Questions & answers 2004

Go to the collection 2001 , 2003 . 2005 . 2007 .

The following questions have been put foreward by the participants of the 2004 (local) course on DEB. The questions were formulated by the participants, after discussions in bi-weekly meetings they also summarized the answers. 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 1.2.1: What do you mean when you state (page 8) "the sequence 'idea, hypothesis, theory, law' is commonly thought to reflect an increasing degree of reliability (...) I treat the terms in this sequence more or less as synonyms. Each idea should be judged on its own merits"? In working with ideas, one always treats some as better established than others, is that not correct?

Answ: That is what I meant; it is important to know how well a particular idea is empirically underpinned, while absolute certainty is not possible. My main objection is that some "Laws" (such as Kleiber's law) seem to be based more on agreement between scientists than on a solid emperical validation. The approach I suggest is to start from assumptions and see how much you can explain from them, and use emperical validation to test and adjust them when necessary.

Quest 1.2.1: Page 10 of the DEB book mentions the concepts of reduction and coherence. Do you think that reduction is fundamentally impossible, or that it is only practically not feasible?

Answ: What I meant is that molecular biology can never offer the solutions of all biological problems, because each problem is at a certain scale in time and space, and these scales determine what processes are important, and which one are less important. If the problem is how to handle traffic jams, details about the functioning of motors of automobiles are irrelevant. If the problem is at the ecological level, and molecular information is hardly helpfull to solve them. Yet the levels from molecular biology and ecology are stepwise linked, which points to the need of coherence in our explanations.

Quest 1.2.1: Why do you consider the concepts of falsification and verification meaningless?

Answ: Some models, like the allometric functions for body size, agree well with experimental observations and therefore one could argue that they have been verified (cf Figure 4.3 page 136). However, these relations are purely phenomenological, describing only a specific set of observations. They were not built on the basis of a set of clear assumptions about underlying mechanisms. Hence, such models neither provide us any insight into (possible) underlying mechanisms, nor do these kinds of models provide testable predictions outside the original range of application. A model that is based on assumptions about mechanisms and that is testable against a wide range of observations is much more useful, even though it may fit the data just as good as or worse than the phenomenological model. In this case, discrepancies between model and observations provide insight into possible underlying mechanisms, leading to new predictions outside the original scope of the model. Hence, it is more important that a model is 'useful', i.e. that it can provide insight into mechanisms underlying the observed phenomena, than that it has been 'verified', i.e. the mere fact that it describes a certain phenomenon well.

Quest 1.2.1: A complex model often deals with a specific problem, while a simple model is often used for a more general one. A simple model that describes a specific problem is in principle not so different from a complex model that describes the same problem, because both describe the same problem. In the simple model, a lot of parameters of the complex model are combined. Can one loke in this way to simple and complex models?

Answ: The behaviour of models is determined by the values of the parameter, which are specific for any particular application. The potential behaviour of the model (i.e. the behaviour as function of the parameter values) can hardly be studied if there are a lot of parameters. This makes that complex models tend to be specific, while simple models have a more general applicability. Sometimes (but not always), a complex model can be approximated by a simple one, or by a set of simple ones. Ideally, a model should follow from a list of assumptions, and the nature of the assumptions defines the generality of a model.

Quest 1.2.4: Regression analysis as a way of analysing scatter is shown to have some methodological drawbacks on p17 of the DEB book. What could be a realistic, but still manageable alternative to this method? And are there any alternatives to the standard deviation as a more appropriate measure for deviation?

Answ: Mechanism frequently translate into a deterministic model; only in exeptional cases we have mechanisms for stochastic aspects. We use regression analysis and measures such as the standard deviation to describe the stochastic part. These techniques are only useful to see how well the model fits a given set of data, and it gives some indication how well the data determine the parameters of the deterministic model.

Sometimes the stochastic scatter changes with the average of a certain variable. In that case, the theory of maximum likelyhood has some good alternatives for standard regression analysis. The mathematics becomes very complicated rather quickly for many alternatives to regression methods, due to interdependencies of variables. Two alternatives are briefly dicussed in the book: deterministic dynamic systems with stochastic inputs and scatter in parameter values of deterministic models. The class of stochastic differential equations frequently suffer from lack of conservation of mass and/or energy.

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Chapter 2: Basic concepts

Quest 2.1: Could you explain in more detail why the individual is/should be the basic unit in DEB-theory?

