Questions & answers 2005

Go to the collection 2001 , 2003 . 2004 . 2007 .

The following questions have been put foreward by the participants of the 2005 course on DEB. The questions were formulated by the participants, after discussions in weekly meetings they also summarized the answers. The questions refer to the given section numbers of the DEB book 2000.

Go to chapters 0 1, 2, 3, 4, 5, 7, 8, 9, 10

Preface 0:

Quest 0: On page XIII, it is stated that DEB theory treats individuals as non linear systems, in contrast with other theory where the individuals are treated in a static sense (i.e. SEB theory, where individuals allocate energy to different compartments in percentage). For me, at the moment, the kappa-rule of the DEB theory appears to follow the same allocation process. What is the differences? What is really dynamic in the DEB theory.

Answ: Chapter 10 discusses the relationship between DEB's and SEB's in some detail. There is little theory behind SEB's; a SEB is basically a list of numbers that apply to an individual at a certain moment and it does not deal with allocation strategies, nor with reserves. It is not possible to access the allocation to growth in SEB, only the energy fixed in new tissue. This same applies for reproduction. All these topics require an analysis of how budgets change in time, and how individuals respond to perturbations in the environment.

Chapter 1: Energetics and models

Quest 1.1.3: If we compare the energy content in comparable structural tissues among species, does this energy content remain constant?

Answ: Not according to DEB theory; all tissues have a structural and a reserve component; this even applies to tissues that are specialized in the reserve function, such as adipose tissue. The abundance of reserve is very sentitive to the nutritional condition of the individual.

Quest 1.2.3: Why are the allometric functions incompatible with the DEB theory? We understood that there is a problem of dimension consistancy. In the case of a comparison between species, if we obtain different values for beta, we won't be able to compare alpha, because of its dimensions. Is it the only reason ?

Answ: The first problem is that allometric functions do not result from assumptions for mechanisms. The fact that they result if the change in a fraction is proportional to that fraction suggests that such assumptions might be formulated in particular cases. The assumptions made in the DEB theory do not give rise to allometric functions, although the numerical behaviour can be very close in praticular applications. See figures 4.3 at {136} and 8.2 at {272} for examples.

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Chapter 2: Basic concepts

Quest 2.1.1: Birds are cited as examples of "demand" system since they can only survive at high food densities, in comparison with "supply" organisms (sea anemones, bivalves...)

But, on page 22, the example of the male penguin (that can lose 40% of its body weight) shows the contrary.

I understand the usefulness of both examples, but their proximity in the text is somewhat "annoying".

Answ: Correct, more explantion would have helped here. Birds are examples of indeterminate growers that loose their capacity to resume growth after they arrived at their final size in a given environment (cf the comments for {293}). As full-growns they do have the capacity to store and cover periods of starvation. The key property of a demand system is the lack of flexability to handle slow growth situations, so starvation, during the juvenile period, in the case of the pinguin.

Quest 2.1.2: On p. 22 it is stated that a volume communicates with its environment over its surface area. Therefore, when feeding is considered in the DEB theory, surface area plays an important role. But the question is: which surface area? In case of a bacterium there might be transport of compounds all over the outer surface of the bacterium, whereas for e.g. a human, the mouth is used for feeding. Is then the surface area of the mouth used or the surface area of the digestive system?

Answ: The surface area that is limiting depends on the feeding rate. If the feeding rate is high, the surface area of the gut is of importance. If it is low, it depends on the food acquisition strategy, which frequently involve active movement in animals. This discussed in more detail in 3.1.2. Frequently several processes are co-limiting; for (strict) isomorphs all the important surface area's are proportional to each other. Bacteria are not isomorphs, but typically mixtures between V0 and V1 morphs (cf 2.2.2).

Quest 2.2.1: At page 25 it is stated that most species are isomorphic, i.e. an individual retains the same shape as it grows in size. According to this paragraph the physiological significance of this is that as a body grows isomorphism results in a constant concentration of substance in the body (given that an organ secretes at a rate proportional to its volume). However this implicitly assumes that organs grow at the same rate as the body.

Answ: In a one-structure system for an isomorph the assumption is indeed that all organs grow in proportion to the whole body. There is no need that secretion by an organ is proportional to its volume. Chapter 4 discusses that nitrogen wast is a weighted sum of a squared and a cubed length, while the kiney is primarily responsible for this excretion in animals. Subsection 5.3.1 presents some thoughts on the relationship between organ size and function, while section 5.3 discusses extensions to more structures (including organs). Presently we work on further elaborations along these lines.

Quest 2.2: From the DEB theory to field observations and applications: how to measure in practise the surface area? In other words, does the surface area refer to the structural body volume volume (i.e. V2/3)? If yes, should the structural body volume be estimated through the equation: V=(dm * L)3, where dm is the shape coefficient?

Answ: The contribution of reserve to length measures is frequently limited. Reserve contributes much more to weight, for instance. Several proportionality factors combine into a single one, and comparison of species can be used to take them apart. The feeding rate of an isomorphic bivalve is proportional to the squared length of its shell. If we compare related species with a very different morphology, we will find very different values for the proportinality factors, while they have a very similar metabolism. The comparison of the species can be used to disentagle the contributions of the different compontents that contribute to the values of the proportionality factors.

Quest 2.2: This is related to the discussion on feeding versus surface area, and to fractal dimensions. On what scale do we measure surface area in organisms? Organisms are not perfectly smooth. If one were to take the intestines, which to a certain extent (and probably with a certain amount of imagination) is fractally convoluted, then with increasing "accuracy" of measurement (i.e. at smaller scales) one would get an increasing estimate of surface area as one adds surface area contributed by villi, then by microvilli, etc. What is the natural scale of measurement then?

Answ: Microvilli show remarkable dynamics, even in a single individual. Some measures are easier to interpret than others, and the scatter also differs a lot. DEB theory aims to capture the board features first, and deals with "details" as modifications on the common basic stucture. Despite this simple approach the theory has a big appetite for data, because of the interaction of variables that we will consider, and nutritional details.

Quest 2.2: This is also related to the discussion on feeding versus surface area. If we look at the "surface area" of organisms: what do we include: earlier discussion focussed on the intestines as the surface area of a human being, but shouldn't we include kidneys and lungs as well? While the acquisition of nutrients is important, homeostasis is also dependent on the excretion of waste products, and therefore the surface area should also include estimates for these.

Answ: The strategy in chapter 3 is to assume first that food is the only limitation, while the nutritional value per food item is constant. This situation is too simple for some applications. Chapter 4 deals with the implications of the assumptions on food acquisition and use for mass fluxes (incuding the generation of nitrogen waste, and the consumption of dioxygen). Chapter 5 then considers co-limitations by independent or partionally dependent inputs (such as food and dioxygen). Chapter 6 finally discusses how the processes are modified by non-essential compounds. You can think of toxicants, but also of natural waste products (such as nitrogen waste) that are not excreted sufficiently fast. The approach to introduce the players of the game one by one is followed for didactical purposes.

Quest 2.2: What is the length of a bivalve? Do we measure it with or without the shell? Is it the shell length or the soft tissue length or no matter what?! How do we measure the structural volume?, with or without the shell, with or without the gonade, with or without the "reserves organs" ? or no matter!

