Resource Allocation to Reproduction in Animals

Biol. Rev. (2014), 89, pp. 849–859. 849 doi: 10.1111/brv.12082 Resource allocation to reproduction in animals

Sebastiaan A. L. M. Kooijman1,∗ and Konstadia Lika2 1Department of Theoretical Biology, VU University Amsterdam, de Boelelaan 1087, 1081 HV Amsterdam, The Netherlands 2Department of Biology, University of Crete, Voutes University Campus, 70013 Heraklion, Crete, Greece

ABSTRACT

The standard Dynamic Energy Budget (DEB) model assumes that a fraction κ of mobilised reserve is allocated to somatic maintenance plus growth, while the rest is allocated to maturity maintenance plus maturation (in embryos and juveniles) or reproduction (in adults). All DEB parameters have been estimated for 276 animal species from most large phyla and all chordate classes. The goodness of fit is generally excellent. We compared the estimated values of κ with those that would maximise reproduction in fully grown adults with abundant food. Only 13% of these species show a reproduction rate close to the maximum possible (assuming that κ can be controlled), another 4% have κ lower than the optimal value, and 83% have κ higher than the optimal value. Strong empirical support hence exists for the conclusion that reproduction is generally not maximised. We also compared the parameters of the wild chicken with those of races selected for meat and egg production and found that the latter indeed maximise reproduction in terms of κ, while surface-specific assimilation was not affected by selection. We suggest that small values of κ relate to the down-regulation of maximum body size, and large values to the down-regulation of reproduction. We briefly discuss the ecological context for these findings.

Key words: animal reproduction, dynamic energy budget, allocation to soma, chicken egg production, selection.

CONTENTS

I. Introduction ...... 849 II. Materials and methods ...... 850 III. Sub- and supra-optimality ...... 851 IV. Selection for maximum reproduction ...... 853 V. Discussion ...... 854 VI. Conclusions ...... 857 VII. Acknowledgements ...... 857 VIII. References ...... 857 IX. Appendix ...... 858 X. The standard deb model with acceleration ...... 858

I. INTRODUCTION Herein we aim to quantify resource allocation to reproduction in animals within the context of DEB theory. Investment in reproduction is subject to intense ecological One of the parameters of the standard DEB model is of and evolutionary debate (Roff, 1992; Stearns, 1992; Flatt & particular interest here: the fraction κ of mobilised reserve Heyland, 2011). Some species have many small offspring, that is allocated to soma (somatic maintenance plus growth), others a few large ones, but we are unaware of a broad as opposed to maturity maintenance plus reproduction. All comparative study of relative investment in reproduction parameters of the standard DEB model have now been compared to growth. This is probably because a single estimated for 276 species, see the add my pet collection metabolic framework is required that applies to all species for at http://www.bio.vu.nl/thb/deb/deblab/add_my_pet/ their full life cycle (including embryo development). Dynamic Species.html. We evaluated the reproduction rate of a fully Energy Budget (DEB) theory offers such a framework for grown female with abundant food for each species and metabolic organisation (Kooijman, 2010). compared it with the value assuming an optimal value of κ,

* Address for correspondence (Tel: +31 20 5987130; E-mail: [email protected]).