Answ: First of all, the individual is the unit of selection. Parameter values are individual-specific and selection acts on parameter values, in the context of the DEB theory (cf work on adaptive dynamics). Behavioural decisions are make at the individual level and affect food uptake (time balances). Toxicants, for instance, affect individuals, which has population consequences. They do not affect populations directly. There is also a more pragmatic side to it, in that modeling and measuring the interactions between an individual and its environment (mass and energy balances) is much easier than doing this for other levels. Besides that, individuals can also be equal to cells (unicellulars) or populations (plants with (temporary) tubers).

Quest 2.1: To what extent are species of higher "trophic levels" more "demand systems" and of lower ones more "supply systems"?

Answ: This is not specificially investigated, however, one expects it to be true in a "sloppy" way.

Quest 2.2.2: Are there any life forms that are neither isomorphs nor V0-morphs nor V1-morphs? One could e.g. think of a cilinder that only grows thicker, not longer. Excluding the contribution of the ends of the cilinder, such a creature would be a V0.5-morph, since area is proportional to the thickness and volume is proportional to the thickness squared.

Answ: Of course, you can think of many different 'morphs'. The V0-, V1- and isomorph have been chosen, because most living creatures resemble one of these 'morphs' or a combination of two of these 'morphs'. The V1-morph is special because the difference between the individual and population levels (partly) disappears for this morph.

Quest 2.2.2: How does DEB cope with, or even predict, irregular growth? For instance, organisms might first develop organ A, then put more effort in developing organ B, etc. How does DEB cope with plants? I'd guess there are pretty large differences between roots and stems, yet they count as one individual. Maybe the question is: how does DEB deal with organisms that live in 2 very different environments at the same time (ground and air)?

Answ: Section 7.7 (page 250) deals with more complex changes of shape during growth. The differences in uptake in roots and shoots of plants makes it necessary to delineate two structures, rather than a single one. Each structure can change in shape during growth in its own way. The description of these changes can easily involve a lot of parameters that complicate the application of the resulting model. From a metabolic perspective, it is not always necessary to follows the changes in shape in great detail.

Quest 2.3.1: On page 31, the 'weak homeostasis' assumption is briefly mentioned. However, it will later turn out to be of great importance, as it severly limits possible kinetics for reserve outflow/availability. Hence, I'd like to hear strong arguments in support of the 'weak homeostatis' assumption: why would you assume individuals of different size (structural volume) to have an identical body composition (i.e. constant structure:reserve ratio) in an environment of constant food availability in steady state?

Btw: steady state here is defined as d[E]/dt = 0, I assume? Rather than dV/dt = dE/dt = 0?

Answ: Indeed, the assumption of 'weak homeostasis' has great implications for reserve kinetics. Individuals of different size have the same body composition, in environments of constant food availability, when the reserve density is in steady state. The composition does depend on food density, however. This is used to access the composition of reserve and of structure. Without the weak homeostasis assumption, this will be very hard, if not impossible.

Quest 2.3.1: Which motivations exist for the 'weak homeostasis' assumption?

Answ: (1) Given 'weak homeostasis', individuals kept in an environment of constant food availability for a long time will ultimately arrive at a constant body composition. Even though they still grow, reserve density (and hence body composition) reaches steady state. This phenomenon provides one of the few (if not only) means of determining the chemical composition (and amounts) of structure and reserves individually (e.g. page 134). Without the 'weak homeostasis' assumption, one would lack a direct means of determining this composition: some model parameters would in fact become impossible to measure.

(2) Most enzymes place extreme demands on the (chemical) environment in order to function. Hence, it seems likely that an organism 'at ease' (in environments of prolonged constant food availabily) will somehow maintain a constant chemical composition: they are in 'weak homeostasis'.

(3) For the DEB V1 morph (often used to represent a population of individuals), 'weak homeostasis' is an obvious requirement. Here, it merely states that the composition of individuals in the population does not depend on the size of the population, given constant food availability. This seems an obvious null-hypothesis: as long as individuals do not influence each other through availability of food, no obvious reason exists for an effect of population size on population composition. Also, a lack of 'weak homeostasis' would cause DEB simplications to deviate from many classic population growth models (e.g. exponential growth), whereas DEB with weak homeostasis very well matches these classic ideas.

Quest 2.4.2: Why are Poisson-processes used in modeling the SU, rather than any other statistical process?

Answ: It is the only process where the individual events have no interaction with each other. Notice that the intensity of the process might vary in time; we are talking about the micro-scale structure in time. Besides this, there's also the more philosophical reason of Occam's razor: if we don't know anything about it, why presume something more complex? Moreover, there's a pragmatic side to this, because it is the only process that is relatively easy to use.

Quest 2.5: On page 53, it is stated that predator-prey conversion is more efficient, if the body compositions match well. Hence it is advantageous for a predator to be similar to its prey. Are there any examples of predators that have evolved towards their prey, i.e. predators that earlier in their evolutionary history had a body composition that was quite different from their prey, whereas later they developed a body composition that matched their prey better?