Answ: This question has no general aswers, else than the thighter the link between the measured variables and the players in the DEB game, the better. The possibility to make the full mass and energy balance would be most ideal (but practice is frequently less ideal). Since parameter values are individual-specific, non desctructive measurements are preferable. There is also as trade-off between relevance of measurements and costs, and this affects the number of measurments that can be taken. The length of shells of bivalves will be a nice quantifier for the size of the structure in many situations, but not during starvation (and recovery from starvation), when the structure is likely to shrink. It has no direct information on reserve, although the change in length has indirect information on reserve. This is why researchers who make the choices should have knowlegde about theory on metabolic organisation.

Quest 2.3.1: At p30 it is stated that "DEB theory assumes no maintenance for energy reserves". I have no precise idea about that, but it seems strange to me to assume that energy reserves, which is living material, does not use energy for maitenance. I think that the exemple of the egg shows that reserves CAN use practically no oxygen, but is it the same when energy reserves are part of an individual?

Answ: Yolk is part of the embryo, and DEB theory assumes that yolk is reserve. So far the quantitative aspects of development support this simple idea. It remains to be demonstrated that the parameter values for the embryo and the juvenile are the same; it this moment there is no firm evidence on the contrary. Without somatic maintenance there would have been no turnover of structure. Reserve has an implied turnover, because they are synthesized from food (or substrate) and used for metabolic purposes (maturity and somatic maintenance, growth, maturation or reproduction).

Quest 2.3.1: How is it possible to have the same reserves composition (strong homeostasis assumption) when the food composition changes (seasonal change for instance)? The relative abundance of the different compounds do not change in some way ?

Answ: Changes in the chemical composition of food translate into changes in the conversion efficiency from food to reserve in a one-reserve system. The metabolism of animals seems to be well-captured by this simple system. Chapter 5 discusses more-reserve systems, which are needed for bacteria, plants and some protoctists.

Quest 2.3.5: At the end of page 36, it is written that for many pratical purposes, entropy (E = TS) can be set to zero. What are these practical purposes ?

Do you mean that for nearly all living organisms, enthalpies (H, obtained with calorimeter) can be substituted for free energie G? [Since G = H - delta TS].

Answ: The practical purpose is the compose an energy balance for an individual and a population, such as a microbial population living in a chemostat. See further the comments for {35}.

Quest 2.6: On p. 57 it is stated that many extinctions (in geological time) are thought to be related to changes in temperature. For homeothermic animals like mammals I would think that direct physiological limitations do not play a major role, except at very high latitudes or during some very extreme geological events. Perhaps food availability (indirectly controlled by temperature, but more still by the water balance?) itself can be regarded as the major threatening factor for mammal species?

Answ: Correct, these indirect effects are meant to be included in the remark. The heating costs for endotherms might also be of importance in some cases.

Quest 2.7: Asexually propagating unicellular organisms are classified as juveniles because they "... take food from their environment though they do not reproduce in a way comparable to the production of eggs or young by most multicellular organisms."

However, when unicellular organisms propagate they have invested in the production of a new independent individual and when multicellular juveniles grow they are "investing" only on themselves.

For this reason, shouldn't unicellular organisms be considered as adults?

Answ: Adults produce eggs that differ in composition from themselves; the reserve of embryo covers its developmental costs during the embryo stage. As a result the embryo changes in composition during that period. When a unicellular divides into daughter cells, the composition of these cells are the same as that of the mother. There is no embryo-stage, because they take up substrate imediately after division of the mother cell.

Quest 2.7 "The puberty is taken to be infinitesimally short" . I'm not sure what does that means.

Answ: Human parents with childern in their puberty will probably think that puberty lasts quite a long time. Behavioural changes reflect considerable changes in physiology. We here focus on one particular physiological change, namely the switch for increasing the state of maturity to investment in reproduction. We further idealize the real world by assuming that this switch is not gradual and lasts a time period, but abrupt.

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Chapter 3: Energy acquisition and use

Quest 3.0: In the previous chapter {60}, a juvenile is defined as a stage in which food is taken but resources are not yet allocated to the reproductive process. At {66}, we read "energy spent on increasing the degree of maturity in juveniles". For me, there is an inconsistency: If juveniles increase their degree of maturity, it would mean, for me, that they're allocating energy to the reproductive process.

Answ: Increasing the state of maturity is much wider than "preparing the gonads for production". It concerns tissue differentiation in general, and installing regulation systems. Some of them have nothing to do with the reproduction process. The immune system, for example, is activated after birth; this also applies to the control of body temperature in endotherms (mainly mammals and birds). The energy allocated to the activity of the immune system and to heating the body is part of somatic maintenance, but the installation of the regulation systems necessary for their proper functionning is part of the maturation process.

Quest 3.1: On {66} it is stated that for some species it is sensible to express food avaibility per surface area or per volume. I don't understand what does this means exactly. Why are cows surface feeders? It's right to consider insectivorous bats as volume feeders?

Answ: Although phrased unscientifically, it would help to ask a cow how much food she has available. The cow would look in the meadow around her and will answer x kg grass per hectare (so per surface area). Grass can be present in a large number of short shoots, or less longer shoots, and within certain ranges this has little effect on the feeding rate. It depends on the behaviour of the bat as well as the insects to what extend the bat is a surface or a volume feeder, or a mixture between the two. Notice that the feeding rate is taken to be proportional to the surface area of the individual in all cases (for surface as well as volume feeders); being surface or volume feeders relates to how food densities should be quantified.

Quest 3.1.1: It is well-known that bivalves are able to produce pseudo feces according to food quantity/quality. Pseudo-feces are particles that are caught on the gill, but not ingested (rejected before ingestion). How does DEB theory deal with this phenomenon? Does this resemble to a squirrel feeding on nuts, but rejecting the shells?

Answ: The particles that constitute pseudo feces are probably selected to be rejected and have little nutritional value for the bivalve. Being of a different type than the food particles, the dynamics of those particles has probably little connection with the particles that actually enter the gut. This resembles the situation in appendicularians (pictures at {117, 188}), which keep out bigger particles with wide mesh in their slime-house, and feed on small particles catched on a fine mesh inside their house. The big particles tend to stick to the wide mesh and block it, which makes it necessary for the inhabitant of the house to leave it and build a new one each two hours. The rejected particles have little contribution to the energetics of the organism. The nut shells that are rejected by the squirrel differ in the sense that their amount is linked to the nuts that are eaten, so their quantitative behaviour resembles real faeces, rather than speudo-faeces. The difference is in the dynamics of the particles that do or do not enter the gut.

Quest 3.1.1: Most measurement methods for the feeding rate make use of changes in food densities so that the feeding rate changes during measurement {70}. There is "an advanced technique that circumvents this problem". Is it an experimental or a calculative method?

Answ: The book points to a paper that describes a technique where coloured raisin particles are added as a tracer, that can be counted acurately after ingestion in the resuspended feces. The resin particles mimic the physics of food particles but cannot be digested.

Quest 3.1.1: At {71} it is stated that "energy costs of transport are proportionnal to surface area". This can easily be understood for aquatic organisms that often have a density close to that of water. In this case, the cost of transport sould be linked to viscosity and surface area. But for terrestrial organisms the costs of transport should be directly linked to weight.

