# Exploring physiological constraints on life-history traits using Dynamic Energy Budgets

Mélanie Debelgarric, Charlotte Récapet

► To cite this version:

Mélanie Debelgarric, Charlotte Récapet. Exploring physiological constraints on life-history traits using Dynamic Energy Budgets. Ecological Modelling, 2025, 501, pp.110993. 10.1016/j.ecolmodel.2024.110993. hal-04942304

HAL Id: hal-04942304

https://hal.inrae.fr/hal-04942304v1

Submitted on 12 Feb 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Exploring physiological constraints on life-history traits using Dynamic Energy Budgets

Mélanie Debelgarric, Charlotte Récapet

<figure><img src="image_3.png" /></figure>

Université de Pau et des Pays de l'Adour, E2S UPPA, INRAE, ECOBIOP, 173 route de Saint-Jean-de-Luz, 64310, Saint-Pée-sur-Nivelle, France

## ARTICLE INFO

Dataset link: https://forgemia.inra.fr/Charlotte
.Recapet/ecomod_110993/-/releases/v1

Keywords:

Life-history theory

DEB theory

Metabolism

Physiological constraints

Evolution

## ABSTRACT

A current challenge in predicting species responses to global change is to understand evolutionary responses to rapidly changing environments and novel environmental conditions. It has been hypothesised that the speed of evolution would be contingent upon highly dependent on evolutionary constraints shaped by resource allocation trade-offs and other physiological mechanisms underlying the expression of traits. However, the majority of models employed to investigate life-history evolution remain phenomenological in nature. They fail to incorporate realistic mechanisms for the transfer and transformation of resources that are in accordance with the established laws of physics and chemistry. Our objective was therefore to explore the full range of life-history strategies that are genuinely available to organisms through realistic metabolic processes and to compare them with the predictions made by classical life-history theories. To this end, we employed the Dynamic Energy Budget (DEB) theory to model the energy allocation of individuals. We studied inter-individual variation by varying the value of energetic primary parameters (i.e. physiological processes) of the model, under constant environmental conditions (optimal temperature and ad libitum food source). Physiological processes that impact both growth and reproduction, such as energy acquisition, allocation and mobilisation, were found to reproduce the predictions of life-history theory to a certain extent. However, some discrepancies remained, mainly because DEB theory accounts for physiological retro-actions that are not articulated in life-history theories. For example, quicker growth had an indirect impact on reproduction and ageing through respectively increased resource acquisition and dilution of damage-inducing compounds. Based on those insights, we propose future directions to integrate physiology, and in particular metabolism, into models of life-history evolution.

## 1. Introduction

Predicting organisms' evolutionary responses to rapid environmental change requires understanding whether the physiology inherited from their evolutionary history might constrain evolution in response to novel environmental conditions (i.e. conditions they never encountered in their recent history; Teplitsky et al., 2014; Linck et al., 2021). Indeed, physiology acts as the integrator of genetic and environmental determinants of processes such as growth, development, reproduction, and senescence, which collectively influence an organism's overall fitness (Ricklefs and Wikelski, 2002; Violle et al., 2007). Over an organism's lifetime, these processes define a sequence of events and traits called life history. Early on, it was observed that different life history traits do not vary independently among individuals, but are often correlated within coherent "life-history strategies" (Tinkle, 1969; Tinkle et al., 1970; Van De Walle et al., 2023). Different hypotheses were put forward to explain those correlations. It was first hypothesised

that trade-offs, where a limited resource has to be shared among different functions, would explain that all life-history traits could not be optimised simultaneously, creating negative correlations between traits (Gadgil and Bossert, 1970; Stearns, 1989; Ricklefs and Wikelski, 2002). For example, plumage colouration in birds is linked to the reproductive success, with the most colourful being favoured by females (Hill, 1991). But in spite of a higher reproduction, they are more likely to be predated, which reduces longevity (Ercit and Gwynne, 2015). Along with genomic constraints (Chang et al., 2023) (such as pleiotropy affecting both survival and reproduction (Garland et al., 2022)), physiological trade-offs would delineate the spectrum of viable life history strategies available to a species. However, a more recent hypothesis was that in response to environmental factors, acting as selective pressures, the co-evolution of life-history traits maximises fitness, and is therefore mainly adaptive (Mangel and Stamps, 2001; Réale

<footnote>* Corresponding author.
E-mail address: charlotte.recapet@univ-pau.fr (C. Récapet).</footnote>
et al., 2010; Stamps et al., 1998; White et al., 2022). Indeed, an organ-
ism's strategy of allocating more energy to survival or reproduction can
be crucial when faced with extreme events, such as seabirds choosing to
survive and delaying reproduction (Cubaynes et al., 2011). Understand-
ing the actual role of resource allocation as an evolutionary constraint is
therefore crucial to predicting life-history strategies, energy allocation
patterns, and behaviours in organisms (Hansen and Pélabon, 2021). In
particular, the physiological mechanisms underlying energy allocation
remain unclear, which restricts our understanding of life history evo-
lution (Braendle et al., 2011; Cohen et al., 2017; Mathot, 2018). Our
objective in this study was to understand how bioenergetic mechanisms
would influence the expression of different life-history traits, hence
defining life-history strategies. The covariation between life-history
traits has been mainly studied through quantitative genetics, which
estimate genetic constraints via additive genetic covariances (Hansen
and Pélabon, 2021). These studies often assume linear relationships
between traits, while traits typically exhibit non-linear relationships,
due to the varying contributions of different underlying processes for
each trait (e.g. Lika et al., 2019). This discrepancy can significantly
alter the outcomes of selection (Hansen, 2006, 2013; Vasseur et al.,
2019). Because it naturally accounts for non-linearity, mechanistic
modelling seems a promising approach to study relationships between
traits and gene-by-environment interactions. An approach which links
physiological processes and expression of traits is the Dynamic Energy
Budget, or DEB, theory (Kooijman, 2010), a conceptual framework
that seeks to explain the allocation and utilisation of energy by living
organisms. By predicting relationships between physiological processes
(driven by “primary parameters” in DEB theory) and observable traits,
it may provide insights into the phenotype-to-genotype map, insights
that proved challenging to obtain empirically (Wagner and Altenberg,
1996; Singh and Krimbas, 2000). We sought to test several predictions
made by life-history theory, based on variation in different physiolog-
ical processes. First of all, the acquisition of resources determines the
total energy available for an organism to allocate to different functions.
It might thus generate a positive correlation between traits, such as
reproduction and survival, at the inter-individual level (van Noordwijk
and de Jong, 1986). Increasing resource assimilation should therefore
increase body size, reproduction, longevity, and development (thus
resulting in decreased age at puberty). Then, increased mobilisation
of the stored energy should favour both growth and reproduction,
but at the expense of reserve (closely related to body mass), which
might result in leaner individuals. Another physiological process at
play is the energy allocation between soma (or future reproduction)
and current reproduction, a central tenet of life-history theory, because
it was postulated as a main basis for trade-offs (Gadgil and Bossert,
1970; Stearns, 1989; Mathot, 2018). In this framework, increased rel-
ative investment in reproduction is supposed to come at a cost to
the soma, for example through reduced growth or more rapid age-
ing (Speakman et al., 2002). But a smaller size consequently decreases
resource acquisition and thus the absolute amount of energy available
to reproduction. As a result, the observed reproductive output is in
reality decreased when allocation to soma is too reduced (Lika and
Kooijman, 2003). Finally, under the disposable soma theory of ageing,
increased investment in maintenance per unit body mass is assumed
to lengthen lifespan, because of more efficient repair of molecular
and cellular damage (Kirkwood and Holliday, 1979). At the same
time, high maintenance costs will decrease the energy available to
growth and reproduction, hence a negative influence on body mass,
size or reproductive output (Garvey et al., 2004; Garvey and Marschall,
2003). Those differences in life-history strategies have been linked to
metabolic rate within a “pace-of-life” or “rate-of-living” syndrome:
a high metabolic rate would be associated to rapid growth in early
stages of life, early reproduction, high reproductive rate but shorter
lifespan (Réale et al., 2010; Royauté et al., 2018; Campos-Candela
et al., 2019; Wright et al., 2019; Závorka et al., 2015). To test those
predictions, we used an individual-based model for *Daphnia magna* to

quantify metabolic processes in an optimal environment (non-limited
food and optimal temperature), based on DEB theory. This innovative
approach has the possibility to uncover the exact processes responsible
for observable trait correlations among individuals, and thus enhance
our overall understanding of evolutionary biology.