Biological Reviews 89 (2014) 849–859 © 2014 The Authors. Biological Reviews © 2014 Cambridge Philosophical Society 850 Sebastiaan A. L. M. Kooijman and Konstadia Lika here defined as the value that maximises reproduction rate. organisation is discussed in Lika & Kooijman (2011). The At an early stage of the formation of this large collection mobilisation rate is such that weak homeostasis is preserved: we reported that most animal species in the collection reserve density, i.e. the ratio of the amounts of reserve invest remarkably little in reproduction (Lika, Kearney and structure, does not change during growth after birth & Kooijman, 2011b). Now, with five times more species as long as food density remains constant. A fraction κ available, we reconsider this observation and report on a of this mobilised flux is allocated to somatic maintenance case-study with different races of chickens, the wild race, and growth (soma), the rest to maturity maintenance and one selected for meat production and one selected for egg maturation (in embryos and juveniles) or reproduction (in production. Selection can be shown to have affected some adults). Food intake is proportional to surface area, which is parameters in a remarkable way. proportional to volume to the 2/3 power in isomorphs, but embryos do not eat. Somatic maintenance is proportional to the amount of structure, maturity maintenance to the II. MATERIALS AND METHODS level of maturity. Maturity has no mass or energy and is quantified as cumulative investment of reserve. Feeding and allocation to reproduction are initiated if maturity reaches The data collection does not consist of randomly chosen threshold values. Allocation to reproduction is accumulated species. Indeed, a randomly chosen sample of all species would consist largely of insects, probably mostly beetles, in a reproduction buffer; the rules for converting this buffer and data on these species are few. The number of extant to eggs are species specific. Investment in an egg is such that undescribed animal species is unknown, but may be large reserve density of the neonate equals that of the mother at relative to the described species. Thus, data availability egg laying (known as the maternal effect). Apart from rules is a serious problem that constrains the choice of species, for food searching and ageing, these few criteria fully specify although we tried to include as many phyla as possible. Apart the standard DEB model. Biomass is, therefore, assumed from sponges, nemerteans and nematomorphs, all phyla to consist of reserve, structure and, possibly, a reproduction with more than 400 species are included, incorporating buffer; these types are treated as (formal) pools of metabolites 13 chordate classes, and all bird and mammal orders each with constant composition. (apart from marsupial moles). The collection spans a Application to a large number of animal species revealed body size range from 10−8 to 108 g, from hairy back that many species accelerate their metabolism after birth Aspidiophorus polystictos to blue whale Balaenoptera musculus. (Kooijman et al., 2011). This can be captured realistically as It includes over 100 different data types on all aspects a simple extension of the standard DEB model by assuming of energetics (growth, reproduction, respiration, product that these species deviate from isomorphy during their early formation, feeding) and all life stages (embryo, juvenile, juvenile phase, where surface area is (temporarily) propor- adult), collected in a collaborative effort involving more tional to volume, rather than to volume to the 2/3 power. than 60 researchers. The parameters of the standard DEB Acceleration affects both specific assimilation and energy model have been estimated using the covariation method conductance, which is why acceleration is of importance to (Lika et al., 2011a) and the software package DEBtool allocation to reproduction. Surface-area-specific assimilation (http://www.bio.vu.nl/thb/deb/deblab/debtool/). The increases during ontogeny and fuels reproduction, and mean goodness of fit is very high, 8.3 on a scale from energy conductance controls reserve mobilisation, so -∞to10, but the mean completeness level of the data is dominates developmental rate and cumulative maintenance low, 2.5 on a scale from 0 to 10; see Lika et al. (2011a)for costs until birth, when feeding starts. This affects the cost criteria. The data, as extracted from the literature, are given per offspring. with references, the species-specific code, the predictions for The most essential feature of the standard DEB model the data that we obtained, the resulting parameter values in the present context is that the energy cost for a and a list of over 100 implied properties can be inspected neonate follows from the cost for structure, maturation for each species. All of this can be found at the website and maintenance, in combination with size at birth. This of the collection (information about the DEB research involves parameters that can be estimated from data on program is available at: http://www.bio.vu.nl/thb/deb/; post-embryonic development; embryo data are available the add my pet collection is available at http://www.bio. for a few species only. To our knowledge, the standard vu.nl/thb/deb/deblab/add_my_pet/Species.html and its DEB model is the only model that captures embryonic and manual at http://www.bio.vu.nl/thb/deb/deblab/add_ post-embryonic development simultaneously. my_pet.pdf). Thereasonwhythesedetailsareofimportanceforthe The standard DEB model is the simplest non-degenerated purpose of quantifying the relative allocation to reproduction model in a family of models implied by DEB theory is that this allocation is a function of parameters, and these that we used to compare animal species. Its quantitative parameters can only be estimated from data if they are specification is presented as an Appendix 1 (see Section estimated simultaneously from all data. This is the essence IX), extended with the acceleration module (see below). It of the covariation method, as described in Lika et al. (2011a), assumes that food is converted to reserve, which is mobilised and is a consequence of thinking in terms of energy and for metabolic applications; the logic behind this particular mass balances: we cannot follow just one flux, we need to