Answ: No, there are no examples known of cow breeds that started to look like grass or of lions that evolved towards buffaloes. However, there are indications that a similar evolutionary process is working in a more subtle way. For instance, if there is very limited calcium in an environment, then the plants will contain little calcium. The herbivores might then evolve into a variant that only needs little calcium. Because the prey contains little calcium, the predator can also evolve into a species with little calcium requirement. This mechanism gives a correlation in chemical composition between prey and predator.

Quest 2.7: Organisms are assumed to have 3 stages in their life-cycles that are rather abrupt. What biological clues point to the existence of non-smooth transitions between the different life stages?

Answ: Of course the transitions are idealized into point events, but on the scale of a lifetime of an individual these transitions are very rapid. Furthermore, there are many examples of swift physiological changes when going from one state to the other, e.g. baby's that are born adapt to their new environment very quickly (breaking down the embryonic type of hemoglobin and replacing it by a new type, the blood circulation changes, etc.)

Quest 2.7: There are three different life-stages according to your own index, embryonic, juvenile and adult. But wat about marsupials? The life stage of the animal in a sac on the belly of the mother is in my point of view not that of a juvenile, because they do not have a direct impact on food supplies in ecological sense. If they were in that stage, then you could say that a developing embryo is also a juvenile because it also recieves food from its mother in the uterus.

Answ: An importent difference between embryo's and juveniles + adults is that embryo's don't get their food via the digestion duct. The theory assumes that the rate at which reserves are mobilized is the same function of reserve and structure for the three life stages.

Quest 2.7: Is it possible to discern an embryonic stage in all organisms?

Answ: No most dividers do not have an embryonic stage, although some have a dormant stage of spores.

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Chapter 3: Energy acquisition and use

Quest 3.0: What is the reason in the DEB-scheme in Figure 3.1 for the difference between unicellulars and multicellulars? Is there a fundamental difference in energy distribution, or are the allocations that are pooled just practically non distinguishable?

Answ: Unicellulars can be considered to be "juveniles". If you only consider this stage, the DEB dynamics can be simplified by pooling somatic and maturity work and pooling structure and maturity; the value of the partitionning fraction does not play an explicite role.

Quest 3.1.1: page 70 What advanced techniques are meant that circumvent this problem of measuring feeding rates that make use of reductions of food density?

Answ: The techniques described in citation [264] make use of tracers (raisin particles) that can be measured with high accuracy in very small amount and are taken up at the same rate as the food.

Quest 3.1.2: Why would the feeding rate be proportional to the surface area? I can imagine that it works for unicellulars, because nutrients are taken up over the whole membrane. However, many organisms take up nutrients at a specific site on their body, e.g. we eat and drink through our mouth. So why would our feeding rate be proportional to our surface area?

Answ: Something should be made clear here. The relevant area is not the skin area of the creature, but the area of its digestive system. The (maximum) food uptake is thought to be proportional to the area of this system, which is proportional to the total surface area in isomorphs.

Quest 3.1.3: Page 73 states that feeding costs show up either as a reduction of food energy gain or as a fixed fraction of maintenance. Why not both? And can the active ('hunting') part of the feeding costs decrease with food density?

Answ: The sentence is not clear indeed; feeding costs can show up as a reduction of food energy gain or as a fixed fraction of maintenance. The active part of the feeding cost is constant, for keeping the model as simple as possible.

Quest 3.4: Why would the assumption that [E] is independent of V apply only if d[E]/dt = 0 and not if the reserve density is changing in time?

Answ: Observations show that [E] depends on V under conditions that cause a change in reserve density, e.g. during the embryonic stage of during hibernation or other forms of starvation. Small individuals consume their reserves faster than large individuals, but they also recover quicker when they start eating again.

Quest 3.4: Reserve acts as a buffer therefore one could expect that through some feed-back-loop mechanism it is directly related to the assumption(s) on homeostasis. Isn't it possible to replace this assumption by a fundamental one?

Answ: So far any effort to either leave out or replace the assumptions of the DEB-model have not improved but rather worsened the quality of the model. Because the assumptions seem so difficult to replace, one would expect an underlying smaller set of more fundamental assumptions from which the assumptions made would follow.

Quest 3.4: In the dynamics of energy the contribution of blood is considered negligible, because the uptake capacity of blood with regard to energy (and nutrients) is low. Then what is the use of blood anyway?