## 2. Material & methods

### 2.1. DEB theory

#### 2.1.1. Description of the theory

DEB theory describes the energy uptake and allocation in organisms. It is an individual-based model which considers that the biomass of a living organism is always composed of at least 2 pools: Reserve *E* and Structure *V*. According to the life stage, some energy may be dissipated for development (quantified as Maturity *E*<sub>H</sub>) in juveniles or stored into a Reproduction buffer *E*<sub>R</sub> in adults (1). The dynamics of state variables *E*, *V*, *E*<sub>H</sub> and *E*<sub>R</sub>, are described by a system of differential equations (1) and constrained by the different energy fluxes (*p*) between these pools. First, the energy assimilated from food resources is stored in the Reserve (*E*). Next, this energy will be mobilised and allocated to somatic processes or to Maturity and Reproduction according to the κ-rule. The κ-rule stipulates that a fixed fraction κ of the energy mobilised from the Reserve will be allocated to growth and somatic maintenance (respectively increase and maintenance of Structure *V*) and a fraction (1-κ) will be allocated to development, maintenance of new functions, and reproduction (respectively increase in Maturity *E*<sub>H</sub>, maintenance of Maturity, and increase of the Reproduction buffer *E*<sub>R</sub>). Maintenance has priority over growth, development and reproduction: somatic maintenance is a fixed polynomial function of Structure and maturity maintenance is proportional to Maturity. Only what remains may be used respectively for growth and development or reproduction. The calculation of those different energetics fluxes is based on a set of primary parameters (Table 1 and Appendix A). Different variants of DEB models exist to characterise organisms with different ecologies (Kooijman, 2014; Llandres et al., 2015; Marques et al., 2018). This study considers the simplest model, called the standard (std) DEB model. In this case, the individual has three life-stages (embryo, juvenile and adult) and does not vary in morphology during its life cycle (isomorphic). The different life-stages are separated by life events: birth (start of autonomous feeding) and puberty (once the organism starts storing reserve specifically for reproduction). The level of Maturity determines the transition between life stages: when Maturity reaches the threshold for a particular transition, such as birth, the organism changes life stage, in this case from embryo to juvenile. Following puberty, the flux previously going to development is reallocated with an efficiency κ<sub>R</sub> to the Reproduction Buffer *E*<sub>R</sub>, which will be used to fuel species- and sex-specific reproductive processes (in particular the production of gametes). Our model only simulates females because *Daphnia magna* mostly use parthenogenesis under benign environmental conditions.

#### 2.1.2. Choice of between-individual varying primary parameters

To test our hypothesis, we selected six primary parameters directly influencing processes referred to in life-history theories: the surface-specific assimilation rate {$\hat{p}_{Am}$}, the fraction of mobilised energy allocated to soma $\kappa$, the volume-specific somatic maintenance rate {$\hat{p}_{M}$}, the maturity maintenance rate $\dot{k}_{J}$, the volume-specific costs of structure [$E_{G}$] and the energy conductance $\dot{v}$ (Table 1). {$\hat{p}_{Am}$} is the maximum assimilation rate per unit of structural surface and influences the incorporation of external resources (such as food) into Reserve *E*. An increase in {$\hat{p}_{Am}$} will therefore have a direct impact on the amount of energy stored in Reserve (Campos-Candela et al., 2019; van Leeuwen et al., 2002; Wang and Widdows, 1993) and in turn contribute to body mass increase (Uchmański, 2016; van Leeuwen et al., 2002). Since energy mobilisation from the reserve is dependent upon the energy stored in reserve, variation in {$\hat{p}_{Am}$} will lead to a change
<figure><img src="image_4.png" /><figcaption>Fig. 1. Outline of DEB theory showing the influence of primary parameters. The boxes (E, V, E<sub>H</sub> and E<sub>K</sub>) represent energy pools. The arrows represent energy fluxes.</figcaption></figure>

in all downstream bioenergetic fluxes and thus in overall life history strategies.

v̇ represents the energy conductance. It is involved in the calculation of the mobilisation rate ṁ<sub>C</sub>. Its variation will cause a difference in the total amount of energy mobilised to fuel the different physiological functions, but will not influence the allocation of energy between them. An increase in v̇ should cause a faster utilisation of Reserve, thus a decrease in E (Campos-Candela et al., 2019), a faster growth, a higher egg production and an earlier puberty (Lika et al., 2011). However, this parameter has no impact on maximum size (Kooijman, 2010).

κ represents the fraction of energy allocated to somatic functions (growth and somatic maintenance), as opposed to reproduction and development. Its variation can therefore considerably modify life history traits (Sadoul et al., 2020). When κ is high, growth is rapid but less energy is available for reproduction. However, when κ is low, the reduced growth will result in low exchange surface, hence reduced assimilation, and in turn reduced reproduction (Lika et al., 2011). The optimum for κ between these two situations is species specific, i.e. dependent on the values of the other parameters.

[p̂_M] and k̂_J represent the volume-specific somatic maintenance rate and the maturity maintenance rate, respectively. The variation of these two parameters will therefore affect the amount of energy used by the organism for its somatic maintenance (p̂_S) and that related to maturity (p̂_J). A high value should cause a slower growth rate and/or lower reproduction (Lika et al., 2011).

[E_G] is the amount of energy needed to create one unit volume of structure. If the value is high, growth will be slower because each

mobilised unit of reserve is transformed into less structure. However, birth and puberty should occur early as more energy is mobilised from the reserve (Lika et al., 2011).

In this study, we chose to vary primary parameters one at a time. It is important to remember that in nature, parameters do not vary independently but rather follow several covariation patterns (e.g. Augustine et al., 2019). However, our goal was no to reproduce naturally occurring empirical patterns but rather to highlight by which mechanisms each parameter can influence the expression of phenotypic and life-history traits, independently from the others. In this way, we can contribute to the generation of sound hypotheses for studying the effects of parameter covariation on the life history of organisms (see Fig. 2).

## 2.2. Database & initialisation

For background values of primary parameters, we chose values estimated for *Daphnia magna* because (i) the life cycle of this species can be described through the simplest type of DEB model, referred to as the std model, and (ii) due to its use in both evolution and ecotoxicology research, its DEB parameters are better estimated than those of other species described by the std model. Parameter values for this species were obtained from its entry in the *AddMyPet* (*AmP*) database (Kooijman and Gergs, 2023). A std DEB model including mortality involves 15 primary and auxiliary parameters (Table 1, Appendix A). We implemented one-at-a-time variation in six primary parameters to evaluate their effect on inter-individual variation in
<figure><img src="image_5.png" /><figcaption>Fig. 2. Hypothesised influence of DEB primary parameters on energy fluxes and pools. The coloured (resp. dotted) arrows represent an increase (resp. decrease) in energy fluxes.</figcaption></figure>

<table><caption>Table 1
Studied variation in DEB primary parameters. Fixed parameters are detailed in Appendix A.</caption><thead><tr><th>Notation</th><th>Description</th><th>Min.</th><th>Max.</th><th>AmP value</th><th>Unit</th></tr></thead><tbody><tr><td>{p̂<sub>Am</sub>}</td><td>surface-specific maximum assimilation rate</td><td>150</td><td>1600</td><td>313.169</td><td>J cm<sup>-2</sup> d<sup>-1</sup></td></tr><tr><td>κ</td><td>fraction of mobilised energy allocated to soma</td><td>0.16</td><td>1.00</td><td>0.58069</td><td>–</td></tr><tr><td>[p̂<sub>M</sub>]</td><td>volume-specific somatic maintenance rate</td><td>350</td><td>3950</td><td>1200</td><td>J cm<sup>-3</sup> d<sup>-1</sup></td></tr><tr><td>k̂<sub>J</sub></td><td>maturity maintenance rate</td><td>0.01</td><td>0.50</td><td>0.2537</td><td>d<sup>-1</sup></td></tr><tr><td>[E<sub>G</sub>]</td><td>volume-specific costs of structure</td><td>1000</td><td>25 000</td><td>4400</td><td>J cm<sup>-3</sup></td></tr><tr><td>ν̂</td><td>energy conductance</td><td>0.15</td><td>0.80</td><td>0.1858</td><td>cm d<sup>-1</sup></td></tr></tbody></table>

the modelled traits. To this aim, we generated 100 different values regularly distributed in a defined interval for each parameter (Table 1). The bounds of the intervals were fixed as the lowest and highest value at which the model could run (i.e. at which the organism was viable). Parameters were varied one at a time, while keeping the others fixed to their value for *Daphnia magna* in the *AmP* database (Kooijman and Gergs, 2023).

Environmental conditions (temperature *T* and food density summarised in the scaled functional response *f*) represent forcing variables in the system. Temperature was fixed through time at 20 °C, which is the optimal temperature for this species (Gerber et al., 2018; Paul et al., 2004). The food density was set at *f* = 1, corresponding to an unlimited resource.

The model was coded in R 4.1.2 using the RStudio interface 2022.12.0 Build 353. The simulation started at fertilisation. The initial amount of reserve was taken as the amount of energy in the egg for a female *Daphnia* fed ad libitum, whereas the initial volume of structure was set to a very small size (Appendix A). The initial values of *E*<sub>H</sub>, *q̇* and *ḣ* were set to zero. The set of differential equations was integrated numerically using the *ode* function from the *deSolve* package, version 1.40 (Soetaert et al., 2010). The integration was performed over 100 days, which is twice than the observed lifespan of the species under different climatic conditions (Adamczuk, 2020: about 50 days). The choice of a longer simulation time was due to the fact that the variation of the primary parameters can be 'beyond reality' and therefore generate lifespans that are not observable in nature.