Biological Reviews 89 (2014) 849–859 © 2014 The Authors. Biological Reviews © 2014 Cambridge Philosophical Society Resource allocation to reproduction in animals 851 follow all fluxes to close balances. For example, investment in so the product of the reproduction rate and the cost per growth must exceed the energy that is fixed in new biomass offspring, the energy investment in reproduction, should to account for the overhead costs of growth. These overhead scale with cubed length and is not sensitive to relative size of costs contribute to respiration, as does maintenance and offspring. Figure 1B confirms this beautifully and the scatter (frequently) overhead costs of reproduction and assimilation is much smaller than in Fig. 1A. (known as specific dynamic action), depending on how and The expectation that the cost per offspring is proportional when respiration has been measured. The partitioning of to maximum length to the power 4 comes from a constant respiration with respect to these endpoints requires that we relative size at birth (so the amount of structure of a neonate consider how feeding, development, growth, reproduction is proportional to cubed maximum length) while the specific and respiration change simultaneously over the life cycle of reserve capacity is proportional to length (Sousa et al., 2008). an individual. Although detailed data on all the processes The latter is given by [Em] ={pAm}/v ,where{pAm} is can be used and has been used to test the ideas behind proportional to maximum length and energy conductance v is DEB theory, they turn out not to be necessary to estimate independent of maximum length (Sousa et al., 2008). Reserve parameters (Lika et al., 2011a). While the use of extensive data capacity reflects the balance between input (assimilation) to must be preferred, this estimation can already be carried out and output (mobilisation) from reserve. It stands for the with very simple data (Lika et al., 2011b), available for many maximum reserve density, so the ratio of the amounts of species. The observation that parameters estimated from reserve and structure of juveniles and adults with abundant simple data from related species tend to be close together food. The embryo has larger reserve densities, since it starts supports the validity of the method. with reserve only, and hardly any structure. At birth the reserve density is the value for the mother at egg formation, the maternal effect. III. SUB- AND SUPRA-OPTIMALITY This prediction is tested in Fig. 2. The result is not very convincing, but Fig. 2B shows that this is mainly due to DEB theory has implied co-variation rules of parameter the greatly elevated specific maintenance costs for some very values among species (Kooijman, 1986a, 2010). Intensive small-bodied species. The waste-to-hurry hypothesis provides parameters do not depend on maximum size, appropriate an explanation for this remarkable phenomenon (Kooijman, ratios of extensive parameters are intensive and maximum 2013), and is again based on the κ-rule for allocation of surface-specific assimilation is proportional to maximum mobilised reserve. Adjustment of maximum structural length structural length. Many physiological quantities (such as involved multiplication by the specific somatic maintenance body mass and respiration rate) can be written as functions divided by the mean specific somatic maintenance. of parameters, so we can evaluate how they should The explanation that DEB theory offers for respiration depend on maximum structural length, without using any being (approximately) proportional to mass to the power 3/4 empirical argument. This reasoning does not account for any is the scaling of reserve density with length (Maino et al., evolutionary adaptation; it is only based on simple chemical 2013). Large-bodied species have relatively more reserve and physical principles (Sousa, Domingos & Kooijman, and somatic maintenance is proportional to structural mass. 2008). Since reserve contributes to mass, mass-specific respiration The reproduction rate is expected to decrease with decreases with mass to the power 1/4, approximately, for maximum (structural) length among species. Maximum fully grown adults. Reserve does not require maintenance, structural length Lm, i.e. the cubic root of maximum see Kooijman (2010) for a more detailed discussion. structural volume, equals Lm = κ {pAm}/[pM]where{pAm}is Reproduction contributes little to respiration because the maximum specific assimilation rate and [pM] is specific female simply exports reserve, wrapped in the form of somatic maintenance. Apart from contributions from the eggs, and little chemical transformation is involved in this reserve and the reproduction buffer, maximum structural process. Yet the reason why reproduction rate is inversely volume is the maximum volume of an individual. Maturity proportional to maximum length and reproduction rate at birth is expected to be proportional to cubed maximum is proportional to cubed length, is the same as for why length (Sousa et al., 2008), which leads to a constant respiration increases (approximately) with length to a power relative length at birth. Figure 1A shows that this trend for somewhere between 2 and 3 (depending on parameter reproduction is actually present in the add my pet collection, values). This illustrates why the processes that make up but large deviations occur. Reproduction is here by an metabolism need to be studied together. individual of maximum size at abundant food. This trend Most work on body-size scaling relations is empirical and is mainly due to species of fish, echinoderms and bivalves body mass plays a dominant role in these studies (Peters, that have a (relatively) large body size, but numerous tiny 1983; Calder, 1984; Schmidt-Nielsen, 1984; Hildrew, eggs. The ocean sunfish Mola mola,forexample,hasa Raffaelli & Edmonds-Brown, 2007). Body mass has maximum mass of 2.3 Mg and produces some 3 × 1010 eggs contributions from structure, scaling with cubed structural per year. Endotherms (birds and mammals) have relatively length, and reserve, scaling with structural length to the large offspring. The cost per egg (or foetus) scales with power 4. The reproduction buffer might also have a structural length to the power 4 (Kooijman, 1986b, 2010), contribution in adults, increasing the scatter. This means

◦ Fig. 1. The expected reproduction rate (R, A) and investment in reproduction (pR,B)at20C as function of the maximum structural length (Lm) among the 276 entries in the add my pet collection. The line, with slope -1 (A) or 3 (B), is based on simple physical and chemical expectations. Colours indicate high-level taxa: blue, Radiata; dark blue, Bilateria; turquoise, Platyzoa; dark turquoise, Lophotrochozoa; green, Ecdysozoa; black, invertebrate deuterostomes; magenta, ectothermic Vertebrata; red, endothermic Vertebrata.

Fig. 2. (A) The reserve capacity [Em] as function of the maximum structural length Lm among the 276 entries in the add my pet collection. (B) Same plot with Lm corrected for differences in specific somatic maintenance. The lines, with slope 1, are based on simple physical and chemical expectations. Colours indicate high-level taxa as in Fig. 1. that the body mass scales with structural length to the power from individuals of maximum size, but DEB theory specifies somewhere between 3 and 4, so reproductive investment the conversion. As explained above, reproduction depends scales with body mass to the power somewhere between 3/4 on a number of parameters that all have been estimated. and 1. These DEB-based expectations are only approximate, Treating subsequently all parameters for a species as given, since DEB theory does not expect allometric relationships we analysed the potential maximum reproduction rate for these quantities. under different κ values. Since data that have been used to estimate DEB Reproduction rate of an individual of maximum size at parameters typically include reproduction data, and the abundant food is a bell-shaped function of κ. For very goodness of fit is typically very high, expected reproduction small (close to 0) and very large (close to 1) values of κ, is typically very close to observed values. Data are not reproduction is not possible. The bounds follow from the always under conditions of abundant food, and also not constraint that mobilisation must be enough to pay maturity

Fig. 3. (A) The survivor function for allocation fraction κ among the 276 animal species in the add my pet collection (blue) and that for the value that maximizes reproduction rate (red). The survivor functions for the beta-distribution are also shown with parameters a = 1.9948 and b = 0.4625 (cyan) and a = 38.9 and b = 42.9 (magenta). (B) The value of κ that maximizes reproduction rate κm as function of κ. The line has slope 1. Colours indicate high-level taxa as in Fig. 1.