Answ: Not according to Fedak & Seeherman (see {73} line 10). The problem in practical applications is that minor components of the budget can easily become very complex. A big elephant can reach higher than a small one and partly feeds on different resources (high branches of trees); this might or might not compensate differences in allocation to activity. Social interactions contribute to the complexity of the problem. The basic DEB model allocates energy to movement proportional to volume of structure (because it is part of somatic maintenance); an extension to an (additional) allocation to structure's surface area would not increase the complexity of the model (because it already deals with heating and osmotic work that links these somatic maintenance costs to surface area's). So far I have not seen data that show convincingly that the deviations from this energy allocation to movement are important enough to be included in the core-theory.

Quest 3.1.1: What is exactly the cruising rate?

Answ: This is the "typical" mean rate of movement over longer distances.

Quest 3.1.2: I very much doubt the assumption that only distance plays a role and not speed, {73}. The energy per distance is likely to increase with speed. Air resistance plays a part, even in running. I think that this assumption (energy expenditure proportional to distance not speed) applies only to small/ and or slow movers. How do speed, distance and animal size co-vary?

Answ: Resistance becomes important at high speed, but the time moving that fast is typically short, so its significance for the overall budget is little. Energy investment into movement in general is typically a minor component of the somatic maintenance costs, which motivated the strategy to keep this module extremely simple. Too simple for particular applications, for instance to understand foraging strategies in the context of behavioural ecology. For these applications we need much more detail in the behavioural module (and also include items as sleeping, territorial behaviour, courtship, agression, migration, etc). We are working on a much more detailed behaviour module, see e.g. Lika & Papandroulakis (2004) Can J Fish Aq Sci 99: 1-11, and papers in prep. The strategy of the DEB theory is to construct a framework that applies to all organisms (bacteria, protoctists, plants, animals) that is as simple as possible, and insert more detailed modules for particular applications. Not all modules are of equal relevance to all applications. The DEB book is about the simple core-framework only. You will see that dispite efforts to keep the framework as simple as possible, the result needs a substantial amount of data to estimate the parameters and test the realism of the predictions. All extensions come with a price in terms of extra parameters and variables. It is relatively simple to make a complex model, but complex to make a simple model that still has the essence of the problem.

Quest 3.1.2: At {72} it is said that costs of locomotion are only 2-15% of the field metabolic rate, which does not make the introduction of many parameters worthwhile. Does the 2-15% also include (common) stress situations such as the cold winter with very low food densities? Should locomotion costs more explicitly be modelled in such a case?

Answ: Many organisms have species-specific survival strategies to cope with meagre seasons. Apart from stress response, we have turpor (e.g. hibernation in winter in temporate climate zones, or other forms of metabolic arrest during dry seasons (sub)tropical zones) and migration. These situations are discussed in chapter 7 and require special attention in applications.

Quest 3.1.2: Feeding costs can be accommodated in two ways within the DEB theory. The first way is when they are proportional to feeding rate. This paragraph's last sentence says that this type of costs can only be accommodated without complicating the model structure if it cancels against digestion efficiency caused by increased gut residence time. Does this mean that gut residence time increases to increase digestion efficiency in order to compensate for any feeding costs increase due to food shortage? So whenever there's a lack of food gut residence time increases, is this right?

Answ: For some species low feeding rate goes with high activity levels for searching food (e.g. think of filtering, which is maximal at zero food density). If organisms keep their gut filled, this also goes with long gut residence times, see figure 3.9 at {82}. This is a a consequence of a simple model for mass transport in guts. Theory to link digestion efficiency to gut residence time is discussed in section 7.3 at {239}.

Quest 3.3: In the last sentences of paragraph on {82} a comparsion is made between bacteria under aerobic and anaerobic conditions. The sections ends with: "This means that the parameter {pAm}, and not {Jxm} is directly relevant to the internal machinery". I am not sure if I really understand this... Does this mean that {pAm} is different under both conditions?

Answ: It is the opposite, the values for {Jxm} differ, while those for {pAm} are much more similar because dioxygen affects primarily the transformation efficiency from substrate into metabolic energy. Under anaerobic situation many organic substrates are converted to compounds such as acetates and ethanol, which are excreted in the environment. These compounds can used as energy sources under aerobic conditions.

Quest 3.4: In the current formulation of the reserve dynamics, the catabolic flux must `compensate' for dilution by growth (see eq. (3.12)). In my opinion, Occam's razor dictates that a formulation of the reserve dynamics without the compensation for growth would be preferrable. My suggestion for an alternative catabolic flux is: pC = v V2/3 [E]/ ([EK] + [E]) where [EK] is a constant.

Answ: Occam's razor is subtle in practice. The book is full of examples of simple assumptions with complex consequences. This proposal might seem simple, but has complex implications at other points. First of all it has one parameter more than the DEB formulation; in that respect it is more complex. It resembles Michaelis-Menten kinetics, but this does not mean that the mechanism is simple, given the fact that reserves are polymers (proteins, carbohydrates, lipids) that must be monomerized before they can play an active role in metabolism. What controls the monomerization process? This refers to the use of the word reserve density rather than reserve concentration in the DEB book; the difference is in spatial micro-structure. It is not obvious at all why MM-kinetics should apply in these complex situations, that involves a very large number of different compounds. Even more troublesome is the observation that this catabolic flux implies that the reserve density dynamics amounts to d/dt [E] = [pA] - [pC] - r [E] where r = d/dt ln V is the specific growth rate. In other words, the reserve density keeps changing as long the individual is growing, so this kinetics gives up weak homeostasis. It will be very hard, if not impossible, to access the chemical composition of reserve and structure in that case. This complicates practical applications considerably (including the application of mass and energy balances). For the DEB kinetics, this is discussed at {150}. Furthermore it is not partitionable. This makes it difficult to understand, for instance, how the number of reserves can be reduced in a smooth way during evolution, and how symbioses between two species can follow the same overall kinetics (all eukaryotes are in fact symbioses). Furthermore (a relative minor point), this catabolic flux has a maximum, v V2/3, so the maximum assimilation rate must be less to avoid an uncontrolled accumulation of reserve. This give involves a more complex cross-linking of different processes.

Quest 3.4: While from a modeling standpoint the issue of partitionable reserves and the working with generalised compounds makes sense, I'm not sure if I buy into the argument that model structure would be drastically affected in multi-compound models when a new compound is identified. Even in multi-compound models one is still able to make modeling decisions based on the relevance of such compounds to the processes at hand. In short if this hypothetical new compound is so important for the processes then perhaps it is not such a bad idea to change model structure.

Answ: My observation was not meant to be much more than to mention that some model structures are more sensitive to such new discoveries than others, and need less rebuilding. I only see this as happy coincidence, because model stucture should be motivated by mechanisms in the first place. We studied symbiontic relationships in more detail since the publication of the book, and I now think that the primary importance of partionability relates to consistency with the evolutionary history, i.e. to understand how two organisms that follow the DEB rules can merge symbiontically to a single new organism that again follows the DEB rules. If not, the DEB model would be species-specific; this merging happened many times in evolution.

Quest 3.5: I was wondering if reproduction was responsible for a decrease of the growth rate. If this is the case, how does DEB theory model this?