Answ: Although blood does not play a major role in the calculations, since its capacity is low, it is important to avoid time lags due to diffusion. Blood functionally has the role of making energy and nutrients quickly available for parts of the body that are not in direct contact with the input source of these substances.

Quest 3.4: Weak homeostasis is an assumption of great influence: it causes d[E]/dt to be proportional to V to some power. This result in a catabolic flux that includes dilution by growth.

I suggest another catabolic flux, one based on chemical mechanisms: the catabolic flux is proportional to concentration, i.e. [E], and does not include dilution by growth. Instead, the differential for [E] now includes dilution by growth, in addition to the assimilation and catabolic flux.

Answ: This alternative does have a very simple chemical mechanism indeed: each "molecule" has a constant hazard rate for partaking in some transformation. The mechanism for the DEB-kinetics is more complex, and discussed in section 7.6 at {246}. The alternative suffers from several problems, however. First, it is not realistic, as is obvious if one considers the initial development of an egg. It would result in a extremely rapid initial development, while the graphs at pages {99-102} clearly show that development starts slowly. Second, if one gives up weak homeostasis, one has to find new ways for separating reserve from structure in observations on biomass. The composition of these generalized compounds makes use of weak homeostasis in the DEB theory (cf Figure 4.2). If it would be difficult, if not impossible, to assess the chemical composition and amounts of reserve and structure, do we still have a useful model? See the comments-file for a further discussion of this alternative.

Quest 3.5: Figure 3.11, page 88: couldn't one interpret the open symbols (for individuals with eggs) as a separate, slightly higher curve?

Answ: The number of young per brood pouch varies.

Quest 3.7.1: How is it possible that reserves are not "passive", yet no maintenance costs are required?

Answ: The turnover rate of compounds of the reserve is implied by the reserve dynamics; the consequence is that they are all equal. Part of the maintenance costs are associated with the turnover of the compounds of the structure. Their turnover rates might all be different. Empirical support is e.g. presented in fig. 3.15 (pages 99/100), where it is seen that eggs initially have no respiration, while the amount of structure of embryo is close to 0, but reserves are large. No respiration implies that no maintenance costs are paid at the start of egg's development.

Quest 3.7.1: Why is the assumption made that the reserve density of hatchlings equals that of the mother at egg formation?

Answ: Under this assumption growth during the juvenile phase at constant food density is of the simple von Bertalanffy type if the mother was exposed to this food density for long enough a period. Moreover, it does not involve any new parameter.

Quest 3.7.1: When one derives equation (3.27) on page 105 (the egg costs equation) from equations (3.18), page 94 and (3.24), page 97, one finds one term is left out in the derived equation (namely Vh/Vm)^(1/3) ). Where did it go?

Answ: The embryo in the egg does not allocate to heating; this allocation only starts after birth. Please note, by the way, that the increase in temperature through breeding leads to an increase in metabolic rates and thus to an increase in body temperature.

Quest 3.7.1: Could you derive from DEB theory that there is an evolutionary benefit in viviparity that lies within the unlimited growth of the fetus, compared to eggs where the amount of reserves is limited?

Answ: DEB theory deals with metabolic mechanisms, not with evolutionary benefits. Viviparity come in two forms: eggs that are carried inside the body during incubation and foetal development, which involves a placenta. It is known from women in extreme startvation that the fetuses are expelled from the maternal body only when the mother can no longer pay for the maintenance costs.

Quest 3.9.1: How are breeding costs modeled in DEB-theory? I should think it involves heating and not eating at the same time.

Answ: These costs are included in the maintenance costs, like all other behavioural traits. If the scientific problem requires more detail on this point, including the fact that feeding and breeding usually do not combine at the same time (sometimes food is supplied by the partner), more detail in the time budgets should be included (at the cost of more parameters).

Quest 3.9.1: Consider two individuals of some species for whom the costs of maintenance and growth are negligible. Then partitionability demands that their catabolic rates are linear in the reserve density. Hence, if one of them has twice the amount of fat reserves compared to the other, its catabolic rate will also be twice as fast. If reproduction effort is also negligible (for instance if they are both males), then the fattest one must develop twice as fast as the slimmest one. So is there any indication that fat individuals mature faster than slim ones?

Answ: Yes, there is a correlation. If food density is low, individuals will have a lower reserve density and hence they produce less offspring. In some species, such as daphnids, this is very clear. The reproductive costs for males are not necessarily smaller than for females, as has been found in the hermaphroditic pond snail Lymnaea stagnalis (research by ter Maat)

Quest 3.10: Is assumption 3a largely made for practical reasons?