maintenance costs, which stay constant following puberty: beta-distribution is given by S(κ) = 1 − I κ (a;b), where I κ (a;b) p p (1 − κ) pC > pJ ,wherepC is the mobilisation rate and pJ is the incomplete beta function. Although the collection the maturity maintenance at puberty (start of reproduction), has grown by a factor of five since Lika et al. (2011b), this see Appendix 1 (Section IX). The amount of reserve in fully extension of available data barely affected the frequency grown adults remains constant for abundant food, so for distribution of κ (Fig. 3A). The optimal κ values also them mobilisation rate equals (maximum) assimilation rate seem to be beta-distributed with mean 0.482 and variance pAm, which is proportional to squared (maximum) length, 0.0034, very different from the actual κ values. The rare while maximum length is proportional to κ (see proposition coelacanth Latimeria chalumnae is among the optimal species; 3.20 in Sousa et al., 2008). The upper and lower bounds for being optimal does not imply great abundance. κ are thus the two positive roots of the cubic polynomial in κ Figure 5 shows the relationship between the ratio of − = p of (1 κ) pAm pJ .Forκ larger than the upper bound not the reproduction rate and the optimized one, sR,andthe enough energy is allocated to maturation and reproduction; acceleration factor sM. The acceleration factor is the factor for κ smaller than the lower bound the maximum size of by which the values for the specific assimilation and energy the organism is too low to allow it to assimilate enough conductance of the neonate have to be multiplied to arrive energy to pay maturity maintenance. These bounds do not at the values for the late juvenile and adult. Figure 5 shows always exist and then reproduction is not possible at all. The that the lophotrochozoans (mostly molluscs) combine a low value of κ at which the bell-shaped function for maximum relative reproduction with a large acceleration, followed reproduction reaches its maximum (κm), depends on most by the ecdysozoans. To what extent these tendencies parameter values, but Fig. 3B shows that in practice the represent an artefact is still an open question, since data maximum is reached for κ close to 0.5. on reproduction for these taxa are typically less reliable. Species in the add my pet collection can roughly be classified Eggs for these taxa are small in size and large in number (see as sub-optimal, optimal and supra-optimal on the basis of Fig. 4), and the data might include substantial measurement the maximum reproduction rate (of a fully grown adult error, which might affect parameter values. Although small with abundant food), relative to the value at optimal κ. relative egg size also occurs in ectothermic vertebrates (mostly Optimal species have a maximum reproduction rate that is fish), echinoderms and tunicates, they seem to be much less at least 80% of the maximum possible for a species with extreme in their relative reproduction, while they do show those parameters while varying κ. Sub-optimal species have considerable acceleration. This is a remarkable result. a lower maximum reproduction and a κ that is smaller than the value that maximizes reproduction; supra-optimal species also have a lower maximum reproduction, but a larger value for κ. Table 1 lists the optimal and sub-optimal species of the IV. SELECTION FOR MAXIMUM 276 species studied, Fig. 3 presents the κ values and Fig. 4 the REPRODUCTION maximum reproduction rates as a fraction of their optimised maximum. The κ values seem to follow a beta-distribution, DEB theory takes the view that parameter values are in terms of approximate empirical description with mean individual-specific and their settings have phenotypic as 0.812 and variance 0.0442. The survivor function of the well as genotypic components. Intra-specific differences are