Answ: DEB theory states that the reproduction rate does not compete directly with growth. Growth is competing with somatic maintenance; reproduction is competing with maturity maintenance. Both types of maintenance have priority. An increase in the fraction kappa would increase growth (for a while), and reduce reproduction. In that sense growth and reproduction are competing indirectly. The motivation does not only come from the details of how rates change in time, but also from qualitative observations, when one can compare males and females, and situations of propagation by fission, or by reproduction (some sea cucumbers can follow both strageties and have an asymptotic size). For most applications the fraction kappa can taken to be constant. Section 7.1 discusses situations where it can (and does) change. It can also be changed by parasites and toxicants (endocrine disrupters).

Quest 3:5 I wonder if you could use parasites or toxic compounds as a tool to study energy allocation by changing the value of kappa, and how this affects reproduction and growth.

Answ: Indeed, I think that this is a very powerful method to analyse metabolic organisation. This is one of the reasons why effects of toxicants gets so much attention in the book. Detailed studies of how parasites affect hosts in a DEB context have been done at the Vrije Universitieit Amsterdam (de Jong-Brink & ter Maat using Schistosoma with pond snails as hosts), but further studies would be most welcome.

Quest 3.5: At {87} it is stated that "The only information the cells have is the energy content of the blood and the body size". It is hard for me to believe that for two reasons. The first one is that in most of ectotherms the cells experience the external temperature, so it's an information cells have. In bivalves, by instance, temperature is assumed to be one of the major factors controlling energy allocation to reproduction process. A second reason is that cells have a lot of other information via hormonal processes. I would be very shocked that DEB theory neglects such processes.

Answ: Correct, the reasoning is too short to be clear. What is missing is an intro like: Suppose that we build a model, with two state variables only (reserve and structure). What options do we have to model allocation if we delineate a compartment "blood" that receives mobilized reserves and fuels somatic and reproductive cells? Temperature affects all rates in DEB theory, as decribed in section 2.6 at {53}, including reproduction. Resources that are allocated to reproduction are first stored in a buffer (see 3.9.1 at {114}), and the buffer emptying rules might involve temperature. The observation that spawning depends on temperature does not mean that allocation depends on temperature. Figure 1.1 illustrates that very similar growth curves can occur in organisms with very different hormonal control systems. This makes one wonder to what extend the understanding of the details for hormonal control systems is required to capture phenemena such as growth, reproduction etc. DEB theory treats hormones as part of the machinery organisms use to fine-tune the rates of different processes. A cell would run into problems when the anabolic machinery is working at a different rate than the catabolic one; DEB theory has several couples of anabolic and catabolic transformations. It shows what needs to be regulated, but not how.

Quest 3.6.1: On {91}, it is written: "Sustained voluntary powered movement seems to be restricted to humans and even this seems of little help in getting rid of weight". I lose weight during wind surfing: Is it because of sustained movement or because of heating costs (because of cold water and weather)?

Answ: Movement costs relative little energy if not pushed into the extreme; heating is much more expensive. An active life style can have a stimulatory effect on metabolism, compared to a sedentary life-style. This is more than just compensate the energy costs.

Quest 3.6.1: Is the production of leaves (of trees) included in maintenance? Why is it not included in growth?

Answ: Leaves typically lasts 1 year, also in evergreen plants and plants in the tropics where they do not synchronize the shedding of leaves. Plants continue to replace leaves even if the plant as a whole does not grow any longer. This shows that leave production is not linked to growth.

Quest 3.6.1: I cannot put up with the thought that moults in crustaceans belong to maintenance and do not depend on feeding rate...And for bivalves, I supposed that shell and mucous belong also to maintenance?

Answ: Daphnids continue to moult during starvation and also if they are fully grown. Their moulting rate is independent of the feeding rate. This shows that their moult production is linked to maintenance. Copepods have a fixed number of moults, and they reproduce in their final moult only. This shows that their moult production is linked to growth, and also that moult production in crustaceans can be reorganized from an evolutionary perspective. I assume that shells in fully grown bivalves don't become thicker, which links their shell production to growth. Fully grown bivalves probably continue to produce mucous, which reveals that mucous production is linked to assimilation and/or maintenance. This depends on how mucous production varies with the feeding rate.

Quest 3.7: On {94}, it is stated that endotherms cannot reach the theoretical maximum volume (or length) because of heating cost. If the global mean temperature increases (climate change), heating cost will decrease, and consequently will the maximum size or volume of endotherms increase?

Answ: Correct, but many other things will change as well. Larger body size means higher food intake, so a depletion of food, and lower ultimate body sizes.

Quest 3.7: An indication in the book, p.{96}, last section before 3.7.1: in animals that have non-permanent exoskeletons (like crustaceans), we usely observe a rapid increase in size (not in structural body volume) during the short time between two moults. This increase relates to the uptake of water (or air for some insects). Then we can consider that the last moult won't mark the end of the growth, even if it will happen in a no-long time. So inside so last carapace, the spider crab keep a volume free for the production of gametes, and perhaps for last new structural biovolume.

I enjoy free-diving, in particular to pick up from the sea some crustaceans or molluscs. And it's well know that most of crustaceans are not good to pick up during the spawning season (summer) because "they are full of water", but "they are full of good flesh" in spring, when they come back to the costs for their reproduction. And it seems to us that the bigger (oldest) crustaceans have a very thick and heavy carapace and are more full of flesh: it's like they become more dense! Does the DEB theory give a bound to the increase of the flesh density inside the carapace?

Answ: Not directly, but indirectly via the feeding rate, and how it depends on flesh content (and possibly carapace size).

Quest 3.7.1: Are there any species for which the post-embryonic energy conductance is different from the embryonic energy conductance? And if so, do these species undergo any peculiar changes in energetics at the molecular level that could explain such a change in energy conductance?

Answ: Sad enough, I do not know of data that can be used to judge wether of not the energy conductances of embryos and juvenile are the same in one species, or even better in one individual.

Quest 3.8: As an example of the relationship between Vp and food density, figure 3.21 is given. Here the volume at first appearance of eggs "appears to be fixed". This is perhaps the case if we only look at the last few points (higher ages) on the graph, but depending on what points you take into consideration, you could infer a number of different relationships. So is there any other evidence for this? Is there perhaps a different (more apt) illustration of this phenomenon?

Answ: The need for more detail of particular model components repends on the aim of the model, but also on the reproducibility of observed patterns. Apart from the high lengths at day 6 (for which the legends present an explanation), the range in length is about 0.3 mm only. Remember that the moment of egg deposition in the brood pouch is (well) after the start of the allocation to reproduction.

Quest 3.8: On {111} it is stated that development costs are proportional to the (somatic) growth rate (eq (3.45), so once an individual is fully grown, it has also fully developed its maturity. Isn't this in contradiction with the fact that some species only reproduce well after they stopped growing? Or do these species voluntarily abstain from sex until they have invested enough energy in the maintenance of their maturity?

Answ: See comments for {111}

Quest 3.8: Is the volume of juvenile/adult transition (Vp) a defined parameter for each species? Or it is usually (but not always) associated with a certain level of accumulated energy, being this the value defined for each species? It's more correct to consider a threshold of accumulated energy or a size threshold?