## 2.3. Outputs of the model

The values of the state variables and energy fluxes obtained from the integration of the std DEB model were used to calculate six observable traits: the maximum growth rate *r*, the body mass at puberty $W_w^p$, the respiration rate at puberty $J_O^p$, the mean lifespan $A_d$, the age at puberty $A_p$ and the reproduction rate $\bar{E}$. Those 6 traits were selected because they define the main axes of life-history variation, such as pace-of-life.

The maximum growth rate referred to the maximum increase in length per unit time during the post-embryonic life. Under constant food and temperature, the standard DEB model predicts a von Bertalanffy growth curve (Bertalanffy, 1934). The maximum growth rate may therefore be calculated as follows:

$$r = \max\left(\frac{dL}{dt}\right), \quad \max(r_B \cdot (L_\infty - L)) = r_B \cdot (L_\infty - L_{\text{min}}) = r_B \cdot (L_\infty - L_{\text{birth}}) \quad (1)$$

where $r_B$ is the von Bertalanffy growth coefficient, $L_{\text{birth}}$ the length at birth and $L_\infty$ the ultimate length. The value of $L_{\text{birth}}$ was estimated as the simulated structural length of the individual just after reaching the juvenile stage. Ultimate length was calculated following section 2.6 in Kooijman (2010) for an ectotherm:

$$L_\infty = f \kappa \frac{\{\dot{p}_{Am}\}}{[\dot{p}_M]} \quad (2)$$
whereas von Bertalanffy growth coefficient was calculated as follows:

$$r_B = \frac{1}{3} \cdot \frac{[\dot{p}_M]}{E_G + \frac{f\kappa[\dot{p}_{Am}]}{\nu}} \qquad (3)$$

Body mass (in mg) was calculated based on structural volume and on the energy included in the Reserve E as follows:

$$W_{\nu} = \left( \frac{0.2V + \frac{E}{\xi_{wE} \cdot 1000}}{0.2} \right) \cdot 10^3 \qquad (4)$$

where $\xi_{wE}$ is a constant parameter representing the whole-body energy density of dry biomass (Appendix A). As a simplification, we assumed eggs were produced continuously and therefore excluded the reproductive buffer from the calculation of body mass. To standardise the analysis, we reported the wet weight of each individual at puberty $W_{\nu}^p$, expressed in milligrams. The metabolic rate of the organism was estimated using the respiration rate $J_O$ (µg h⁻¹), i.e. oxygen consumption per unit time. DEB theory derives the respiration rate from the matrix of energy fluxes p in the organism (in J d⁻¹):

$$\dot{p} = [\dot{p}_A \ \dot{p}_D \ \dot{p}_G] \qquad (5)$$

Energy fluxes were converted to fluxes of mineral elements (in h⁻¹), based on the chemical transformations corresponding to the different fluxes:

$$\dot{J}_M = -(n_M \cdot n_O^{-1}) \cdot \eta_O \cdot \mathrm{diag}(\dot{p}) \qquad (6)$$

where $n_M$ was the matrix of chemical indices for minerals, $n_O$ for organics and $\eta_O$ the mass converter (Appendix B).

$$\begin{align*}
\eta_O &= \begin{bmatrix} -\eta_{XA} & 0 & 0 \\ 0 & 0 & \eta_{VG} \\ \mu_E^{-1} & -\mu_E^{-1} & -\mu_E^{-1} \\ \eta_{PA} & 0 & 0 \end{bmatrix}, & n_M &= \begin{bmatrix} 1 & 0 & 2 & 0 \\ 0 & 2 & 1 & 0 \\ 0 & 0 & 2 & 0 \end{bmatrix} \\
n_O &= \begin{bmatrix} n_{CX} & n_{HX} & n_{OX} & n_{NX} \\ n_{CV} & n_{HV} & n_{OV} & n_{NV} \\ n_{CE} & n_{HE} & n_{OE} & n_{NE} \\ n_{CP} & n_{HP} & n_{OP} & n_{NP} \end{bmatrix}
\end{align*}$$

Finally, in order to calculate the respiration rate $\dot{J}_O$, the molar flux of oxygen per day was then converted to a mass flux per hour (µg h⁻¹):

$$\dot{J}_O = -\dot{J}_{M,*3} \cdot (32 \times 10^{-6}/24) \qquad (7)$$

In order to be able to compare the different individuals, since the parameters vary from one individual to another, we chose to calculate the respiration rate at puberty. As $\dot{J}_O$ is the global metabolic rate and increases with body mass, we presented the mass-specific respiration rate $m\dot{J}_O$ (µgO² mg⁻¹ d⁻¹), obtained by dividing the respiratory rate at puberty $\dot{J}_O^p$ by the body mass at puberty $W_{\nu}^p$. In DEB theory, age-related mortality (i.e actuarial senescence) is assumed to be proportional to the concentration of cellular damages (Maury and Poggiale, 2013), which increases at a rate proportional to the intracellular concentration of reactive oxidative substances (ROS) and other damage inducing compounds. The amount of these damage inducing compounds is itself proportional to the rate of energy mobilisation $\dot{p}_C$ (Kooijman, 2010; van Leeuwen et al., 2010). Survival was thus calculated following the equations 6.3 to 6.5 in Kooijman (2010), which are a simplification applicable when the growth period is short relative to lifespan. To calculate the survival $S$, and then the lifespan, we integrated two additional states variables, the acceleration of ageing $\ddot{q}$ and the hazard

rate $\ddot{h}$:

$$\ddot{q}(t) = \frac{6\dot{h}_W^3}{\dot{h}_G}(\exp(\dot{h}_G t) - 1) \\ \ddot{h}(t) = \frac{6\dot{h}_W^3}{\dot{h}_G^2}(\exp(\dot{h}_G t) - 1 - \dot{h}_G t) \qquad (8)$$

$$S = \exp\left(\frac{6\dot{h}_W^3}{\dot{h}_G}\left(1 - \exp(\dot{h}_G t) + \dot{h}_G t + \frac{\dot{h}_G^2 t^2}{2}\right)\right)$$

$$; \text{ where } \dot{h}_W^3 = \frac{\dot{h}_G \dot{e} \dot{v}}{6L} \text{ and } \dot{h}_G = \frac{\dot{e} \dot{G} \dot{v} L^2}{L_m^3}$$

The predicted mean lifespan for each individual was then calculated as the adaptive Simpson quadrature function of $S$ divided by the somatic maintenance rate coefficient $k_M = [\dot{p}_M]/[E_G]$:

$$\begin{align}
t_M &= \Gamma\left(\frac{3}{4}\right) / \dot{h}_W \notag \\
A_d &= \frac{t_M}{[\dot{p}_M]/[E_G]} \tag{9}
\end{align}$$

The age at puberty $A_p$ was defined as the moment when the threshold $E_H^p$ is reached and the organism starts allocating energy to the Reproduction Buffer $E_R$.

Finally, the reproductive rate $\bar{E}$ was defined as the mean number of eggs produced per day over the whole duration of the individual's life. It was calculated as the cumulative energy invested in reproduction $E_R$ when reaching the mean lifespan $A_d$, divided by the energy required for the production of one egg $E_0$ and by the lifespan of the organism:

$$\bar{E} = \frac{(E_R/E_0)}{(A_d - A_b)} \qquad (10)$$

with $A_b$ corresponding to the age at birth and $A_d$ the mean lifespan.

### 3. Results

The variation in phenotypic and life-history traits generated by variation of the different primary DEB parameters is shown in Fig. 3. The observed variation and underlying mechanisms are described below for each parameter. Additionally, some traits used as intermediate steps in calculations and whose patterns might help interpretation are depicted in Appendix D: ultimate Length $L_\infty$, von Bertalanffy growth rate $v_B$ and whole-body metabolic rate at puberty $\dot{J}_O^p$.

#### 3.1. Specific assimilation {$\dot{p}_{Am}$}

Increased assimilation resulted in a high weight at puberty despite an earlier puberty, thanks to a much more rapid growth and to increased storage in the reserve. The maximum size was also increased (Eq. (2)). The organism had to expend more energy to maintain its larger structure, which combined with the increase in other fluxes of dissipated energy, resulted in higher total respiration rate, whereas the mass-specific metabolic rate remained constant. The lifespan slightly increased, implying that the dilution of damages through increased growth counteracted their increased production due to a higher mobilisation flux.