Table 1. Species of the add my pet collection that have a sub- grow during their reproductive stage, but start reproduction optimal allocation fraction κ (left, 11 species) and the optimal directly when in the final moult. Birds seem unique in this one (right, 35 species). All other 227 species have a supra-optimal respect. Seasonal cycling is probably responsible for the fact κ. The maximum reproduction rate (R) is given as a fraction of that most bird species only start reproduction in the year the value it would have with an optimal κ (Rm). If this fraction is after their birth. Husbandry data, such as for the budgerigar less than 0.8, a species is either sub- or supra-optimal. For Gallus Melopsittacus undulatus shows that reproduction is possible gallus,IR= Indian River much earlier if seasonality is excluded. Birds’ metabolism is typically down-regulated in non-breeding seasons. Optimal species R/Rm Up-regulation prior to and during migration shows that they Chironex eckeri 1.00 manage to tune their metabolic rate to prevailing conditions. Hydra viridissima 0.99 Pelagia noctiluca 1.00 The actual reproduction patterns of birds in the field do not Beroe ovata 0.89 necessarily match their potential. Using field-collected data, Sagitta hispida 0.97 and converting cumulative reproductive output over a year to Aspidiophorus polystictos 0.92 Crassostrea gigas 0.86 a daily mean reproduction rate leads to very large (close to 1) Daphnia hyalina 0.93 values of κ and very low values of the maturity maintenance Diaphanosoma brachyurum 0.95 rate coefficient kJ matching the observed pattern of a late Oikopleura dioica 0.87 onset of reproduction. In our opinion, these extreme values Eptatretus stoutii 0.84 Lampetra planeri 0.91 are an artefact that relates to the simplification of effects of Raja clavata 0.98 seasonality. A more realistic approach would be to account Chlamydoselachus anguineus 0.98 for the cycles in up- and down-regulation of metabolism. Heptranchias perlo 0.96 Husbandry data for chickens will suffer less from the effect Heterodontus portusjacksoni 0.91 Chiloscyllium plagiosum 0.89 of seasonal variation in environmental conditions. However, Sphyrna lewini 0.96 adaptations to cycling are not completely eliminated, even in Thymallus thymallus 1.00 this species, and they still have regular ‘resting’ periods where Sardina pilchardus 0.86 Danio rerio 0.98 reproduction ceases. Pimephales promelas 0.91 Chickens have been domesticated for several millennia, Trisopterus luscus 0.96 and races have been selected to maximise meat or egg pro- Sparus aurata 0.84 duction. Figure 6 and Table 2 illustrate what this selection Zoarces viviparus 0.86 Thunnus thynnus 0.96 means in terms of parameter values. The meat-producer Mola mola 0.99 race Indian River (IR) is reared only to puberty (after which Latimeria chalumnae 1.00 it would die anyway) and is typically harvested at the peak Crinia nimbus 0.99 of integrated production: mass minus birth-mass divided by Heteronotia binoei 0.96 Tiliqua rugosa 1.00 time. The first remarkable observation on the wild race (Red Sceloporus undulatus 0.87 Jungle fowl, RJ) is that the actual value of κ is lower than Gallus gallus WL 0.97 the value that maximises reproduction (Fig. 6A). Secondly, Mirounga leonina 0.98 Phocoena phocoena 0.91 the White Leghorn (WL), which has been selected for egg production has a value of κ close to that maximising Sub-optimal species R/R m reproduction. The maximum specific assimilation rate {pAm} Asplanchna girodi 0.16 of female IR is similar to that of the wild-type RJ, but that of Folsomia candida 0.62 WL is much lower. {pAm} decreased for WL males relative Oikopleura longicauda 0.64 Thalia democratica 0.27 to values for RJ males, and was even lower in IR males. It Hippocampus whitei 0.70 is remarkable that selection on production did not increase Pleuronectes platessa 0.71 {pAm}, despite increasing maximum size. Figure 6B shows Geocrinia vitellina 0.65 the cumulative body mass increase; farmers typically harvest Gallus gallus IR 0.68 Gallus gallus RJ 0.19 at the maximum value of this statistic. The DEB-based pre- Myrmecophaga tridactyla 0.63 diction of this peak is realistic for the meat-producer IR. This Bos primigenius Holstein 0.78 case study indicates that where selection acts to maximise reproduction, κ takes an appropriate value and our method of estimating the parameters is successful in recognising this. typically small compared to inter-specific differences. The effect of selection on (DEB) parameters can be studied on chickens, because the wild race is still available and selection V. DISCUSSION has taken place in well-understood different directions. Yet birds have some remarkable properties that require Our results suggest that κ is not set on the basis of maximising discussion. First, birds typically start reproducing long after reproduction; the question then remains: what factors do their body mass has reached an asymptote. Quite a few control the value of κ? The sub-optimal (= low) values of κ ecdysozoans only reproduce in their last moult, so do not in Table 1 are puzzling in this context.

Fig. 4. (A) The survivor function for maximum reproduction as a fraction of the optimized maximum (sR) among the 276 animal species in the add my pet collection. (B) Maximum reproduction rate (Rm) at optimal value of κ as a function of the actual maximum reproduction rate R. The line corresponds to R = Rm. Colours indicate high-level taxa as in Fig. 1.

around 1400 J d−1 cm−3, while that of equally small aphids and tardigrades is much closer to the typical value of ◦ 20 J d−1 cm−3 at 20 C. In a short season of high resource productivity, food availability is not a problem. However, when resources are scarce, a high maintenance cost will not be the best strategy and they have to switch to torpor. Species that utilise resources that are more constant over time might reduce their κ to reduce their minimum food requirements, while exhibiting an economical metabolism (low maintenance). Why then do other species have a large κ, close to 1? A possible reason is to increase body size to avoid size- dependent predation or to increase their ability to average resource availability over space and time. Large body size provides a greater reserve capacity to allow smoothing of temporal variations in food availability, large home Fig. 5. The ratio of the maximum reproduction rate to the ranges and a reduction in predation risk. It also allows optimised one (sR) as a function of acceleration factor (sM) greater movement speed and distance for migrating to for the 276 entries in the add my pet collection. Colours environments with higher food availability. These effects indicate high-level taxa as in Fig. 1. The lophotrochozoans follow directly from the co-variation rules implied by DEB (dark turquoise), ecdysozoans (green), exothermic vertebrates (magenta) and invertebrate deuterostomes (black) accelerated theory (Kooijman, 1986a;Nisbetet al., 2000; Lika et al., considerably, but they segregate in this scatter plot from low to 2011a). However, the difference between a large value high relative reproduction rate. for κ and a very large one (= closer to 1; the frequency distribution in Fig. 3 shows that there are many of We here suggest that some species have a low κ to reduce these), will have little effect on maximum body size, but body size; since maximum structural length is proportional affect reproduction to a significant extent. Hence a more to κ. The minimum food density that allows survival important reason for a very large value of κ might be to increases with body size, together with the risk of not reduce reproduction, avoiding exhaustion of resources via finding enough food. This logic relates directly to the ‘waste- intra-specific competition. Survival of periods of low food to-hurry’ hypothesis (Kooijman, 2013), that suggests that availability might be a much stronger selective criterion specific somatic maintenance costs are (greatly) increased than maximisation of reproduction; avoidance of over- in species that use peaking resources to boost production exploitation of the environment might be part of this survival (growth and reproduction) and these species remain small, strategy. Predator–prey systems might co-evolve in terms of with a short life cycle. This hypothesis helps to explain why parameter settings, κ being one of these, where stability and the specific maintenance costs of copepods and daphnids is robustness might be more important than absolute values.