Answ: Partly. The assumption does specify the initial condition of a juvenile in a way that does not require any parameters. In that sence it is practical. This condition also has two theoretical motivations. First, it gives von Bertalanffy growth under constant feeding conditions for the whole juvenile and adult period. Second, it links organisms that propagate by reproduction (read: eggs) smoothly to those that propagate by division.

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Chapter 4: Uptake and use of essential compounds

Quest 4.2: Why are there three powers in DEB (assimilating, dissipating, and growth)?

Answ: The definition of dissipating power is given in (3.58), {124}; note that more dissipates than is specified by this power (as overhead in assimilation and growth). Now, if we do not include either reserves or maintenance everything is invested in growth (as is done in Monod's model), so there's just one indepenent flux (assimilation or growth), all other fluxes are proportional to this one. When we include maintenance, we have a second independent flux; specifying two of the three fluxes gives enough information to calculate the third one (using energy and mass conservation). When we include reserves, however, two fluxes do not determine the third one. Including allocations to development and/or reproduction in the way the DEB theory does this via the kappa-rule, does not give new independent fluxes.

Quest 4.3: Are the discontinuous transitions in the graphs in figure 4.1 {132} due to life-stage switches?

Answ: Yes. Furthermore, as you can see, the flux for faeces does not show this transition, and the flux for reserves becomes negative in the first part of the graph, correspoding to the embryonic stage.

Quest 4.4: Why would the respiration rate expressed in CO2 be the same as expressed in O2 {135}? I'd say C and O are also present in other compounds then CO2 and O2.

Answ: These fluxes aren't the same, only under certain conditions, see {137} and {138}.

Quest 4.4.3: For individuals not reproducing by division, the amount of damage-inducing compounds seems to increase with 'respiration' (i.e. maintenance and growth). The hazard rate (= dying probability?) seems in turn to follow the accumulated amount of damage-inducing compounds. Is this right? Then, what happens with species reproducing by division? Accumulated damage is transferred unto daughters? This seems not to be the case (as the hazard rate depends is independent of an individuals history). But why?

Answ: First, the hazard rate is not a probability, but a probability rate. If you multiply the hazard rate by a time increment, you have the probability of dying somewhere in this increment, given that the organism is alive.

In the DEB approach, aging does not depend on the mode of propagation (reproduction or division). Rather, aging operates differently in multicellulars than in unicellulars. If a cell is affected by aging, it ceases growing and starts to produce damage, which accumulates in a multicellular organism. This applies to each cell in a multicellular organism. The hazard rate depends on the accumulated damage.

After publication of the 2nd edition of the DEB book, research on the modeling of death by aging has continued. This has resulted in a more elaborate description of the process of death, which responds more realistically to caloric restriction and - unlike the description in the book - is capable of producing common survival curves such as in Figure 4.7.

Quest 4.4.3: I personally don't believe that radicals can cause enough damage to DNA because the more radical a radical is, the shorter is its life time and the lesser it's change to encounter DNA.

These are my own thoughts about aging: Every time DNA is translated, 1 of 1000 bp is mis-translated (maybe even more). These errors are fixed by 'repairing enzyms'. But because repairing enzymes can also be mis-translated, the errors will eventually accumulate and cause the cell to die. Can aging be coupled to the number of celdivisions?

Answ: A multicellular organism consists of many types of tissues, and cells in many tissues (e.g. animal muscle, kidney, liver, nerve) only divide in the embryonic and early juvenile stages. The typical characteristics of ageing only develop much later.

Quest 4.4.3: At the bottom of page 139 it is stated that by introducing a hazard rate one obtains an explanantion for why dormancy prolongs life span. However, one can freely choose a hazard rate function; a priori one could choose a hazard function that is lower during dormancy or one could choose a different hazard function. So isn't this hazard rate just a part of a mathematical description, with which you can fit any death rate by adjusting the hazard function, without any deeper insights?

Answ: One can indeed freely choose a hazard function and therefore the mere concept of a hazard function doesn't provide a detailed explanation for anything. However, just the idea of introducing a hazard function and a distribution of survival times is a leap forward. Toxic compounds are e.g. considered to have a lethal effect after a certain amount time and the fact that there is a distribution of survival times is usually ignored. Using the concept of a hazard function one can at least describe the mortality as a function of time and then one can start to think about mechanisms that can cause such a time behaviour.

Quest 4.4.3: Every time DNA is translated, 1 of 1000 bp is mismatched. These errors are fixed by 'repairing' enzymes. But because repairing enzymes can also be mis-translated, the errors wil eventually accumulate and cause the cell to die. Can aging be coupled to the number of celdivision?