#### 3.2. Energy conductance $\dot{v}$

When energy conductance increased, more energy was mobilised from the reserve both for growth and development. However, body mass at puberty decreased due to smaller reserve and earlier puberty. Increased energy conductance also contributed to higher respiration rates, as well as increased mass-specific respiration rate. Lifespan was shorter, which could explain the decreased reproductive rate since the organism died at a smaller size. In this case, increased growth did not compensate for the increase in damaged compounds. Although the range of traits variation appears small compared to those generated by variation in other parameters (Fig. 3), variations in energy conductance
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Covariation between primary parameters and traits. The units of primary parameters are detailed in Table 1. The red curves correspond to a positive correlation and conversely the blue ones for a negative correlation. The yellow curves stand for no significant correlation (or an ellipse for the relation between kappa and the reproduction rate). The dotted lines correspond to the value of primary parameters in AmP (detailed in Table 1). An essential point to clarify is that data from the relation between Ē in function of {ρ̂$_{Am}$} and [ρ̂$_{M}$] has been truncated for the visualisation, because there are really high numbers of eggs per time for extreme values of both parameters (respectively 477 eggs/h for {ρ̂$_{Am}$} = 1600 and 78 eggs/h for [ρ̂$_{M}$] = 350).</figcaption></figure>

overall reproduced a fast-slow continuum. Indeed, high values of this
parameter generated individuals with more rapid growth, earlier pu-
berty, smaller size at puberty, higher mass-specific metabolic rate and
shorter lifespan, compared to individuals with low values of energy
conductance.

3.3. Fraction of mobilised energy allocated to soma κ

When energy allocated to soma increased, growth was fast and
puberty occurred later, hence a larger body mass at puberty. We also
observed a high respiration rate: the increase in somatic maintenance
and overheads of growth was compensated by the decrease in maturity
maintenance (which remains constant after puberty) or overheads of
reproduction. However, mass-specific respiration rate decreased. The
lifespan slightly increased. We observed a non-monotonous relationship
between kappa and egg production, consistent with our prediction.
When a large fraction of energy was invested in growth, the absolute
amount available to reproduction might decrease; but when a large
fraction of energy was invested in reproduction, growth was reduced
leading to lower assimilation and therefore less energy available for all
biological processes including reproduction. Thus, the optimal value in
terms of egg production was intermediate.

3.4. Somatic maintenance [$\dot{p}_M$]

A higher [$\dot{p}_M$] resulted in a slightly lower body mass at puberty,
because more energy is preempted for maintenance and thus not avail-
able for growth at any given size. Both whole-body and mass-specific

metabolism was also higher due to the higher quantity of energy
dissipated for somatic maintenance. Lifespan was shorter because of
a lower dilution of damages by growth and an increased mobilisa-
tion flux which increases damages. The age at puberty was slightly
increased and reproductive rate was reduced, through the effect of
lower growth and therefore lower assimilation, and in the later case,
through reduced lifespan. In conclusion, individuals with a high value
in somatic maintenance [$\dot{p}_M$] had less energy available for both growth
and reproduction.

3.5. Maturity maintenance rate coefficient $\dot{k}_J$

Parallel to the somatic maintenance, maturity maintenance is a
dissipation process proportional to maturity. That is why we did not
observe any consequence of its variation on growth or lifespan. How-
ever, increased maturity maintenance slowed down development, with
a later age at puberty. Reproduction rate slightly decreased through
the combined effect of later puberty and reduced energy flow into
reproduction. We observed an increased respiration rate which was
mostly due to increased size at puberty, because mass-specific respi-
ration rate remained fairly constant. In conclusion, the variation of $\dot{k}_J$
mostly impacted age at puberty and reproductive rate but produced few
other effects.

3.6. Volume-specific costs of structure [$E_G$]

When volume-specific costs of structure [E<sub>G</sub>] were high, we ob-
served a decrease in growth rate and body mass at puberty, consistent
with the need for a larger amount of the reserve to produce the same amount of structure. On the other hand, the total metabolic rate increased until reaching a maximum value around the parameter value for *Daphnia magna*, and then decreased, whereas mass-specific metabolic rate strongly increased. Despite the lower dilution by growth, the lifespan was longer due to a lower mobilisation flux. Because of the lower assimilation due to a smaller size, less energy was available for development and reproduction: the organism had a later puberty and a slightly smaller reproductive rate. Apart from the effect on mass-specific metabolic rate, variation in [$E_G$] thus reproduced a fast-slow pace-of-life continuum. In fact, lower values of [$E_G$] were linked to fast strategies (rapid growth, increased reproduction, early puberty and short life span).

# 4. Discussion

## 4.1. How do DEB primary parameters influence predicted traits?

This research investigated the relationship between primary physiological parameters and organismal traits predicted by DEB theory. Those predictions were mostly consistent with those of life-history theory, but some differences remained. Some of those differences came from theoretical discrepancies between life-history theory and Dynamic Energy Budget theory. Firstly, as predicted by the acquisition vs. allocation hypothesis, increasing resource assimilation resulted in increased growth rate, earlier puberty, longer survival and higher reproductive rate. Such effects of alterations in assimilation efficiency have been observed in a wide range of organisms (Wang and Widdows, 1993; Stavrakidis-Zachou et al., 2019; Thomas et al., 2019; Sadoul et al., 2020). Although the overall increase in energy fluxes through the organisms also translated into an increase in total respiration rate, the rapid growth meant that mass-specific respiration rate decreased. The dilution of damage-inducing compounds also explained the increased lifespan. This mechanism differed from life-history theory which hypothesises that increased resource acquisition will allow the organism to invest more in maintenance. Following DEB theory, maintenance cost per unit structure, a primary parameter, remained fixed. This means that when more energy was assimilated, the increase in assimilation increased structural volume, which in turn increased somatic maintenance $\dot{p}_S$. Thus, the link between assimilation and maintenance was not driven by a increased investment in maintenance per unit structure, but by an increase in structural volume.

Life-history theory assumes that organisms face a trade-off between investing in reproduction or investing in somatic growth and survival (Stearns, 1989; Niven and Laughlin, 2008). Most studies focus on the existence of a negative correlation between (1) lifespan and/or growth rate and (2) reproduction. However, modelling of this physiological constraint through DEB theory did not support a monotonous and negative effect of allocation to structural growth on reproduction. Conversely, we found that reproduction rate was optimised at an intermediate value of $\kappa$ (around 0.65), while extreme values (either low or high) resulted in a diminution of reproductive outcomes. Indeed, reduced investment growth had an indirect effect on reproduction by reducing the exchange surface for resource acquisition (Lika and Kooijman, 2003).

Two parameters mostly reproduced a pace-of-life continuum. More rapid mobilisation from the reserve had only limited effect on traits, because at the tested values, weak homoeostasis (constant ratio of reserve on volume) mostly controls the mobilisation flux. The observed relationships were however consistent with a pace-of-life variation: rapid growth, earlier puberty and decreased lifespan, together with higher respiration rates. Similarly, an increase in the costs of structure resulted in slower growth and lower weight at puberty, and consequently lower respiration rate (i.e. metabolic rate), later puberty and lower reproduction. This additionally confirmed that the use of DEB theory may translate the existing trade-off between reproduction

and growth. This was also found by Sadoul et al. (2020), who modelled a negative effect on growth in European sea bass but no, or at least less, impact on reproduction. Increased costs of structure also allowed for a longer lifespan by reducing energy mobilisation, due to weak homoeostasis. Despite this reduction in energy use, mass-specific metabolic rates strongly increased due to slower growth.

Maintenance processes should enhance lifespan following life-history theory. However, DEB theory distinguishes somatic from maturity maintenance, leading to some differences. An increase in somatic maintenance costs leads to reduced growth rates, later puberty and reduced weight at puberty, whereas an increase in maturity maintenance did not affect growth rate, so that the later puberty led to increased weight at puberty. The total respiration rate at puberty increased in both cases, but for different reasons: increased mass-specific respiration rate for somatic maintenance but larger body mass at puberty for maturity maintenance. Because lifespan depends on the mobilised energy and on the volume of structure, higher somatic maintenance resulted in shorter lifespan because cellular damages were diluted in a smaller volume of structure, whereas maturity maintenance did not affect lifespan. Higher maintenance costs reduced reproductive rate either through reduced size hence food intake (for maturity maintenance) or through later puberty (for maturity maintenance).