Fig. 6. Comparison of energetics of three races of female chicken Gallus gallus: Red Jungle fowl (green), White Leghorn (blue), Indian River (red). (A) Reproduction R as function of allocation fraction κ. The circles indicate the actual value. (B) Mass (W ) minus birth mass (W b)pertime(t) as a function of time. DEB parameters are given in Table 2.

Table 2. The parameters of the standard DEB model estimated for the male (m) and female (f) chicken Gallus gallus of the races Red Jungle fowl (RJ), the egg-producer White Leghorn (WL), and the meat-producer Indian River (IR). The parameters were ◦ estimated using data from Schutz et al. (2002). The parameters are given for 20 C, using an Arrhenius temperature T A = 19794 K. Reproduction efﬁciency is set at κR = 0.95 for all cases. The dry to wet mass ratio was set to 0.38 for RJ and WL and 0.30 for IR

Parameter Symbol Unit RJ,f RJ,m WL,f WL,m IR,f IR,m

−1 −2 Specific assimilation rate {pAm} Jd cm 427 372 270 301 435 178 Energy conductance v cm d−1 0.0083 0.0090 0.0113 0.0111 0.00965 0.0155 fraction to soma κ — 0.2486 0.4317 0.5051 0.4306 0.3492 0.6734 −1 −3 Specific somatic maintenance cost [pM]Jdcm 21.38 26.82 15.79 14.39 18.09 9.739 −1 Maturity maintenance rate coefficient kJ d 0.0025 0.0039 0.0020 0.0020 0.0020 0.0011 −3 Specific cost for structure [EG]Jcm 9918 9864 9948 9947 7709 10600 b 4 4 4 4 4 4 Maturity at birth EH J 8.99 × 10 4.61 × 10 8.14 × 10 9.72 × 10 9.12 × 10 7.43 × 10 p 6 6 6 6 6 6 Maturity at puberty EH J 2.67 × 10 1.65 × 10 2.87 × 10 3.68 × 10 6.53 × 10 2.69 × 10

Frequent ecological disasters involving introduced species birds do not feed their offspring democratically. The biggest may provide evidence of this. young, which beg most loudly for food, are fed to satiation, Supporting evidence for the hypothesis that reduced κ while smaller nestlings may die from starvation when food is functions to reduce reproduction comes from the crested scarce. Birds are near the demand end of the supply–demand penguin Eudyptes spp., which shows egg dimorphy. A small spectrum and such species may be more vulnerable to egg is laid ﬁrst, followed by a much larger one. DEB sub-maximal food intake rates. Extensive parental care is theory correctly predicts that the large egg will hatch earlier typical for demand species (‘eat according to need’, like (Kooijman, 2010), in which case the small egg is discarded endotherms), but much less common in supply species (‘eat by the parents. Crested penguin parents can only raise a what is available’, like most ectotherms). Surprisingly, we also single chick, the small egg functions as insurance, probably to found supra-optimality in most supply species. This ﬁnding compensate for the high frequency of infertility in this species. of extensive supra-optimality in supply species invites further A similar situation occurs in the shoebill Balaeniceps rex which research analysing reproductive suppression, in combination also produces two eggs, despite the parents having the ability with survival of periods of low food availability. only to raise a single chick. The controlling factor here is Allocation to reproduction should be considered in the not the physiology of producing more than one egg, but the context of evolutionary optimisation. Statistics such as ecology of raising chicks. This family-planning phenomenon population growth rate and life-time reproductive output is probably widespread in species with extensive parental are perhaps more relevant and are also (slightly different) care, which frequently includes defence of a territory during optimum functions of κ (Fig. 7), if ageing is the only cause the breeding season to guarantee an adequate food supply of death. DEB theory has an ageing module not used herein for offspring. It is also frequently observed that altricial that couples the ageing rate to energetics. However, for

reproduction differ by orders of magnitude, not subtle differences. Table 1 shows that only 13% of species have a value of κ that leads to a reproduction rate that exceeds 80% of the maximum possible reproduction for a species with that properties. Given the rigour of our procedure, and the size of the database, we see this conclusion of lack of maximisation as empirically valid. (5) So can the allocation fraction κ actually be optimised for maximum reproduction? The case study of the chicken strongly suggests that this can occur. Natural selection, therefore, does not appear to be selecting for maximum reproduction. (6) We hope that these results stimulate further contributions to the add my pet collection, and improvements to existing entries in terms of data and estimation of parameter values.