I take a concrete example. In our experimental studies (in controlled conditions), we can produce mature young oysters in very low food conditions, i.e. animals with low reserves. By dissection and in histology (5 mum thin sections), we can confirm that oysters start to mature without almost any reserve. So that means young animals can invest in reproduction, so can become adults in limiting food conditions that don't allow them to make any reserve (or a very little). It appears to us that oysters try to invest the little energy they manage to pick up from their environment "directly" to reproduction. It's just an illusion because of the no-growth we observe. In DEB terms, the kappa energy allocation is just enough for maintenance. And so, in this case, oysters prefer to invest in their reproduction than in their growth. For conclusion, oysters (and perhaps the main part of bivalves), seem to become adult at a threshold size, and not for an threshold of accumulated energy (neither at a given age).

Answ: Parameter values at taken to be specific for an individual. The variation of parameter values between individuals of the same species under identical circumstances (food, temperature) vary little relative to the between-species variation. The DEB theory assumes that a stage transition occurs when a threshold is reached for the accumulated investment into maturation (see assumption 4 at {121}). This occurs at a fixed structural volume if the specific maturity maitenance costs has a special value, for which there is no theoretical explanation.

Reserve cannot be seen through a microscope; only indirectly via growth-dependent changes in body composition. That fact that oysters grow to substantial size means that they do allocate to somatic growth.

Quest 3.8: What's in fact the maturity maintenance? It's "just" the maintenance of regulating mechanisms and concentration gradients?

Why doesn't it belong to the somatic maintenance? It's just because, after adult age somatic maintenance costs still increase with size and maturity maintenance costs don't (because they're related to a certain level of maturity which, after adult age, is independent of size)?

Why the maturity maintenance does not increase with the size of gonads?

Answ: Reserve does not require maintenance in DEB theory, which also applies to the buffer of reserve that is already allocated to maintenance. The size of the gonad probably reflect (part of) this allocated reserve. Maturity maintenance includes much more than gonads only (see other questions)

Quest 3.8: I thought the concept of maturity maintenance was quite clear for me, but I don't understand the two examples (daphnids and pond snails) given to support the existence of maturity maintenance.

Answ: The example with the daphnids shows that allocation to development (maturation plus maturity maintenance) must exist, because a substantial allocation to reproduction at length 2.5 mm is not accompanied by a reduction in growth, or an increase in ingestion or respiration. The example with the poind snail shows that maturity maintenance must exist, because a change in the partition fraction kappa (via a change in light/dark cycle) resulted in the predicted change in size at the onset of reproduction.

Quest 3.8: I don't understand the sentence "If maturity maintenance did not exist, animals kept at the lower food density would never reproduce, while those at a slightly higher food density would invest at a rate (..)".

Answ: We here compare two food levels that result in ultimate sizes just below and above the size at reproduction Vp. The calculated rate is rather large, while the observed reproduction rate is close to zero.

Quest 3.8: Why is maturity maintenance included?


Quest 3.8: How does DEB theory take into account the cost for metamorphosis, when larvae (juvenile) change their body to acquire the adult form?

Answ: The costs for new tissues are quantified in [EG], which might differ in the different life stages if the morphologies differ. In holometabolic insects, the larval (juvenile) structure is decomposed and used as reserve to synthesize the adult tissues, see section 7.8; the pupa development has many similarities with the embryonic development.

Quest 3.8: An adult pays less maintenance (somatic plus maturity) than a juvenile per unit of structural volumeI. Does this make the juvenile more vulnerable than adults in a `bad' environment (low food, high temperature)?

Answ: Intuition can easily be wrong in questions like these. Suppose the juvenile has length Lj, and the adult La, and they both eat just enough to cover their maintenance costs, so fj {pAm} Lj2 = [pM] Lj3 + [pJ] Lj3, and fa {pAm} La2 = [pM] La3 + [pJ] Lp3. The question can then be reformulated in: does fj > fa apply for all possible choices for Lj and La such that Lj < Lp < La? Let us first consider the situation fj = fa. Writing c = (1 + [pM]/[pJ])-1, we have La2 Lj = La3 (1 - c) + c Lp3. This curve in the (Lj, La)-plane separates (Lj, La)-combinations in which the juvenile is better off from that in which the adult is better off. For c = 0, we have that the juvenile is always better off. Another problem is how well the juvenile can handle no-growth situations. This depends where the species is in the supply-demand spectrum.

Quest 3.8: At {111} it is stated that for daphnids Vp is independent of food density. Does DEB theory assume that Vp is independent of food density? In the manila clam the size where reproduction begins (first gemetogenesis) is generally assume to be 20 mm, but I observed mature gonads on 15 mm individuals which were grown in good environmental conditions (temperature and food). So I think that Vp is not a fixed specific constant...

Answ: If size at the start of allocation to reproduction is not constant, this is evidence that specific maturity maintenance [pJ] deviates from [pM](1 - \kappa)/\kappa. The reasoning can then be reversed and this size-dependence can be used to arrive at estimates for the correct value.

Quest 3.9: At the end of {115}, it is written that 'the bit of energy that was not sufficient to build the last egg .../... still remains in the buffer'. In some cases, we can also suppose that eggs cannot be spawned during the reproductive season (for several reasons). In that case, what would be their future in the DEB machinery ?

Answ: The most simple buffer handling rule for reserves that have been allocated to reproduction is that left-overs from a previous spawning event remain in the buffer. I am not aware of data to be able to test the realism.

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Chapter 4: Uptake and use of essential compounds

Quest 4.1: I found the notation confusing, where e.g. C can mean the element carbon as well as the compound carbon dioxide.

Answ: I understand this, but symbols with the full CO2 as index become not easy to read in more complex formulas. The book works with elemental balances (not compound balances) and fluxes of compounds (not fluxes of elements). The context defines the meaning. If there would be enough characters, with each compound having its own character, you need a very good memory (or extensive cross-referencing to the symbol table) to read the formulas.

Quest 4.2: Last paragraph on {129}. "Reserves and reserves in the reproduction buffer are added together", so (E+Er). Assumptions in Table 3.3 imply that the sum of both fluxes is a weighted sum of the three basic powers(?) but this does not necessarily hold for each of them.

What fluxes are we talking about? In this paragraph we haven't referred to fluxes, could it be E flux and Er flux? When it's said that this does not hold for each of them, what is each referring to? To the both fluxes or to the three powers?

Answ: The flux JE = d/dt ME is the increase in reserve and flux JEr = d/dt MEr is the increase in the reserve buffer for reproduction. Only the sum of these two fluxes is a weighted sum of the three basic fluxes (assimilation, dissipation and growth), and not each of them. This can be seen by just adding the expressions for the two fluxes as they are given.

Quest 4.3: After an attentive reading of the chapter 4 (first half), I still don't understand why the reproduction power pR is not included in the three groups of basics powers {129}, just pG for instance? Since pR is not included in the basics powers, then the oxygen flux {135} is, by construction, not related to pR. In the case of bivalves (again) and some other marine invertebrates, does it mean that the respiration rate of their gonads (sometimes more than half of the total body weight) would be nil?

Answ: A power is a basic power if all mass fluxes (we delineated four organic and four mineral compounds) and dissipating heat can be written are weighted sums of these powers. We are looking for the smallest set of basic powers with this property (`basic' does not mean `important'). It turns out the basic DEB structure has three basic powers (assimilation, dissipation and growth). From a chemical perspective, reproduction represents a flux of reserve because embryos start as reserve, with hardly any structure. On top of that the individual can change its reserve. For monitoring changes in the amounts of compounds, we have to look at the sum of these two reserve fluxes. The overhead costs of reproduction are included in the dissipation power. Reproduction does contribute to the use of dioxygen; DEB theory allows to quantify its contribution to the total flux of dioxygen.