## 4.2. Linking DEB & evolution

We showed that bioenergetic parameters may shape the range of life-histories available to an organism. Some of those mechanisms could not be captured in the more qualitative predictions of classical life-history theory. Hence, bioenergetic parameters may constrain the optimisation of life-history strategies, influencing growth, reproduction and survival. However, our approach did not explicitly include any measure of fitness or any realistic simulation of selection. Our study is thus only a first step in delineating a research programme for physiologically-explicit evolutionary theory. First, simulations were performed under optimal environmental conditions, whereas the allocation of energy towards growth, maintenance, and storage tissues is influenced by various factors such as predation risk, resource availability, and seasonal changes (Louati et al., 2020; Mogensen and Post, 2012). Seasonal variation in food availability results in different reproductive output relative to constant environments (Mariño et al., 2021). Variations in temperature can influence how energy is allocated to processes like growth and lipid storage, ultimately affecting growth, metabolism and reproduction rates in both ectotherms and endotherms (Niven and Laughlin, 2008; Speakman, 2005; Speakman et al., 2002; Morash et al., 2021; Maino et al., 2016). In freshwater organisms, hypoxia may also modulate physiological parameters (Wang and Widdows, 1993). Moreover, organisms often prioritise growth in size during periods of high predation risk, shifting towards energy storage as seasons change (Ivan and Höök, 2015; Jacobs et al., 2012). This dynamic allocation strategy helps in maximising survival and reproductive success by adapting to environmental conditions and balancing trade-offs between growth, maintenance, and storage tissues. To generalise, phenotypic plasticity in physiological processes themselves allows life-history to adjust to a changing environment in a short time scale. Thus, phenotypic plasticity could be a short-term evolutionary driver via phenotypic alterations and potentially lead to the selection of a set of life-history traits in a longer time-scale (Ricklefs and Wikelski, 2002). Future studies would therefore investigate the responses to environmental variation both between individuals and within one individual's life cycle. Another limitation of our study is that the effects of different parameters were tested one-at-time, whereas selection would optimise a combination of parameters. Indeed, many physiological processes interact together to define the expression of traits (through antagonistic or synergetic interaction, for example). A change in one parameter could therefore change the effect of another. For example, a high assimilation compensates for low mobilisation
leading to a high biomass due to abundant reserve in the New Zealand
pigeon (Mariño et al., 2021). A solution is to vary simultaneously
several primary parameters to get a full understanding of the actual
physiology-to-phenotype mapping resulting from DEB theory. Never-
theless, this preliminary investigation allows us to understand the
influence of each physiological process (represented through the DEB
primary parameters). This is essential to establish the predictive power
of future further investigation to determine the expression of the traits
(and evolutionary potential) when the parameters interact, and perhaps
to identify some selection. Moreover, the methods presented in this
study can help to establish the influence of toxicant and ecological risk
assessments at the individual level, as has already been done by Martin
et al. (2013), or even at the population level (Jager and Zimmer, 2012),
thus helping to fill existing data gaps in this field (Accolla et al., 2020).

A proper investigation of selective processes could not overlook
genetics and reproductive dynamics. For evolution to take place over
the long-term, traits must be heritable, i.e. part of their variation must
be related to genetic variation (Heino and Dieckmann, 2008). Indeed,
genetically-based traits have a stronger impact on ecological dynamics
than plastic-induced traits (Therry et al., 2019). Genetic variation
in physiological response ranges increases adaptability based on ge-
netic information, contributing to adaptive potential (Gregorius, 1997).
However, it was recognised early on that the evolution of variability
itself is crucial to evolutionary processes (Waddington, 1942). Since
primary parameters govern plasticity in DEB theory, they are perfect
candidates to investigate the evolution of plasticity. However, the
genetic basis for DEB parameters remains little known due to empirical
difficulties in obtaining adequate data at the individual level (see Jager,
2013; Oliveira et al., 2024, as examples). Hence the approaches we
delineate below all make the assumption that primary parameters are
fully genetically determined (no plasticity) and vary independently
from each other within the limits of a viable organism (no epistasis),
focussing on the plasticity and epistasis emerging from the bioenergetic
model itself. However, given the evidence for covariation between
primary parameters among species (Augustine et al., 2019; Kooijman
and Augustine, 2022; Kooijman, 2020; Lika et al., 2020; Marn and
Kooijman, 2022), they most likely exhibit correlations within species
as well.

Acknowledging these limitations, there would be several routes to
integrate DEB theory and evolutionary theory. DEB theory has already
been used to simulate individual-variable life histories based on physio-
logical parameters through individual-based population models (Jager
et al., 2004; Monaco et al., 2019; Nisbet et al., 2016). However, very
few studies sought to investigate actual selective processes using DEB
theory, mostly using adaptive dynamics (Kooi and Van Der Meer, 2010;
Troost et al., 2005). A first approach would be to estimate the adaptive
value of organisms with different sets of primary parameters under
different environmental regimes through lifetime reproductive success
and individual intrinsic rate of increase (Caswell, 2001; Brommer et al.,
2002). Given the computation resources and time required to run a
large set of models including variation in both primary parameters
and environmental variables, this simple approach might be the most
accessible in the short term. Adaptive dynamics would provide a more
refined estimate of fitness through invasibility, at the cost of slightly
increased computing time. Such optimisation approaches would how-
ever not account for ecological and reproductive interaction between
individuals. This is why integration of DEB theory into population-
based models including simplified genetics (or demogenetic models)
would be necessary to really assess the constraints posed by physiology
on the evolution of traits in realistic conditions (Nisbet et al., 2000; Ivan
and Höök, 2015; Lamarins et al., 2022).

5. Conclusion

By studying the variation of DEB primary parameters, we could see
the emergence of varied profiles of traits, sometimes unexpected from a

life-history theory perspective, but explicable in terms of bioenergetics.
In particular, DEB theory was able to capture complex physiological
retro-actions, such as the indirect effects of growth on resource ac-
quisition and dilution of damaged cellular compounds, which resulted
in non-monotonous or counter-intuitive relationships. Our results thus
call for a deeper integration of physiological mechanisms into mod-
els of biological evolution, especially when studying evolution in the
face of rapid environmental change. Despite the computational chal-
lenges, such integration could build on a range of existing approaches
combining ecological processes, intraspecific variability and genetic
transmission of traits, but rarely those three together. In this frame-
work, life-history traits will be considered as emerging properties of
the physiological traits under selection. Fully exploiting this approach
will however require more extensive testing of some key assumptions in
DEB theory (Kearney and White, 2012) and estimations of the plasticity
and genetic basis for its primary parameters in a wider range of species.

CRediT authorship contribution statement

Mélanie Debelgarric: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Formal analysis, Data curation, Conceptualization. Charlotte Récapet: Writing – review & editing, Writing – original draft, Validation, Supervision, Software, Methodology, Funding acquisition, Conceptualization.

Declaration of Generative AI and AI-assisted technologies in the
writing process

During the preparation of this work the authors used QuillBot (a
Learneo, Inc. business) in order to improve the writing. After using this
tool/service, the authors reviewed and edited the content as needed and
take full responsibility for the content of the published article.

Funding

This work was supported by the ECODIV department of INRAE
(French National Research Institute for Agriculture, Food and the Envi-
ronment) and by the iSite E2S (Energy and Environment Solutions) of
University Pau Pays de l'Adour (PhD stipend to M. Debelgarric).

Declaration of competing interest

The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.

Acknowledgements

The authors would like to thank Jacques Labonne and two anony-
mous reviewers for valuable suggestions on previous versions of this
work.

Appendix A. Fixed parameters of the dynamic energy budget model

Primary parameters directly determine the dynamics of the state
variables, whereas auxiliary parameters link state variables to observ-
able traits (see Table A.1).

Appendix B. Chemical parameters of the dynamic energy budget model

Chemical parameters for the respiration rate $J_O$ (Eq. (7)). The table
gives the values of chemical indices $n$ for each conditions (for example,
chemical index for Carbon and Food is noted as $n_{CX}$). See Table B.1.
<table><caption>Table A.1</caption><thead><tr><th>Description</th><th>Notation</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td colspan="4">Primary parameters - Fixed</td></tr><tr><td>maturity at birth</td><td>E<sup>b</sup><sub>H</sub></td><td>0.01379</td><td>J</td></tr><tr><td>maturity at puberty</td><td>E<sup>b</sup><sub>H</sub></td><td>0.3211</td><td>J</td></tr><tr><td>surface-specific somatic maintenance</td><td>{p<sub>T</sub>}</td><td>0</td><td>J d<sup>-1</sup> cm<sup>-2</sup></td></tr><tr><td>Arrhenius temperature</td><td>T<sub>A</sub></td><td>6400</td><td>K</td></tr><tr><td>Weibull aging acceleration</td><td>h<sub>a</sub></td><td>0.0003105</td><td>d<sup>-2</sup></td></tr><tr><td>Gompertz Stress coefficient</td><td>s<sub>G</sub></td><td>-0.3</td><td>-</td></tr><tr><td colspan="4">Auxiliary parameters - Fixed</td></tr><tr><td>shape coefficient</td><td>δ<sub>M</sub></td><td>0.264</td><td>-</td></tr><tr><td>whole-body energy density of dry biomass</td><td>ε<sub>wE</sub></td><td>1.53172 × 10<sup>6</sup></td><td>J g<sup>-1</sup></td></tr><tr><td colspan="4">Starting values of state variables - Fixed</td></tr><tr><td>initial length (embryo)</td><td>L<sub>0</sub></td><td>10<sup>-6</sup></td><td>cm</td></tr><tr><td>energy costs of one egg</td><td>E<sub>0</sub></td><td>0.0446106</td><td>J</td></tr></tbody></table>