Fig. 7. Scaled reproduction rate (R, red), lifetime reproductive output (N , blue) and specific population growth rate (r, green) as functions of allocation fraction κ. Scaling is applied with respect VII. ACKNOWLEDGEMENTS to the maximum, which these functions reach at κ = 0.48, 0.55 and 0.52, respectively. Parameter values are provided in We would like to thank all contributors to the add my pet Table 2. collection, especially Carlos Teixeira, who contributed most bird entries, Starrlight Augustine, who contributed most most species ageing is not the dominant cause of death, so entries on radiata, and Paulus Schuckink for his help with these functions cannot considered to be ‘predictions’ for the the chicken data. natural situation. Very few of the yearly 3 × 1010 offspring of the ocean sunfish Mola mola will reach puberty, while the single chick of crested penguin Eudyptes spp. has a relatively high probability of reaching that state. Substantial predation VIII. REFERENCES is the rule for all species with many tiny offspring, i.e. most ectotherms, but the specification of general quantitative Calder, W. A. III (1984). Size, Function and Life History. Harvard University Press, Cambridge. rules for this population thinning is still a challenge. We need Flatt,T.&Heyland, A. (eds) (2011). Mechanisms of Life History Evolution; The Genetics species-specific ecosystem models to evaluate links between and Physiology of Life History Traits and Trade-offs. Oxford University Press, Oxford. κ Hildrew,A.,Raffaelli,D.&Edmonds-Brown, R. (2007). Body Size: The Structure and these ecological statistics, which are beyond the scope and Function of Aquatic Ecosystems. Cambridge University Press, Cambridge. of this review. Kooijman, S. A. L. M. (1986a). Energy budgets can explain body size relations. Journal of Theoretical Biology 121, 269–282. Kooijman, S. A. L. M. (1986b). What the hen can tell about her egg; egg development on the basis of budgets. Journal of Mathematical Biology 23, 163–185. Kooijman, S. A. L. M. (2010). Dynamic Energy Budget Theory for Metabolic Organisation. VI. CONCLUSIONS Cambridge University Press, Cambridge. Kooijman, S. A. L. M. (2013). Waste to hurry: dynamic energy budgets explain the (1) Animal reproduction follows the expected simple need of wasting to fully exploit blooming resources. Oikos 122, 348–357. Kooijman,S.A.L.M.,Pecquerie,L.,Augustine,S.&Jusup, M. (2011). Scenarios inter-specific relationship with maximum (structural) length, for acceleration in fish development and the role of metamorphosis. Journal of Sea where reproduction rate decreases with maximum length Research 66, 419–423. Lika,K.&Kooijman, S. A. L. M. (2011). The comparative topology of energy and energy investment in reproduction increases with cubed allocation in budget models. Journal of Sea Research 66, 381–391. maximum length. Lika,K.,Kearney,M.R.,Freitas,V.,van der Veer,H.W.,van der Meer, (2) Reproduction rate data show substantial scatter due to J., Wijsman,J.W.M.,Pecquerie,L.&Kooijman, S. A. L. M. (2011a). The ‘covariation method’ for estimating the parameters of the standard Dynamic Energy differences in relative size of neonates; energy investment in Budget model I: philosophy and approach. Journal of Sea Research 66, 270–277. reproduction is not affected by these relative size differences Lika,K.,Kearney,M.R.&Kooijman, S. A. L. M. (2011b). The ‘covariation and the scatter is much reduced. method’ for estimating the parameters of the standard Dynamic Energy Budget model II: properties and preliminary patterns. Journal of Sea Research 66,278–288. (3) The energy cost per neonate is proportional to Maino,J.,Kearney,M.,Nisbet,R.M.&Kooijman, S. A. L. M. (2013). Reconciling maximum length to the power 4; the substantial scatter theories for metabolic scaling. Journal of Animal Ecology 83, 20–29. in these data is mostly caused by large differences in specific Nisbet,R.M.,Muller,E.B.,Lika,K.&Kooijman, S. A. L. M. (2000). From molecules to ecosystems through dynamic energy budget models. Journal of Animal somatic maintenance that mainly affect maximum length; Ecology 69, 913–926. this can be explained by the ‘waste-to-hurry’ hypothesis Peters, R. H. (1983). The Ecological Implications of Body Size. Cambridge University (Kooijman, 2013). Press, Cambridge. Roff, D. A. (1992). The Evolution of Life Histories. Chapman & Hall, New York. (4) Most species have a value of κ that differs greatly Schmidt-Nielsen, K. (1984). Scaling: Why is Animal Size so Important? Cambridge from that maximising reproduction. Actual and maximum University Press, Cambridge.

Schutz,K.,Kerje,S.,Carlborg, O., Jacobsson,L.,Andersson,L.&Jensen,P. where pA is assimilation power and pC is mobilisation (2002). QTL analysis of a Red Junglefowl White Leghorn intercross reveals trade-off in resource allocation between behaviour and production traits. Behavioural Genetics power; d 32, 423–433. L3 = p / [E ] , (A2) Sousa,T.,Domingos,T.&Kooijman, S. A. L. M. (2008). From empirical patterns dt G G to theory: a formal metabolic theory of life. Philosophical Transactions of the Royal Society of London B 363, 2453–2464. = − Stearns, S. C. (1992). The Evolution of Life Histories. Oxford University Press, Oxford. where pG is growth power and pG κpC pS where κ 3 2 is allocation fraction to soma and pS = [pM] L +{pT}L , is somatic maintenance power, with volume-specific and surface area-specific somatic maintenance [pM]and{pT}, IX. APPENDIX respectively, and [EG] is specific cost for structure; and