Quest 4.3: I thought that the reduction degree of O2 was 0 (and not (-4) but I agree that the reduction degree of O in H20 is (-2) and (+1) for H), see {131}.

Answ: You can find more on reduction degrees in: R. J. P. Williams, J. R. R. Frausto Da Silva (1996) "The Natural Selection of the Chemical Elements: The Environment and Life's Chemistry" Clarendon Pr.

Quest 4.3.2: The maximum molar reserve density is defined as mEm = [MEm]/ [MV] = MEm/ MV (see {122} and {411}), but should it not be defined as mEm = MEm/ MVm?

Answ: The notation might be confusing here, because it does not make explicit what changes in time, and what remains constant. Suppose we look as an individual that has been exposed to high food levels for a long time. It has structural mass MV and reserve mass MEm (because ME is at its maximum value), which both increase in time towards some asymptote. The asymptotic structure got a special symbol, namely MVm, but there is no special symbol for the asymptotic reserve; it is still indicated by MEm, but now for an individual of structural mass MVm. An individual of structural mass MV has structural volume V. If we focus on volume-specific masses, then we notice that [MV] = MV/ V and [MEm] = MEm/ V are constants, and so is mEm. This constant also applies to a fully grown individual with structural mass MEm and structural volume Vm, so mEm = MEm/ MVm = [MEm]/ [MVm] is also correct as long as we realize that [MVm] = [MV] only for V = Vm, because MEm, MV and V co-vary in time. The confusion is that MEm changes in time as long as the individual is growing, while MVm is a constant. The background behind this notational choice is that food conditions vary in practice, so ME varies for a individual of any given structural mass MV, which changes orders of magnitude slower.

Quest 4.4.1: On {138} it is written : 'the respiration rate is THEN proportional to pC if the contribution via assimilation is excluded'. I have difficulties to follow and understand the reasons that lead to this conclusion? Is this conclusion valid from embryos to adults?

Answ: Animal physiologists (as opposed to microbiologists) frequently assume that RQ is constant. The section evaluates what this means in terms of constraints on the composition of reserve relative to structure. If the RQ is constant indeed, the dioxygen consumption (excluding assimilation) is proportional to the catabolic flux (i.e. the reserve mobilization flux), which has been my motivation to call the reserve mobilization flux the catabolic flux, because around 1940 the literature typically interpreted respiration this way (wrongly I think in DEB context). The value of this section is that if biomass composition depends on the growth rate in ways that are inconsistent with the constraint, the RQ cannot be constant. Assuming that it is constant then gives inconsistencies. DEB theory allows that RQ varies, and that it can vary is well known in microbiology.

Quest 4.4.1: The table concerning lipids, carbohydrates and proteins gives energetic value for each compound. I used approx. the same value for carboh. and lipids (Brody coeff.), but the value I used for proteins is higher that the value in your table. Is there a problem with the conversion factor given by Brody? The value you give is the gibbs free energy of the compound?

Answ: It is the gibbs free energy, but it varies considerably among species. There are many different proteins.

Quest 4.4.3: It is stated at {143} that endotherms could possess possible additional mechanisms to get rid of free radicals. Which kind of mechanisms could that be, and how could these depend on size? Perhaps the suggestion that larger (endothermic) species are more vulnerable in evolutionary terms ({145}) does not hold because of these additional mechanisms?

Answ: All organisms have free radical protection mechanisms, one of them being specialized proteins that capture free radicals (superoxide dismutases). These proteins differ between species and their affinity for free radicals is very much species-specific. The argument in the book is that by elimination of the effects of free radicals, the genetic diversity in the gonads is reduced and so the adaptation rate of ecophysiological properties across generations in an evolutionary time frame where envorimental conditions change.

Quest 4.6: I'm not familiar with the Monod and Marr-Pirt models. Is it possible to describe these models in few words ?

Answ: The paragraph points to {315} where it is explained that the Monod model results from the DEB model for V1-morphs, if the amount of reserves and the maintenance costs reduce to zero. The reserves can be reduced by increasing the reserve turnover rate kE, and the maintenance is reduced to zero by [pM] = 0. The Marr-Pirt model is like Monod's model, but it has maintenance paid from structure, rather than reserve. As long as growth is not negative, this model results from the DEB model for V1-morphs, if the amount of reserves is set to zero. If substrate availability is not enough to support growth, the specifications differ, as discussed in 10.3.2 where assimilation models are compared to net production models.

Quest 4.6: On {147} it is stated: "If product formation is independent of one or more energy fluxes, mass balance equations dictate that more than one product must be made under anaerobic conditions..." Why is this?

Answ: This is to create enough degrees of freedom to close the mass balance for all elements simultaneously. For aerobic situations, the flux of dioxygen follows from the 4 organic fluxes as shown. Given anearobic conditions, we know that the three weight coefficients (that link dioxygen flux to the three basic powers) must all be equal to zero, which gives 3 constraints. These three constraints fully determine how some product is linked to the three basic powers. If we know that one (or more) of these three weight coefficients is zero, there must be another product.

Quest 4.7: On {149} it is mentioned that the fermentation process in figure 4.8 is described with only 17/ 11 = 1.5 parameters per curve. I can indeed count 11 curves, but what are the 17 parameters?

Answ: The legends for Fig 4.8 show 21 parameters. We have, however, 3 constraints for the weight coefficients of dioxygen (because of anaerobic conditions) and one for the maximum throughput rate. This latter can be written as a function of parameters, for which we have a value. This reduces the number of free parameters with 4.

Quest 4.8: In those very bad commercials you see once in while, they advertise with losing weight using a "sauna belt". This is a heat producing belt that stretches over your complete belly and makes you sweat heavily. I can only imagine you lose weight very temporarely, because you lose water. Or might there be another reason for the weight loss, i.e. is transpiration associated with a significant energy investment (activating sweat glands etc.)? Or is the metabolism increased (in the sauna I sometimes encounter that my heart rate goes up!)?

Answ: If it is true that you lose weight in the form of reserve in this way, I would have no explanation. The reverse, namely by cooling the body so that it starts heating to achieve a constant core temperature is more easy to understand.

Quest 4.8: At {151} it is said that water emission via urine is incorporated in the composition of nitrogenous waste. This means that at very low concentrations of nitrogenous waste in urine, the composition of the nitrogenous waste would almost be equal to the compostion of water.

What I would like to know is: Are low concentrations of nitrogenous waste (e.g. urea) common? (I suppose that also depends on water intake and water loss via respiration & evaporation). Does the DEB model provide information on the composition of e.g. urine (other than the elemental compostion)?

Answ: Yes these low concentrations are common, and avoid toxic effects. DEB theory in chemically and biologically implicit, so it does not provide informations about the composition.

Quest 4.8: On equation 4.34 where do this values come from: (0 1 yHO 0)?

Answ: These four coefficients are summed after multiplication by the fluxes of carbon dioxide, water, dioxygen and nitrogen waste. The text explains why the water flux can be linked to the dioxygen flux (due to water loss via respiration via lungs), and the coupling parameter is here called yHO. This water flux is just added to the water flux that follows from metabolism.