Answ: There is evidence that organisms which live on 70% of their maximum food, live longer than organisms which live on 100%, which implies that processes involved with food assimilation and use play a part in aging. Caloric restriction does not directly affect division of cells in tissues. Organism have different tissues with different division rate's. This mechanism seems problematic for unicellulars.

Quest 4.5.1: Why translates the condition that RQ, UQ and WQ are state-independent to the condition that the elemental composition of reserve must equal that of structure?

Answ: In animal physiology, the RQ is frequently assumed to be independent of the state of an individual (size and feeding condition, or in our case, amounts of structure and reserve). If we exclude, experimentally, contributions from assimilation, the RQ in a DEB context is given in (4.15), page 138. Since it depends on pD/pG, it does, generally, depend on the state of an individual. If condition (4.16) applies, however, the RQ no longer depends on the state. Condition (4.16) relates the elemental composition of reserve to that of structure. All elemental frequencies are expressed relative to carbon, and we have three of them (H, O, N). If a similar condition (4.27) applies, the UQ becomes independent of the state of an individual. Another similar condition can be derived for the WQ. But if we have three conditions, and three degrees of freedom in the composition of reserve relative to that of structure, we lost all degrees of freedom. The three conditions can only apply simultaneously if the elemental frequency of reserve equals that of structure. We can include more elements, but then we must also consider more ratios XQ. The whole discussion about the ratios is included for the reason that if condition (4.16) does not apply, the RQ cannot be treated as being constant, and we have to deviate from common practice in animal physiology.

Quest 4.8: Water is also formed as a product of metabolic reactions. Is this included in the water balance?

Answ: In most cases water is hardly rate limiting, and we can conclude from the SU-concept there are no problems then. Roughly we just say that what is lost due to respiration and transpiration must be compensated by drinking. If water would be co-limiting, we need theory that is discussed in Chapter 5.

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Chapter 5: Multivariate DEB models

Quest 5.: I presume the intermediate steps (from light to reserves) are modeled as a SU.

Answ: Indeed, the details are discussed in 5.1.3. Because SU dynamics is based on fluxes, photons can formally be treated as particles that arrive. The photo system extracts a fixed amount of energy from a (metabolically useful) photon, irrespective of its energy content (which depends on the wavelength).

Quest 5.1.1: You hypothesize that substrates can be bound to so-called carriers. The amount of carriers is taken to be proportional to structural mass MV, as is appropriate for V1-morphs? Explain! I'd expect it to be surface-related, or am I confusing nutrient uptake with substrate concentrations inside the body?

Answ: One of the DEB assumptions is that uptake is proportional to surface area. If the amount of carriers is also proportional to surface area, uptake is proportional to the amount of carriers as well. Surface area is proportional to (structural) volume, so to structural mass, in V1-morphs. This makes that the amount of carriers should be proportional to mass in V1-morphs. This type of reasoning pushes the strong homeostsis assumption to the extreme.

Quest 5.1.1: Page {162} states: jX = j1 + j2, but I assume only at concentrations of glucose and fructose that are not too high, or not?

Answ: No, this also applies for high concentrations in the case of parallel processing. The idea is that each carrier is linked to its own machinery to transform the substrate it can bind to reserve, and that the total flux that enters the reserve equals the sum of the fluxes that passes the various carriers. If not, we would have an accumulation of intermediary metabolites, which cannot be accomodated in a single reserve single structure system.

Quest 5.1.3: The production stage of a Synthesizing Unit is assumed to last an exponentially distributed time interval (see paragraph 2.4.2), which means that the minimum production time is equal to 0 (in fact, this is even the production time with the highest probability density). Is this a valid assumption for the reactions described in paragraph 5.1.3? The energy transfer within Photosystems II and I must take a finite amount of time, so shouldn't these SU's have a minimum production time unequal to zero?

Answ: The exponential probability density function with parameter k states that the probability that the time interval is less than some small time increment dt equals 1 - exp(- k dt), which is close to k dt for very small dt. This probability goes to zero if dt goes to zero. The energy transfer within PS II and I will be fast, relative to the overall rate of the transformation from photons plus carbon dioxide to carbohydrate. Moreover, the expression for the (mean) rate of the SU will not change if we replace the assumption of an exponentially distributed time interval by the assumption that the time interval is some fixed (positive) value.

Quest 5.2.1: The "specific maintenance requirement jEi,M for reserve i is taken to be constant." I thought the maintenance costs for reserves were 0?

Answ: Correct; "for" must be read as "that is paid from". rather than "that is required for".

Quest 5.2.1: "In view of the very small values, the reserves hardly contribute to total biomass". I don't understand this, regarded in general DEB-theory.