d X. THE STANDARD DEB MODEL WITH E = p , (A3) ACCELERATION dt H R where p is maturation power and p = (1 − κ) p − p and The standard DEB model has three state variables, energy in R R C J p is maturity maintenance power. Maturation ceases, and reserve E, structural length L and maturity E . Maturity has J H allocation to reproduction starts when E = E p (or l ≥ l ); no mass or energy and is quantified as cumulative (dissipating) H H p this allocation involves the same power p .Foetal(and energy investment. Life-stage switches are linked to maturity R bud) development (mammals, several fish, salps, cnidarians) by threshold values, which are fixed parameter values: birth b, represents a variation on egg development, where metabolic metamorphosis j, puberty p. The lengths at which these switches occur (l , l and l ) are not parameters, but b j p pA 2 X t = el , (A4) depend on food history, ( ) [and so on the scaled functional p L2 response f (t)]. Temperature affects all rate parameters. The Am m changes in the state variables are simple functions of the where {pAm} is maximum specific assimilation, Lm is scaled powers, which are given in Table A1: maximum structural length and e is the scaled reserve density of the mother. The reserve density of a neonate, d 3 E = pA − pC, (A1) E/L , equals that of the mother (maternal effects); this dt rule determines the energy cost of an egg or foetus, apart from the reproduction efficiency κR, which quantifies the

−1 overhead costs for reproduction. During acceleration in the Table: A1 The scaled powers p*({pAm} Lm) ,for*= A early juvenile, {pAm} and energy conductance v increase (assimilation), C (mobilisation), S (somatic maintenance), J with length; the scaling in Table A1 uses the values of (maturity maintenance), as specified by the standard DEB model {pAm} and v at birth. No metabolic acceleration occurs if with acceleration and without heating costs for an isomorph j b 3 E = E (i.e. l = l ); metabolic metamorphosis might (e.g. of scaled length l = L/Lm,scaledreservedensitye = Ev/(L H H j b 3 {pAm}) and scaled maturity density uH = κEH/([EG] Lm )at in bivalves) or might not (e.g. in cephalopods) coincide with scaled functional response f = X/(K +X), where X denotes the a morphological one. The ratio lj = lb is the acceleration food density and K the saturation constant. Maximum length factor by which the values of {pAm} and v at birth are Lm = κ{pAm}/[pM] has only this interpretation in the absence multiplied to arrive at those after metamorphosis. The = p b of acceleration, where lj lb. Parameters: allocation fraction κ, juvenile stage is absent if E = E (i.e. l = l = l ); this = { } = H H p j b investment ratio g [EG]v/(κf pAm ), maintenance ratio k kJ occurs in e.g. Oikopleura spp. and all insects that we examined. [EG]/[pM] The expression for the mobilisation power pC follows from the weak homeostasis requirement: the chemical composition Early of the individual does not change during growth in constant Scaled Embryo juvenile Last juvenile Adult environments (possibly after a short adaptation period). power 0 < l ≤ lb lb < l ≤ lj lj < l ≤ lp lp < l ≤ 1 Feeding is proportional to structural surface area, and so to pA 2 l 2 lj 2 lj 2 2 0 fl l fl l fl l L in isomorphs, i.e. individuals that do not change in shape {pAm}Lm b b b / + / + pC 2 g+l 2 gl/lb+l 2 glj lb l 2 glj lb l during growth. Environmental conditions (temperature and 2 el g+e el g+e el g+e el g+e {pAm}Lm osmotic concentration) are assumed to be such that surface- pS 3 3 3 3 2 kl kl kl kl coupled maintenance costs (heating in endotherms, osmotic {pAm}Lm pJ p work in freshwater organisms) are negligible. The powers { } 2 kuH kuH kuH kuH pAm Lm for ingestion and defaecation apply to the environment, and not to the individual, so are excluded from Table A1. The L is structural length, E reserve, E maturity, v energy conductance, H modules incorporating food searching and ageing from the κ allocation fraction to soma, {pAm} specific maximum assimilation rate, [EG] specific cost for structure, [pM] specific somatic standard DEB model are not included here. maintenance cost, kJ maturity maintenance rate coefficient, lb The nine parameters (with units) of the standard DEB scaled length at birth, lj scaled length at metamorphosis, lp scaled model with acceleration are: specific maximum assimilation −1 −2 −1 length at puberty. rate {pAm} (J d cm ), energy conductance v (cm d ),

−1 −3 specific somatic maintenance [pM](Jd cm ), maturity A number of auxiliary parameters are required for various −1 maintenance rate coefficient kJ (d ), specific cost for types of conversion: dry to wet mass, length to mass, mass to −1 −3 structure [EG](d cm ), reproduction efficiency κR (no energy. They are: the shape coefficient δM (no units), specific b −3 units), maturity at birth EH (J), maturity at metamorphosis density of structure dV (g cm ), chemical potential of reserve j p μ −1 EH (J) and maturity at puberty EH (J). E (J C-mol ), chemical indices for hydrogen, oxygen and The remaining four primary DEB parameters that nitrogen of reserve (V) and structure (E) nHV,nOV,nNV,nHE, are not included here are: specific searching rate {F m} nOE,nNE (no units). These parameters depend on the type of 3 −1 −2 (dm d cm ), digestion efficiency κX (no units), ageing measurement, not on the structure of the DEB model. The −2 acceleration ha (d ) and Gompertz stress coefficient (no DEB model obtains respiration from the conservation law units). The assumption {pT}=0ismade. for chemical elements, which involves the chemical indices.

(Received 12 June 2013; revised 18 December 2013; accepted 31 December 2013; published online 11 February 2014)