Quest 4.8: I can imagine that there is a certain minimum uptake of water for an individual. If water shortages are so severe that this minimum uptake cannot be reached, maybe this can be seen as a special case of starvation. I can imagine that if the drinking rate comes below a certain value, the organism will dry out and die rapidly. Because this occurs so rapidly, death due to water shortage can maybe be seen as instant death?

Answ: Death by lack of water differs from death by starvation, because it can occur with a lot of reserve. The section on the water balance works out the amount of water that must come in to compensate the amount that comes out as a result of metabolism and other losses (respiration and transpiration in terrestrial organisms). The balance can partly be closed by variations in composition (e.g. of nitrogen waste), but the possibilities are limited. This gives constraints on behaviour, and environments where organisms can live. Since DEB parameters are involved, these constraints can be species-specific.

Quest 4.8.1: I don't understand the meaning of doubly labelled water and I specially don't understand the following sentence: "A few additional simplifying assumptions are also useful to obtain a simple interpretation of the results, such as labelled and unlabelled body water are completely mixed, and loss of label other than via water and carbon dioxide loss, is negligible."

Answ: In doubly labelled water both the hydrogen and the oxygen atoms are replaced by heavier isotopes (a heavier isotope of hydrogen is deuterium). The difference between a normal atom and a isotope of that atom can be detected. This allows you to follow the atoms from a water molecule. DEB theory tells how the dynamics of water relate to respiration (i.e. dioxygen, carbon dioxide), and what assumptions are necessary to have an easy interpretation of the results. The section is also meant to make clear that if these assumptions do not apply, the results of experiments with doubly labelled water are not easy to interpret. The nice thing with this technique is that it can be applied to individuals that live in the field without disturbance.

Quest 4.9.1: What is the difference between pT and pT+? And does it represent the energy flux necessary to maintain an endotherm's body temperature? Is pTH heat lost by evaporation and pTT heat lost by transpiration?

Answ: PT+ is the total heat that dissipates; it have several contributions, amoung which pT, which is the heat that endotherm generate to keep their body at a target temperature. pTT is the heat lost via convection and radiation; it shows that an individual can only lose heat this way if the body temperature exceeds the environmental temperature. pTH is the heat lost by evaporating water in terrestrial environments. This is linked to losses via respiration and transpiration.

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Chapter 5: Multivariate DEB models

Quest 5.2.3: The steady state reserve density mE2 is maximal if ... while expenditure is minimal .. when JE1,C = JE1,M = JE1,A or mE1= jE1,M/kE.

What do the indexes 1 and 2 stand for in this sentence? I think they stand for two different nutrients, and if that's true, then I believe the sentence says that:

Nutrient 2 density is maximal as long as, nutrient 2 assimilation is maximal and nutrient 1 expenditure is minimal. If we are talking about two different nutrients in fact, then I think that one of them is an essential one (nutrient 1) while the other is not (nutrient 2), am I right or have I just mixed up everything?

Answ: The indices 1 and 2 stand for reserves; reserve are generalized compounds, and synthesized from a collection of substrates. A special case is that the collection has just one member, and that the substrate has the interpretation of a nutrient. Growth is fueled by both reserves, both are essential, but in many situations only one of them does most of the limitation of growth. Since this is a swith-free model, both reserves contribute to the limitation, but the limiting effect of the abundant one is really small. The non-limiting reserve is still essential; if it would no be present, growth would cease.

Quest 5.2.6: From the diagram in Figure 5.6 I understand that: C02 + light ->EC; NO3 -> EN; (C02 + light) + NH3 + NO3 -> E. But to what is NH3 converted? What does the empty box represents? Does it represent the ammonia reserve and you just don,t name it because even though ammonia is stored before it,s used, it has a very low storage capacity and a very high turnover rate?

Either way, if I'm allowed to say so, I think that there should be a reference to the empty box on the figure legend, in case I'm correct, I could only draw this conclusion (box = ammonia "reserve") two pages ahead.

Answ: Correct, it would have been more clear to introduce an ammonia-reserve formally, and then let the capacity skrink down to zero by increasing the turnover rate. Since this would require an extra state variable, and some extra lines of formulae, I directly presented the limit, where there is no ammonia reserve. Otherwise ammonia as nutrient, and as reserve are treated in the same way as any other nutrient and reserve.

Quest 5.2.6: Equation (5.27) give:
jE,Am = general reserves maximal assimilation flux
jNH,A = ammonia assimilation flux
jNO,A = other-nitrogen assimilation flux
jCH,A = carbohydrates assimilation flux


  1. Is jNO,A referring to any nitrogen substrate (nitrite, nitrate, urea, amines, amino acids and organic compounds in case of plants with mycorrhizae) assimilation flux or is it just nitrate and nitrite assimilation fluxes?

    Answ: It includes all these nitrogen species, bacause all can be stored without much problems. Ammonia is too toxic to store. Wehere or not these are all relevant depends on the situation

  2. Shouldn't the last two fluxes be written as jEN,A and jEC,A instead of jNO,A and jCH,A? What is the difference? I'm not including jNH,A in my question because I presume that we don't consider ammonia to have a real reserve due to the reasons I stated on my question about 5.2.6 Ammonia-Nitrate interactions.

    Answ: jE,A is the flux of synthesised (general) reserve as function of arriving substrate fluxes, from the environment, not from other reserves. The carbohydrates originate from CO2 and light, but are not stored first, before use, in this formulation. Synthesized carbohydrates that are not processes this way, are either stored in a carbohydrate reserve, or excreted.

  3. What are the subtracting fluxes referring to? First I thought they could be referring to rejected molecules that are fed back to the reserves, but then I red {177}'s first sentence and saying that ammonia is excreted not being fed back to reserves. So I presume that my first impression is wrong.


  4. The minus sign has nothing to do with rejection. The derivation is given at {42}.
  5. What is the difference between j' and j? I couldn't find any reference to j' on notation and symbols or in the text.

    Answ: The prime is used to indicate that we multiplied with the binding probability (given an arrival event), and the yield coefficient. So j' has the interpretation of a scaled j, without any effect on the dimension (so I used the same symbol).

Quest 5.3.2: At {182} it states "In the shoot, nitrate is received from the root, and carbohydrate is photosynthesized. The resulting compound is stored in the reserves ER and ES, respectively."

I don't understand what resulting compound we are talking about. Is it carbohydrate or is it both nitrate and carbohydrate compounds? Because after reading {182}, I think that this is what happens:

Shoots obtain carbon while roots obtain nitrate. Roots send nitrate up to the shoots and they repay with carbohydrates. When both roots and shoots have both compounds they transform it into generalized reserves (ER and ES, respectively). Although, there is a part of carbon and nitrogen in the roots and shoots that is not used for generalized reserves, they are stored in specialized reserves: shoots carbon reserve (ECS), shoots nitrogen reserve (ENS), roots carbon reserve (ECR) and roots nitrogen reserve (ENR).

When the plant needs to use carbon and nitrogen it mobilizes them from specialized reserves and afterwards it joins this compounds with those coming from generalized reserves. The next step consists of using them for development and /or reproduction and growth and somatic maintenance.

What I presume what happens next is that part of the mobilized compounds end up not being used because the SU's reject them and instead of being wasted they are feed back to roots and shoots generalized reserves (ER and ES) the part of mobilized compounds that is not rejected is translocated in order to "feed" development and /or reproduction and growth and somatic maintenance.