<table><caption>Table B.1</caption><tbody><tr><td colspan="5">Chemical parameters - Fixed</td></tr><tr><td colspan="5">Chemical indices n for organics</td></tr><tr><td></td><td>Food (n<sub>sX</sub>)</td><td>Reserve (n<sub>sE</sub>)</td><td>Structure (n<sub>sV</sub>)</td><td>Faeces (n<sub>sP</sub>)</td></tr><tr><td>Carbon (n<sub>Cs</sub>)</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Hydrogen (n<sub>Hs</sub>)</td><td>1.8</td><td>1.8</td><td>1.8</td><td>1.3</td></tr><tr><td>Oxygen (n<sub>Os</sub>)</td><td>0.5</td><td>0.5</td><td>0.5</td><td>0.5</td></tr><tr><td>Nitrogen (n<sub>Ns</sub>)</td><td>0.15</td><td>0.15</td><td>0.15</td><td>0.15</td></tr><tr><td>Chemical potential (J C-mol<sup>-1</sup>)</td><td>525 000</td><td>500 000</td><td>550 000</td><td>480 000</td></tr><tr><td>Specific density for dry weight (g cm<sup>-3</sup>)</td><td>0.17</td><td>0.17</td><td>0.17</td><td>0.17</td></tr><tr><td colspan="5">Chemical indices n for minerals</td></tr><tr><td></td><td>CO<sub>2</sub> (n<sub>sC</sub>)</td><td>H<sub>2</sub>O (n<sub>sH</sub>)</td><td>O<sub>2</sub> (n<sub>sO</sub>)</td><td>NH<sub>3</sub> (n<sub>sN</sub>)</td></tr><tr><td>Carbon (n<sub>Cs</sub>)</td><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Hydrogen (n<sub>Hs</sub>)</td><td>0</td><td>2</td><td>0</td><td>3</td></tr><tr><td>Oxygen (n<sub>Os</sub>)</td><td>2</td><td>1</td><td>2</td><td>0</td></tr><tr><td>Nitrogen (n<sub>Ns</sub>)</td><td>0</td><td>0</td><td>0</td><td>1</td></tr></tbody></table>

<table><caption>Table C.1</caption><thead><tr><th colspan="4">Ecological variables - Fixed</th></tr><tr><th>Description</th><th>Notation</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>scaled functional response</td><td>f</td><td>1</td><td>-</td></tr><tr><td>reference temperature</td><td>T<sub>ref</sub></td><td>293.15</td><td>K</td></tr></tbody></table>

## Appendix C. Values of ecological forcing variables

See Table C.1.

## Appendix D

See Fig. D.4.
<figure><img src="image_7.png" /><figcaption>Fig. D.4. Comparative analysis of primary parameters and additional traits. Each panel shows the variation of three different traits (final length $L_{∞}$, von Bertalanffy growth rate $r_B$ and total metabolism represented by $J_{0B}$) as a function of the six different DEB parameters selected. Smooth lines indicate trends modelled using spline regression, with dashed red vertical lines highlighting AmP values.</figcaption></figure>

## Data availability

The full code used to produce the results in this article is available at https://forgemia.inra.fr/Charlotte.Recapet/ecomod_110993/-/releases/v1 under a Creative Common Attribution 4.0 International licence.

## References

Accolla, C., Vaugeois, M., Rueda-Cediel, P., Moore, A., Marques, G.M., Marella, P., Forbes, V.E., 2020. DEB-tox and data gaps: Consequences for individual-level outputs. Ecol. Model. 431 (April), 109107. http://dx.doi.org/10.1016/j.ecolmodel. 2020.109107.

Adamczuk, M., 2020. Population dynamics and life history traits of *Daphnia magna* across thermal regimes of environments. Sci. Total Environ. 723, 4–11. http://dx.doi.org/10.1016/j.scitotenv.2020.137963.

Augustine, S., Lika, K., Kooijman, S.A., 2019. Why big-bodied animal species cannot evolve a waste-to-hurry strategy. J. Sea Res. 143, 18–26. http://dx.doi.org/10. 1016/j.seares.2018.06.002.

Bertalanffy, L., 1934. Untersuchungen über die gesetzlichkeit des wachstums. Wilhelm Roux' Arch Entwicklungsmechanik Org. 131 (4), 613–652. http://dx.doi.org/10. 1007/bf00650112.

Braendle, C., Heyland, A., Flatt, T., 2011. Integrating mechanistic and evolutionary analysis of life history variation. In: Flatt, T., Heyland, A. (Eds.), Mechanisms of Life History Evolution. Oxford University Press, pp. 3–10. http://dx.doi.org/10. 1093/acprof:oso/9780199568765.003.0001.

Brommer, J.E., Merilä, J., Kokko, H., 2002. Reproductive timing and individual fitness. Ecol. Lett. 5 (6), 802–810. http://dx.doi.org/10.1046/j.1461-0248.2002.00369.x.

Campos-Candela, A., Palmer, M., Balle, S., Álvarez, A., Alós, J., 2019. A mechanistic theory of personality-dependent movement behaviour based on dynamic energy budgets. Ecol. Lett. 22 (2), 213–232. http://dx.doi.org/10.1111/ele.13187.

Caswell, H., 2001. Matrix population models: Construction, analysis, and interpretation. In: Encyclopedia of Environmetrics, second ed. Sinauer Associates, Inc., URL: https://books.google.fr/books?id=CPsTAQAAIAAJ.

Chang, C., Moiron, M., Sánchez-Tójar, A., Niemelä, P.T., Laskowski, K.L., 2023. What is the meta-analytic evidence for life-history trade-offs at the genetic level? Ecol. Lett. 27 (1), 1–14. http://dx.doi.org/10.1111/ele.14354.

Cohen, A.A., Isaksson, C., Salguero-Gómez, R., 2017. Co-existence of multiple trade-off currencies shapes evolutionary outcomes. PLoS One 12 (12), 1–20. http://dx.doi. org/10.1371/journal.pone.0189124.

Cubaynes, S., Doherty, P.F., Schreiber, E.A., Gimenez, O., 2011. To breed or not to breed: A seabird's response to extreme climatic events. Biol. Lett. 7 (2), 303–306. http://dx.doi.org/10.1098/rsbl.2010.0778.

Ercit, K., Gwynne, D.T., 2015. Darwinian balancing selection: Predation counters sexual selection in a wild insect. Evolution 69 (2), 419–430. http://dx.doi.org/10.1111/ evo.12579.

Gadgil, M., Bossert, W.H., 1970. Life historical consequences of natural selection. Amer. Nat. 104 (935), 1–24. http://dx.doi.org/10.1086/282637.

Garland, T., Downs, C.J., Ives, A.R., 2022. Trade-offs (And constraints) in organis- mal biology. Physiol. Biochem. Zool. 95 (1), 82–112. http://dx.doi.org/10.1086/ 717897.

Garvey, J.E., Marschall, E.A., 2003. Understanding latitudinal trends in fish body size through models of optimal seasonal energy allocation. Can. J. Fish. Aquat. Sci. 60 (8), 938–948. http://dx.doi.org/10.1139/f03-083.

Garvey, J.E., Ostrand, K.G., Wahl, D.H., 2004. Energetics, predation, and ration affect size-dependent growth and mortality of fish during winter. Ecology 85 (10), 2860–2871. http://dx.doi.org/10.1890/03-0329.

Gerber, N., Kokko, H., Ebert, D., Booksmythe, I., 2018. Daphnia invest in sexual reproduction when its relative costs are reduced. Proc. R. Soc. Lond. [Biol.] 285 (1871), http://dx.doi.org/10.1098/rspb.2017.2176.

Gregorius, H.R., 1997. The contribution of the genetics of populations to ecosystem stability. Silvae Genet. 45 (5-6), 267–271.

Hansen, T.E., 2006. The evolution of genetic architecture. Annu. Rev. Ecol. Evol. Syst. 37, 123–157. http://dx.doi.org/10.1146/annurev.ecolsys.37.091305.110224.

Hansen, T.F., 2013. Why epistasis is important for selection and adaptation. Evolution 67 (12), 3501–3511. http://dx.doi.org/10.1111/evo.12214.

Hansen, T.F., Pélabon, C., 2021. Evolvability : A quantitative-genetics perspective. Annu. Rev. Ecol. Evol. Syst. 52, 153–175. http://dx.doi.org/10.1146/annurev- ecolsys-011121-021241.

Heino, M., Dieckmann, U., 2008. Detecting Fisheries-induced life-history evolution: An overview of the reaction-norm approach. Bull. Mar. Sci. 83 (1), 69–93.

Hill, G.E., 1991. Plumage coloration is a sexually selected indicator of male quality. Nature 350 (6316), 337–339. http://dx.doi.org/10.1038/350337a0.

Ivan, L.N., Höök, T.O., 2015. Energy allocation strategies of young temperate fish: An eco-genetic modeling approach. Can. J. Fish. Aquat. Sci. 72 (8), 1243–1258. http://dx.doi.org/10.1139/cjfas-2014-0197.