Answ: Generally, reserves do contribute to the total mass of the cell. The remark relates to phosphate and vitamin B12; the absolute amounts of these two compounds is really small, compared to the mass of the rest of the cell.

Quest 5.2.2: kappaEi could be made dependent on JEi,M to take into account that an organism may put effort into keeping reservoir levels high.

Answ: We would loose weak homeostasis in that case. It also does not help to make it a function of jEi,M, since this is a constant. Notice that excretion is only substantial as long as the reserve density is high.

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Chapter 7: Case studies

Quest 7.1.5: You state that "deviation from the kappa-rule is necessary", because maintenance alone cannot be paid given standard allocation. Is kappa really that fixed? The data on the next page (different allocation with different light cycles) implies a hormonal-induced variable kappa. In the next paragraph, you imply the existence of a switch. How "smooth" do you consider this switch, and couldn't it be such that there is a "smooth" range for kappa in the whole range of overabundant food to starvation to death, i.e., kappa is not fixed, but in the higher ranges (no starvation) the function is almost flat, so that it can be approximated as being fixed?

Answ: Section 3.4 shows that the assumptions behind reserve dynamics allow that kappa can be some function the amount of structure, but it should not depend on the reserve (density). Section 8.3.5 discusses determinate growers, which cease growth at puberty. Indeed, section 7.1.5 shows that kappa can depend on the day/light cycle. Section 3.5 discusses the situation where parasites change the value of kappa. A certain class of toxic compounds, the endocrine disrupters, will probably also have kappa as target parameter. Recently we found SU formulations that are fully consistent with the DEB structure, where maintenance is always paid from both reserve and structure, with a priority for reserve. The switch model is a limiting case for this more elaborate model without any switch (at the cost of one extra parameter).

Quest 7.1.7: Hibernation leads/is associated with lower maintenance costs, because parts of the structure are no longer turned over (when they decay, it is left that way). Aging is associated with oxygen-consumption, and dioxygen-consumption is associated with maintenance. That way hibernation leads to stalling of the aging process. Is this correct?

Answ: If dioxygen-consumption goes down, the free radical production goes down and so the degradation of functional proteins to non-functional proteins. This means that the need for turnover of structure also reduces. Damage that is built up as a result of the aging process, will do so less fast if dioxygen consumption is reduced. Hazard rate is linked to the damage.

Quest 7.2: Has any experiment been done to see if the surface of unicellular agregates change with either size, concentration or temperature? Can this be related to diffusion limited agregation?

Answ: Yes, see fore instance Logan & Wilkinson (1991) Biotech Bioeng 38: 389-396 and Brandt & Kooijman (2000).

Quest 7.3: What is the value of more sophisticated models of digestion for DEB and isn't it in practice easier to determine an effective surface from experiments?

Answ: The section on digestion is included to study implications of the assumptions that digestion efficiency is independent of the size of the individual and of the feeding rate. Both factors affect the gut residence time, and this time might have a link with digestion efficiency. Moreover it illustrates how each module in the most simple model that is discussed in chapter 3 can be replaced by more sophisticated modules (at the prize that more parameters and state variables are involved).

Quest 7.3.1: Is it correct that the straight line in Fig. 7.17 does not originate in the origin (0,0)? Is that point the dissipating heat when no food is ingested?

Answ: No, the data relate to steady-state situations, and when no energy is taken up, no heat can dissipate. So formally, the line should go through the origin. The intercept is well within the mean deviation from the line, so the numerical effect is negligible. The point is a bit academic, since no species can live on substrates with small chemical potentials.

Quest 7.8: Where does the rest of the weight of the pupa go in fig. 7.24? Is it all dissipated as CO2?

Answ: The figure shows wet weight; most of the weight loss will be water, a minor part went lost as CO2.

Quest 7.9.1: 4th paragraph: TA is expressed in kK. What is that?

Answ: This stands for kilo-Kelvin, so TA = 10000 K.

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Chapter 8: Comparison of species

Quest 8.1: "Dwarfing" {266} is the effect you see with populations (of large animals) on islands compared to populations on the mainland, or not? The idea is that on islands the food density is subject to more variation; reduction in body size means achieving a more constant homeostasis (via reserve density)?

Answ: First of all, besides the question what an island is, large animals are known to live on islands, among them the extinct moa's of New Zealand and the monitor lizard of Komodo. On the basis of DEB theory, dwarfing can be expected in populations that experience a rather constant food supply in combination with low loss rates. This will result in a population size that is close to the carrying capacity. In that situation the individuals hardly reproduce and the food intake is low. More on this can be found on {332}.

Quest 8.3.4: On {292} you talk about the subsequent selection processes that thin randomly. The idea is that selection does not work randomly, not? Then what happens when there is non-random selection?

