2: On {273} "mean gut residence time of food particles is thus independent of body size". This is of major ecological significance because it determines which type of food can be digested. The poorly digestible substrates can only be used by animals with a big body size?. Aren't the previous affirmations contradictory?

Answ: Correct, the text is not clear. It should more clearly have stated that interspecies differences in gut residence times are caused to differences in relative gut volume (according to DEB theory). So, it is a morphological argument in the first place.

Quest 8.2.2: On {287} "life span", it is argued that long life expectancy is correlated with sophisticated behavioural and physiological control mechanisms (e.g., birds vs. mammals, since the brain size to body size ratio and life expectancy to body size ratio are both higher in birds). In the papers ( and it is argued that long life expectancy was required to allow for increase in brain size for primates, since large brain size implies a larger juvenile period and only if the species lives longer does the additional investment pay off. In the DEB framework can this coevolutionary process (larger brain size and longer life expectancy) be expected in the bulk of a stable population (maybe testing like the bang-bang vs. continuous growth reproduction strategies) or are exogenous shifts (like sudden shortage or abundance of food supplies) required to trigger the process?

Answ: Brains grow fast, relative to the rest of the body, so brains cease growth at a relatively early age. A direct causal relationship between brain size and expected life span is beyond the present scope of the DEB theory.

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Chapter 9: Living together

Quest 9.1.1: Reading the first paragraph of {302} about constrains on parameter values of competing species I understood that DEB organism's parameters were also used for a global population. But on {313} discussing the conversion efficiency from prey to predator Bas K. starts by assuming that its value (3rd line) is the same we would consider for an organism and then on the 15th line talks about Y at the population level. Why don't they have the same value? Do or do not organisms parameters apply to all non structured populations? Parameters constrains are based on a weak homeostasis assumption applied to two different trophic related species? Why is that so? Does this rules out the known oscillatory behaviour of prey/predator systems?

Answ: At the sub-organismic level we have the conversion of food into reserve, and of reserve into structure; the conversion coeffcients are constant. At the supra-organismic level we still can study the conversion of food into biomass, but the conversion coefficient is not longer constant, because several other processes are involved as well (maintenance, death); they depend on environmental conditions (growth rates, so food levels). For V1-morphs the relationships between the conversion coefficients at sub- and supra-organismic level are still rather simple; for isomorphs they are more complex. Conversion coefficients at the supra-organismic level are only meaningful at steady state, or as an average over a limit cycle. Populations can show complex asymptotic behaviour, also in DEB contexts, but this only means that thinking in terms of conversion coefficients becomes less useful. Yet, they help to close mass balances at population level.

Quest 9.1.3: What are the constraints on the production of hydrogen such that biomass ratio between the species does not change, and the two species behave as a single one, at least in steady state? The interest in the question is to derive evolutionary constraints on the origin of syntrophy? What is the importance of a constant biomass ratio between species? If it is not constant, there is no evolution?

Answ: The interest of the question of constant biomass ratios is in the evolution of homeostasis and in the critical examination of a basic problem for all models that are not species-specific: We know that symbiogenesis is common; if each of the members follow DEB rules, can the symbiosis follow DEB rules as well? If not, we have found many exceptions to DEB rules on formal grounds already. This problem is meanwhile more completely addressed in Biol Rev, including a detailed discussion on the constraints of parameter values. If the constraints are not fulfilled, the ratio of biomasses of hosts and symbionts depends on environmental conditions in a more complex way. This is not problem for the DEB theory, nor for evolution. It can be a problem of ecosystem analysis, because complex micro-behaviour might result in complex macro-behaviour.

Quest 9.1.3,at {308}: What is a "nitrogen flux to the symbiosis"?

Answ: In the coral case, you can think of the nitrogen from proteins of the shrimps that the polyps are catching. The anorganic nitrogen concentration in oligotrophic waters will be very small.

Quest 9.1.4: Parasitism is explained as evolving from a looser syntrophic relationship. In the end of ch. 8 it is argued that simplification in bacteria (reduction in metabolic plasticity) is expectable since reduced DNA size decreases the duplication period. Question: It is known (I think) that parasitism usually involves the simplification of morphological traits and also metabolic plasticity. This makes sense because the host usually provides a more homeostatic environment as the environment of the wild free parasite. Is there a general trend toward simplification, when the environment becomes more homeostatic? What can explain this in the DEB framework, in the case of eukariotes, since here DNA size is not energetically relevant?

Quest 9.1.4-5: Sections 9.1.4 and 9.1.5 are only descriptive (among others). What is the purpose for the model?

Answ: These sections are a natural continuation of the discussion on all possible trophic interactions among species (sections 9.1.1-4) and their intermediary forms. We have to extend the DEB rules for the metabolic behaviour of individuals with rules for interactions between species in order to model phenomena at the population and ecosystem level. You can see this description as an introduction to the more technical material in the rest of the chapter.

Answ: Although a systematic study still needs to be done, I expect that parasites in hosts will have little storage capacity (low value of [Em]). Many will have adaptations to a micro-aerobic environment, which makes them energetically less efficient, so high values for yXE and yEV. They possibly have to fight host's immune system, which can increase their specific maintenance costs [pM].

Quest 9.2.1: The DEB model predicts what happens in transient states; these steady states aren't the best part. What happens when there are suddenly changes in feeding conditions, changes in biomass composition, or changes of the number of substrates? Can these changes immediately incorporated at the population level? Could these models reproduce extremes conditions? Could these models incorporate limiting conditions? What happens when one species population increases suddenly?

Answ: Since the DEB model covers situations of responses of individuals in changing environments, so it can make predictions for how populations should respond to changes. For this purpose one has to integrate the partial differential equation (9.38) numerically. All these questions can be answered with "yes", but in practice it is quite some work to find appropriate parameter values. This chapter starts simple, and steady state analysis is important to judge and compare the potential of the model with respect to alternatives. Steady states are rare in nature, indeed.

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Chapter 10: Evaluation

Quest 10.3.2: Ren & Ross, 2001, A dynamic energy budget model of the Pacific oyster Crassotrea gigas, Ecol. Modelling 14: 105-120. These authors made a net production model which only has some resemblance to the assimilation model that is discussed in the book. They knew the existence of the assimilation model, so why did they use a net production model?

Answ: Jeffry Ren replied: There are a few reasons for the choice of a net production model, but the most important one is the application of the model. The aim of the model as the authors mentioned is to make it applicable to the oyster farming ecosystems, so that it can be incorporated into an ecosystem model to provide needed information for management of oyster aquaculture. It is therefore NOT a theoretical model. To meet the purpose, the authors tried to limit the number of parameters by adopting the current allocation rule and also other changes e.g. maintenance. Since available information about the animal's physiology is rather limited, the authors found it difficult to derive parameters when follow DEB exactly. Therefore, as discussed in the paper, it is easy way (if not the only way given the available information) to develop functions and parameterisation of feeding and allocation processes.

Bas Kooijman responded: It is true that net production models are more frequently used (at the moment) than assimilation models, which makes it easier to use published parameter values. This can easily be misleading, however, because many different net production models exist, and the models might differ in aspects that affect parameter values. Moreover, net production models have more parameters than assimilation models, and they do not imply useful body-size scaling relationships. These relationships can be used in assimilation models to obtain educated guesses for the parameter values of a species of interest, using known parameter values of other species. There should be no difference between theoretical and practical models. If a model is too complex, it should be simplified for particular applications (if possible of course).

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