Jacobs, G.R., Breck, J.E., Höök, T.O., 2012. Growth-mediated seasonal energy allocation patterns of young-of-year largemouth bass (*Micropterus salmoides*). J. Fresh. Ecol. 27 (1), 63–76. http://dx.doi.org/10.1080/02705060.2011.606983.

Jager, T., 2013. All individuals are not created equal; Accounting for interindividual variation in fitting life-history responses to toxicants. Environ. Sci. Technol. 47 (3), 1664–1669. http://dx.doi.org/10.1021/es303870g.

Jager, T., Crommentuijn, T., Van Gestel, C.A., Kooijman, S.A., 2004. Simultaneous modeling of multiple end points in life-cycle toxicity tests. Environ. Sci. Technol. 38 (10), 2894–2900. http://dx.doi.org/10.1021/es0352348.

Jager, T., Zimmer, E.I., 2012. Simplified Dynamic Energy Budget model for analysing ecotoxicity data. Ecol. Model. 225, 74–81. http://dx.doi.org/10.1016/j.ecolmodel. 2011.11.012.

Kearney, M.R., White, C.R., 2012. Testing metabolic theories. Amer. Nat. 180 (5), 546–565. http://dx.doi.org/10.1086/667860.

Kirkwood, T.B., Holliday, R., 1979. The evolution of ageing and longevity. Proc. R. Soc. Lond. [Biol.] 205 (1161), 531–546. http://dx.doi.org/10.1098/rspb.1979.0083.
Kooi, B.W., Van Der Meer, J., 2010. Bifurcation theory, adaptive dynamics and dynamic energy budget-structured populations of iteroparous species. Phil. Trans. R. Soc. B 365 (1557), 3579-3590. http://dx.doi.org/10.1098/rstb.2010.0173.

Kooijman, S.A., 2010. Dynamic energy budget theory for metabolic organisation, third edition. In: Dynamic Energy Budget Theory for Metabolic Organisation, third ed. Cambridge University Press, Cambridge, http://dx.doi.org/10.1017/CBO9780511805400.

Kooijman, S.A., 2014. Metabolic acceleration in animal ontogeny: An evolutionary perspective. J. Sea Res. 94, 128-137. http://dx.doi.org/10.1016/j.seares.2014.06.005.

Kooijman, S.A., 2020. The comparative energetics of petrels and penguins. Ecol. Model. 427 (May), 109052. http://dx.doi.org/10.1016/j.ecolmodel.2020.109052.

Kooijman, S.A., Augustine, S., 2022. The comparative energetics of the carnivorans and pangolins. Conserv. Physiol. 10 (1), http://dx.doi.org/10.1093/conphys/coac052.

Kooijman, S.A., Gergs, A., 2023. *AmP Daphnia magna*.

Lamarins, A., Fririon, V., Folio, D., Vernier, C., Daupagne, L., Labonne, J., Buoro, M., Lefèvre, F., Piou, C., Oddou-Muratorio, S., 2022. Importance of interindividual interactions in eco-evolutionary population dynamics: The rise of demo-genetic agent-based models. Evol. Appl. 15 (12), 1988-2001. http://dx.doi.org/10.1111/eva.13508.

van Leeuwen, I.M., Kelpin, F.D., Kooijman, S.A., 2002. A mathematical model that accounts for the effects of caloric restriction on body weight and longevity. Biogerontology 3 (6), 373-381. http://dx.doi.org/10.1023/A:1021336321551.

van Leeuwen, I.M., Vera, J., Wolkenhauer, O., 2010. Dynamic energy budget approaches for modelling organismal ageing. Phil. Trans. R. Soc. B 365 (1557), 3443-3454. http://dx.doi.org/10.1098/rstb.2010.0071.

Lika, K., Augustine, S., Kooijman, S.A., 2019. Body size as emergent property of metabolism. J. Sea Res. 143 (April 2018), 8-17. http://dx.doi.org/10.1016/j.seares.2018.04.005.

Lika, K., Augustine, S., Kooijman, S.A., 2020. The use of augmented loss functions for estimating dynamic energy budget parameters. Ecol. Model. 428 (April), 10910. http://dx.doi.org/10.1016/j.ecolmodel.2020.10910.

Lika, K., Kearney, M.R., Freitas, V., van der Veer, H.W., van der Meer, J., Wijsman, J.W., Pecquerie, L., Kooijman, S.A., 2011. The "covariation method" for estimating the parameters of the standard Dynamic Energy Budget model I: Philosophy and approach. J. Sea Res. 66 (4), 270-277. http://dx.doi.org/10.1016/j.seares.2011.07.010.

Lika, K., Kooijman, S.A., 2003. Life history implications of allocation to growth versus reproduction in dynamic energy budgets. Bull. Math. Biol. 65 (5), 809-834. http://dx.doi.org/10.1016/S0092-8240(03)00039-9.

Linck, E.B., Freeman, B.G., Cadena, C.D., Ghalambor, C.K., 2021. Evolutionary conservation will limit responses to climate change in the tropics. Biol. Lett. 17, 20210363. http://dx.doi.org/10.1098/rslb.2021.0363.

Llandres, A.L., Marques, G.M., Maino, J.L., Kooijman, S.A., Kearney, M.R., Casas, J., 2015. A dynamic energy budget for the whole life-cycle of holometabolous insects. Ecol. Monograph. 85 (3), 353-371. http://dx.doi.org/10.1890/14-0976.1.

Louati, D., Benmiled, S., Bellamine, N., Saoud, B., 2020. HermaDEB: An evolutionary IBM for energy allocation in hermaphrodites. Ecol. Model. 424, 109008. http://dx.doi.org/10.1016/j.ecolmodel.2020.109008.

Maino, J.L., Kong, J.D., Hoffmann, A.A., Barton, M.G., Kearney, M.R., 2016. Mechanistic models for predicting insect responses to climate change. Curr. Opin. Insect Sci. 17, 81-86. http://dx.doi.org/10.1016/j.cois.2016.07.006.

Mangel, M., Stamps, J., 2001. Trade-offs between growth and mortality and the maintenance of individual variation in growth. Evol. Ecol. Res. 3, 583-593.

Mariño, J., Dufour, S.C., Hurford, A., Récapet, C., 2021. Resource and seasonality drive interspecific variability in a Dynamic Energy Budget model. http://dx.doi.org/10.1101/2021.06.02.446572, bioRxiv.

Marn, N., Kooijman, S.A., 2022. The comparative energetics of the turtles and crocodiles. Ecol. Evol. 12 (6), 1-22. http://dx.doi.org/10.1002/ece3.8996.

Marques, G.M., Augustine, S., Lika, K., Pecquerie, L., Domingos, T., Kooijman, S.A., 2018. The AmP project: Comparing species on the basis of dynamic energy budget parameters. PLoS Comput. Biol. 14 (5), 1-23. http://dx.doi.org/10.1371/journal.pcbi.1006100.

Martin, B.T., Jager, T., Nisbet, R.M., Preuss, T.G., Hammers-Wirtz, M., Grimm, V., 2013. Extrapolating ecotoxicological effects from individuals to populations: A generic approach based on Dynamic Energy Budget theory and individual-based modeling. Ecotoxicology 22 (3), 574-583. http://dx.doi.org/10.1007/s10646-013-1049-x.

Mathot, K.J., 2018. Models of pace-of-life syndromes (POLS): a systematic review. Behav. Ecol. Sociobiol. 72 (3), 41. http://dx.doi.org/10.1007/s00265-018-2459-9.

Maury, O., Poggiale, J.C., 2013. From individuals to populations to communities: A dynamic energy budget model of marine ecosystem size-spectrum including life history diversity. J. Theoret. Biol. 324, 52-71. http://dx.doi.org/10.1016/j.jtbi.2013.01.018.

Mogensen, S., Post, J.R., 2012. Energy allocation strategy modifies growth-survival trade-offs in juvenile fish across ecological and environmental gradients. Oecol. 168 (4), 923-933. http://dx.doi.org/10.1007/s00442-011-2164-0.

Monaco, C.J., Porporato, E.M., Lathlean, J.A., Tagliarolo, M., Sarà, G., McQuaid, C.D., 2019. Predicting the performance of cosmopolitan species: dynamic energy budget model skill drops across large spatial scales. Mar. Biol. 166 (2), 14-27. http://dx.doi.org/10.1007/s00227-018-3462-4.

Morash, A.J., Speers-Roesch, B., Andrew, S., Currie, S., 2021. The physiological ups and downs of thermal variability in temperate freshwater ecosystems. J. Fish Biol. 98 (6), 1524-1535. http://dx.doi.org/10.1111/jfb.14655.

Nisbet, R.M., Martin, B.T., de Roos, A.M., 2016. Integrating ecological insight derived from individual-based simulations and physiologically structured population models. Ecol. Model. 326, 101-112. http://dx.doi.org/10.1016/j.ecolmodel.2015.08.013.