Answ: A better term for random would have been stochastic, in this case; the sentence is not meant to imply that each individual has exactly the same survival probability. The situation is as follows: imagine bacteria living in a forest. Once in a while a mouse drops dead. Bacteria that manage to reach this substrate will grow and divide rapidly. The one that grows fastest produces the most offspring. When the substrate is finished, the bacteria enter a stage of turpor (sometimes as spores) and will spread through the environment. Most will eventually die by starvation, but the fastest growing bacteria will probably have the largest chance to survive the starvation period, because it occurs in most copies.

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Chapter 9: Living together

Quest 9.2.2: The solution of equation (9.21) is assumed to be an exponential function. Of course, this is what one expects intuitively, but I don't see any reason why the growth couldn't be of a different functional form. Or am I missing something?

Answ: A standard procedure in the solution of any integration problem is the suggest a solution, and then demonstrate that it actually is a solution by differentiation of the solution. Mathematical sophistication then requires to demonstrate that it is the only solution.

Quest 9.2.2: Neonates that give birth to new neonates contribute significantly to unstructured populations (page 326). When the population is not at steady state, I can imaging that this is an important thing to remember. But when a population is at steady state, I think this contribution maybe a bit lesser important. Am I right?

Answ: DEB theory shows that populations grow slowly at low reserve, and so food densities. In these cases juvenile periods are long. DEB-structured models are then likely to deviate from non-structured ones. The differences can be reduced by chosing appropriate parameter values.

Quest 9.4: In the Canonical Community model several nutrients such as nitrate are excluded for simplicity. Doesn't this have an effect on stoichiometry? E.g. the molecular composition of ammonia is different from nitrate, so I presume that all the urination, respiration, watering etc. quotients (section 5) become different if nitrate is replaced with ammonia 'for simplicity'.

Answ: Correct. If nitrate is treated as being ammonia, it would affect the dioxygen flux. As long as no transformation is limited by dioxygen, this hardly matters, except for the fact that the values for dioxygen will deviate. There are quite a few situations in which the difference between ammonia and nitrate is essential indeed.

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Chapter 10: Evaluation

Quest 10.3: How well can in practice DEB be coupled to calculations on other models?

Answ: If the assumptions behind those other models are consistent with the DEB assumptions there is no problem. However, few alternative models are explicitly based on a set of assumptions, which makes the condition difficult to judge in practice. It is not simple at all to reconstruct assumptions behind a given model on the basis of the mathematical structure only.

Quest 10.3.1: The text suggests (!?) DEB could be comparable to SEB (or vice versa) for (non-growing) adults under excellent food conditions (f = 1), or not? If SEBs do not include overhead costs, then how is it possible that DEB = SEB in steady state?

Answ: Comparable here means "can be compared with", and not "is similar to", let alone "is equal to".

Quest 10.3.1: How does SEBs model embryo?s or (growing) juveniles?

Answ: SEBs do not deal with reserves, and cannot handle embryos.

Quest 10.3.1: {365}: Aren't there any respiratory measurements over longer periods of time than "a few minutes"? What conclusions can in general be drawn from "minute-measurements" (because I don't get it)?

Answ: Many measurement techniques would produce artificial results if extended over a longer period. It is frequently possible to repeat the measurements and determine how respiration varies in time. Weather or not extension is possible is not the issue, however. It issue is in the interpretation of the measurments.

Quest 10.3.2: What physiological data could support the existence of switches in net production models? How should these switches work then?

Answ: If food intake is not sufficient to pay maintenance costs, a situation that can occur instantaneously, any net production model should specify what happens next. Letting the organism die is not realistic. Paying maintenance from other sources involves a switch. The observation that the organism does not die supports such a switch (although there are also other possibilities; "support" is much weaker than "demonstrate"). This switches can involve chemical signals, such as glucose concentration in blood.

Quest 10.3: The pro's and con's (especially the pro's) of DEB with respect to alternative formulations are reviewed. A lot of emphasis is placed on issues such as consistency and scope of application. But isn't the main barrier in getting the DEB model accepted rather a matter of marketing? DEB is quite complicated; a lot of people either don't understand it, or they think it will be too much of an effort to understand or they simply haven't even heard about DEB.

Answ: The DEB theory has a very simple structure, compared with the complexity of the living systems that it aims to catch. It does indeed take quite some effort to get the idea, which is inherent to any non-trivial quantitative theory. Several attempts has been done to present the theory in non-technical form for various forums, which did stimulate its use. The best marketing is in the ability of researchers to understand patterns in data using DEB theory, where other theories fail.

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