Answ: Almost correct. Allocations to the partner (root for shoot, and shoot for root) are after storage, not directly from assimilates (i.e. compounds that are synthesized from substrates and/or nutrients that are taken up from the environment). First we have the translocation flux, which is a fixed fraction of the mobilized general reserve (supplemented with the generalized reserves that are synthesized from the specialized nitrogen and carbon reserves). This very much resembles the kappa-rule. Second we have the excreted fluxes, so a fixed fraction of the rejected fluxes of specialized reserves. The excretion is now not to the environment, but to the partner.

Quest 5.3.2: Is binding probability \rhoNO the probability of assimilating ammonia before it assimilating nitrate reserves {183}? If that is so, why is it called \rhoNO instead of \rhoNH.

Answ: No, \rhoNO stands for the binding probability of NO. By tuning both binding probabilities relative to each other, we can quantify the preference of one type above the other.

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Chapter 7: Case studies

Quest 7.1.5: During this chapter, we learn that energy allocation, more precisely the value of kappa, can change because of several reasons : 1. during prolonged starvation, 2. according to photoperiod, 3. but also because of parasitism,

Is this list complete? Can we imagine other external factors having an effect on kappa? For example, under starvation, it is supposed that kappa could increase? At the opposite, can we suppose that under `extremely rich condition', kappa could decrease to maximise egg production ?

Answ: Kappa can also change in response to certain chemicals (endocrine disruptors); in the end all changes in kappa are mediated chemically, either by compound produced by the organism itself (photoperiod), by other organisms (parasites), or by compounds taken up from the environment. I never saw reproduction data that could only be fitted by decreasing kappa under rich conditions. Such a decrease should result in a decrease of growth, and if growth is already zero, in shrinking. See, however, the section on emergency and suicide reproduction.

Quest 7.1.7: Intertidal molluscs and other marine invertebrates spend a significant time in emerged conditions and switch their metabolism partly to an anaerobic mode (but not systematically).

How does DEB theory deal with emersion period for this kind of animal? Does the cost of maintenance remain constant between emersion and immersion period? What about the catabolic flux? Can we say, for intertidal organism, that the emersion period can be treated in DEB as a dormancy state?

Answ: I have not seen data on the physiological activities of bivalves in during emersion. Since there are almost two tidal cycles in a day, emersion lasts a few hours at most. Digestion activety (so assimilation) is likely to proceed. I expect that maintenance also proceeds (so no torpor state). The anaerobic situation that will develop must give rise to fermentation products, which might accumulate inside the shell till immersion.

Quest 7.3: The parameter k (with a dot) and with an index (X, g, P..., see for example fig. 7.15)) is used at several occasions. I can't find it in the notation and symbols part. How is it defined? What is its dimension?

Answ: kX yXg is decribed as "a rate constant for digestion" at {240} line 22; kX itself has not been introduced formally. The choice of symbol already indicates that its dimension is "per time", and it has a "decay" connotation. It stands for the specific dissappearence rate of X, so of food.Its use in fig 7.15 is somewhat inconsistent because food is quantified in mg POM, rahter than in C-mol. So I should not have been using J_Xm. The book does not have a symbol for "weight per time". I should have been using wX JXm for with purpose.

Quest 7.9.2: In chapter 3.5 the kappa-rule had been introduced, which based on the observation that Daphnia does not reduce growth or increase their ingestion rate when they start to reproduce (Figure 3.11). The energy used for reproduction is the flux that was spend on the increase of the state of maturity in juvenile, i.e. 1-kappa of the catabolic flux minus the maturity maintenance costs.

Now the increase in growth for man in figure 7.29 is explained by a change in assimilation AND in kappa. Why can't the additional energy for growth come from a higher surface-area-specific assimilation rate only?

Answ: If this would be the only change, the curve at the start of the adult state would be above the data points. We also need a change in kappa to arrive at an excellent fit.

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Chapter 8: Comparison of species

Quest 8:


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Chapter 9: Living together

Quest 9.1.1: I don't understand the formula of r (specific growth rate) line 1 {302} r = (f kE - g kM) / (f + g)

Answ: The growth rate for V1-morphs is derived in (3.38) at {108}, from the growth rate for isomorphs given in (3.18) by multiplying all parameters with surface area (here only the energy conductance v and the max surface-area-specific assimipation rate {pAm}, which is hidden in the maximum structural volume Vm) by the shape correction function (which is for V1-morphs proportional to structural length). The result for V1-morphs is much simpler than for isomorphs. In the presented form the specific growth rate only applies for steady state situations, where the scaled reserve density e equals the scaled functional response f (growth is from reserve, not from food directly). The flux f kE relates to mobilized reserve, and g kM to maintenance losses, so the difference is used for growth. The factor (f + g) stands for the costs of growth, the first term refers to the costs for making reserve, the second one for structure.

Quest 9.1.2: I don't understand why the formula of r1 (donor growth rate) for the direct transfer is a function of the scaled functional response f {303}, while for the indirect transfer it is a function of scaled reserve density e {304}?

Answ: The direct transfer section considers a steady state situation where we have e = f, the indirect transfer section also includes transient states, where e can differ from f. Growth is always from reserve, never from food directly.

Quest 9.1.5: In the slides for chapter 9 it is said (slide 12) that predators protect consumers (their prey) against pathogens via preference for weak individuals. I would like to mention that this does not hold for parasites with a complicated host cycle (different host species in a parasite's life cycle). Here, a disease cannot spread within a host/prey species. Only predation makes later infections possible.

Answ: Correct, in a few species the parasites switches between prey and predator as host. In such cases the situation can be complex, where the prey can still hamper the propagation of the parasite by keeping prey densities low. The protection offered by predators to suppress the propagation of parasites in prey is strong if both the parasite and the predator have a strong effective preference for the weak prey, rather than the strong prey.

Quest 9.3.2: In equation (9.41) the time derivate of age is given: da/dt. Isn't this always equal to one?

Answ: Usually yes, indeed. The term stands there for consistency reasons, cf eqn (9.40). Moreover is it sometimes helpful to work with physiological age, rather than calender age. In that case da/dt can be different from one, and even vary in time.

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Chapter 10: Evaluation

Quest 10.3.2: On {366} is written: "Maintenance in net production models is paid for by food if possible, but from reserves if necessary, which requires an extra parameter for maintenance costs." and "The number of parameters ... is a measure of the complexity of a model".

To me it seems that it is implied here that a net production model is less useful, just because it needs an extra parameter for maintenance. In my opinion this is a bit misleading, as an extra parameter should not be a problem if it contributes towards the goodness of the model. Or does the example serve to show that both approaches are equally good, but the DEB model needs less parameters for it?

Answ: Models can be compared with each other on the basis of several criteria (e.g. consistency, generality, explanatory potential, support and complexity) as discussed in 10.2. When it comes to quantify the complexity of a model, assimilation models (as worked out in the DEB theory) are less complex than the more popular net production models (if quantified by the number of parameters). Whether or not it is a good idea to introduce an extra parameter to improve the performance of a model is another problem, and I am convinced that such a switch is necessary for a net production model, since we all know that organisms simply do not die rapidly during starvation. The chapter identifies a lot of serious problems for net production models, and I think that the conclusion must be that production models are very much inferior to assimilation models.

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