Nisbet, R.M., Muller, E.B., Lika, K., Kooijman, S.A., 2000. From molecules to ecosystems through dynamic energy budget models. J. Anim. Ecol. 69 (6), 913-926. http://dx.doi.org/10.1046/j.1365-2656.2000.00448.x.

Niven, J.E., Laughlin, S.B., 2008. Energy limitation as a selective pressure on the evolution of sensory systems. J. Exp. Biol. 211 (11), 1792-1804. http://dx.doi.org/10.1242/jeb.017574.

van Noordwijk, A.J., de Jong, G., 1986. Acquisition and allocation of resources: Their influence on variation in life history tactics. Amer. Nat. 128 (1), 137-142. http://dx.doi.org/10.1086/284547.

Oliveira, D.F., Marques, G.M., Carolino, N., Pais, J., Sousa, J.M., Domingos, T., 2024. A multi-tier methodology for the estimation of individual-specific parameters of DEB models. Ecol. Model. 494 (June), 110779. http://dx.doi.org/10.1016/j.ecolmodel.2024.110779.

Paul, R.J., Zeis, B., Lamkemeyer, T., Seidl, M., Pirow, R., 2004. Control of oxygen transport in the microcrustacean daphnia: Regulation of haemoglobin expression as central mechanism of adaptation to different oxygen and temperature conditions. Acta Physiol. Scand. 182 (3), 259-275. http://dx.doi.org/10.1111/j.1365-201X.2004.01362.x.

Réale, D., Garant, D., Humphries, M.M., Bergeron, P., Careau, V., Montiglio, P.O., 2010. Personality and the emergence of the pace-of-life syndrome concept at the population level. Phil. Trans. R. Soc. B 365 (1560), 4051-4063. http://dx.doi.org/10.1098/rstb.2010.0208.

Ricklefs, R., Wikelski, M., 2002. The physiology/life-history nexus. Trends Ecol. Evolut. 17 (10), 462-468. http://dx.doi.org/10.1016/S0169-5347(02)02578-8.

Royauté, R., Anderson, M., Courtney, B., Ned, R.G., 2018. Paceless life ? A meta-analysis of the pace-of-life syndrome hypothesis. Behav. Ecol. Sociobiol. 72 (3), 1-10. http://dx.doi.org/10.1007/s00265-018-2472-z.

Sadoul, B., Geffroy, B., Lallement, S., Kearney, M., 2020. Multiple working hypotheses for hyperallometric reproduction in fishes under metabolic theory. Ecol. Model. 433, 109228. http://dx.doi.org/10.1016/j.ecolmodel.2020.109228.

Singh, R., Krimbas, C. (Eds.), 2000. Evolutionary Genetics: From Molecules to Morphology. Cambridge University Press, p. 702.

Soetaert, K., Petzoldt, T., Setzer, R.W., 2010. Solving differential equations in R: Package deSolve. J. Stat. Softw. 33 (9), 1-25. http://dx.doi.org/10.18637/jss.v033.i09.

Speakman, J.R., 2005. Body size, energy metabolism and lifespan. J. Exp. Biol. 208 (9), 1717-1730. http://dx.doi.org/10.1242/jeb.01556.

Speakman, J.R., Selman, C., McLaren, J.S., Jean Harper, E., 2002. Living fast, dying when? The link between aging and energetics. J. Nutr. 132 (6 SUPPL. 1), 1583S-1597S. http://dx.doi.org/10.1093/jn/132.6.1583s.

Stamps, J.A., Mangel, M., Phillips, J.A., 1998. A new look at relationships between size at maturity and asymptotic size. Amer. Nat. 152 (3), 470-479. http://dx.doi.org/10.1086/286183.

Stavrikidis-Zachou, O., Papandroulakis, N., Lika, K., 2019. A DEB model for European sea bass (Dicentrarchus labrax): Parameterisation and application in aquaculture. J. Sea Res. 143 (January 2018), 262-271. http://dx.doi.org/10.1016/j.seares.2018.05.008.

Stearns, A.S.C., 1989. Trade-offs in life-history evolution. Funct. Ecol. 3 (3), 259-268. http://dx.doi.org/10.2307/2389364.

Teplitsky, C., Robinson, M.R., Merilä, J., 2014. Evolutionary potential and constraints in wild populations. In: Charmantier, A., Garants, D., Kruuk, L.E. (Eds.), Quantitative Genetics in the Wild. Oxford University Press, pp. 190-208. http://dx.doi.org/10.1093/acprof:oso/9780199674237.003.0012.

Therry, L., Cote, J., Cucherousset, J., Finn, F., Buoro, Y., Blanchet, S., 2019. Genetic and environmental contributions to the impact of a range-expanding predator on aquatic ecosystems. J. Anim. Ecol. 88 (1), 35-46. http://dx.doi.org/10.1111/1365-2656.12938.

Thomas, Y., Flye-Sainte-Marie, J., Chabot, D., Aguirre-Velarde, A., Marques, G.M., Pecquerie, L., 2019. Effects of hypoxia on metabolic functions in marine organisms: Observed patterns and modelling assumptions within the context of Dynamic Energy Budget (DEB) theory. J. Sea Res. 143 (January), 231-242. http://dx.doi.org/10.1016/j.seares.2018.05.001.

Tinkle, D.W., 1969. The concept of reproductive effort and its relation to the evolution of life histories of lizards. Amer. Nat. 103 (933), 501-516.

Tinkle, D.W., Wilbur, H.M., Tilley, S.G., 1970. Evolutionary strategies in lizard reproduction. Evolution 24 (1), 55-74. http://dx.doi.org/10.2307/2406714.

Troost, T.A., Kooi, B.W., Kooijman, S.A., 2005. When do mixotrophs specialize? Adaptive dynamics theory applied to a dynamic energy budget model. Math. Biosci. 193 (2), 159-182. http://dx.doi.org/10.1016/j.mbs.2004.06.010.

Uchmański, J., 2016. Individual variability and metapopulation dynamics: An individual-based model. Ecol. Model. 334, 8-18. http://dx.doi.org/10.1016/j.ecolmodel.2016.04.019.
Van De Walle, J., Fay, R., Gaillard, J.M., Pelletier, F., Hamel, S., Gamelon, M., Barbraud, C., Blanchet, F.G., Blumstein, D.T., Charmantier, A., Delord, K., Larue, B., Martin, J., Mills, J.A., Milot, E., Mayer, F.M., Rotella, J., Saether, B.E., Teplitsky, C., Van De Pol, M., Van Vuren, D.H., Visser, M.E., Wells, C.P., Yarrall, J., Jenouvrier, S., 2023. Individual life histories: neither slow nor fast, just diverse. Proc. R. Soc. Lond. [Biol.] 290 (2002), http://dx.doi.org/10.1098/rspb.2023.0511.

Vasseur, F., Fouqueau, L., De Vienne, D., Nidelet, T., Violle, C., Weigel, D., 2019. Nonlinear phenotypic variation uncovers the emergence of heterosis in arabidopsis thaliana. PLoS Biol. 17 (4), 1–26. http://dx.doi.org/10.1371/journal.pbio.3000214.

Violle, C., Navas, M.L., Vile, D., Kazakou, E., Fortunel, C., Hummel, I., Garnier, E., 2007. Let the concept of trait be functional! Oikos 116 (5), 882–892. http://dx.doi.org/10.1111/j.2007.0030-1299.15559.x.

Waddington, C., 1942. Canalization of development and the inheritance of acquired characters. Nature 150, 563–565. http://dx.doi.org/10.1038/150563a0.

Wagner, G.P., Altenberg, L.E.E., 1996. Complex adaptations and the evolution of evolvability. Int. J. Org. Evol. 50 (3), 967–976. http://dx.doi.org/10.1111/j.1558-5646.1996.tb02339.x.

Wang, W.X., Widdows, J., 1993. Calometric studies on the energy metabolism of an infaunal bivalve, *Abra tenuis*, under normoxia, hypoxia and anoxia. Mar. Biol. 116, 73–79. http://dx.doi.org/10.1007/BF00350733.

White, C.R., Alton, L.A., Bywater, C.L., Lombardi, E.J., Marshall, D.J., 2022. Metabolic scaling is the product of life-history optimization. Science 377, 834–839. http://dx.doi.org/10.1126/science.abm7649.

Wright, J., Bolstad, G.H., Araya-Ajoy, Y.G., Dingemanse, N.J., 2019. Life-history evolution under fluctuating density-dependent selection and the adaptive alignment of pace-of-life syndromes. Biol. Rev. 94 (1), 230–247. http://dx.doi.org/10.1111/brv.12451.

Závorka, L., Aldvén, D., Näslund, J., Höjesjö, J., Johnsson, J.I., 2015. Linking lab activity with growth and movement in the wild: Explaining pace-of-life in a trout stream. Behav. Ecol. 26 (3), 877–884. http://dx.doi.org/10.1093/beheco/arv029.