Substantial intraspecific variation in energy budgets: biology or artefact?

Dynamic energy budget (DEB) models provide a mechanistic description of life-histories in terms of fluxes of energy through biological processes. In these models, life-histories are a function of environmental conditions and of fundamental traits of the organism relating to the acquisition, allocation, and use of energy. These traits are described by the parameters of the DEB model, which have been estimated for over 2500 species. Recent work has aimed to compare species on the basis of differences in DEB parameters. We show that caution is required in such analyses, because (i) parameter estimates vary considerably as an artefact of the types of data used to fit the models, and (ii) there is substantial intraspecific variation in parameter values, reflecting biological differences among populations. We show that similar patterns of growth and reproduction can be reproduced with very different parameter sets. Our results imply that direct comparison of DEB parameters across populations or species may be invalid. However, valid comparisons are possible if differences in the types of data used to fit the models are taken into account. We estimated DEB parameters for 16 populations of Trinidadian guppy, identifying differences in resource allocation and metabolic rate consistent with evolved life-history differences among these populations. Variation in parameter values was substantial: if intraspecific variation in DEB parameters is greater than currently measured levels of interspecific variation, the detection of broad-scale patterns in energy budgets across species will be challenging.


Introduction
: Schematic of the standard dynamic energy budget model. State variables are given in boxes, processes are shown in plain text. Processes (including ageing, not depicted) are determined by 14 parameters, described in Table 1. Arrows represent fluxes of energy through the system via biological processes and state variables. A fraction κ of mobilised reserve is allocated to somatic work, where somatic maintenance costs must first be met before the remainder is allocated to growth. Reserve allocated to reproductive work (1 − κ) is first used to meet maturity maintenance costs, and then used to attain sexual maturity (in juveniles) or produce offspring (in adults).

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Overview of methods 99 We estimated the parameters of the standard dynamic energy budget model for sixteen guppy populations, Table 1: Parameters of the standard DEB model and the primary biological processes that they control. Two further parameters, the shape coefficient δ m and the zoom factor z, fully describe the shape of the organism, link structure V to physical measurements, and allow comparisons between species of different size and shape. Symbols follow the standard DEB notation (Kooijman, 2010 (Table 1) and their interactions with environmental conditions (namely, temperature and food availability). 125 The model captures the biological processes of feeding, assimilation of food, defecation, mobilisation of 126 assimilated energy, allocation of mobilised energy to somatic or reproductive work, maintenance costs of 127 somatic and reproductive work, somatic growth, attainment of maturity, reproduction, and ageing ( Figure   128 1, Table 1, Table 2). Data on the growth and reproduction of individuals at more than one level of food

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Estimating DEB parameters and predicting metabolic rate 132 The majority of the data that we used to fit population-specific DEB models came from three sets of 133 common garden experiments, in which guppies sampled from sixteen population were reared at either 134 high or low levels of food availability (Reznick and Bryga, 1996;Reznick et al., 2004Reznick et al., , 2005 (Table 3). To compare populations across all datasets, we then fit sixteen population-specific 155 DEB models using the same level of data availability (Table 3).

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Both zero-variate and uni-variate observations can be described as functions of primary DEB param-157 eters, state variables, temperature, and food availability. Because DEB parameters appear in multiple 158 auxiliary models of observable relationships, model fitting is not a straight-forward process. All rela-159 tionships must be modelled simultaneously because no single parameter is specific to a single type of  (Table 2) at high and low food levels. To achieve a better fit of the models to 185 the data, we introduced two additional parameters: the first captured a delay in the onset of development, 186 T0 (measured in days) and the second was a low-food level specific assimilation efficiency κX low . The 187 parameter T0 was included as an additive term in the auxiliary model for age at birth only. For modelling 188 growth, reproduction, and survival at low food levels, we used κX low in place of κX in the standard DEB 189 model.

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Although metabolic rate data (oxygen consumption) were only used to fit models with data availability 191 level 3 (Table 3), we predicted metabolic rates from the parameter sets for each population, using the  Each population-specific set of data and the MATLAB scripts required to estimate the parameters 200 presented in this manuscript are available to download from the AmP online repository (AmP, 2020) (see 201   Table S1).

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Assessing model fit and differences among parameter sets 203 We assessed goodness of fit of the models to the data by calculating the mean error of the predictions 204 relative to the data, for each set of observations used to fit the model (Marques et al., 2018). The overall 205 fit of the model is described by the mean relative error, which is the grand mean of the relative error terms 206 from each set of predictions and observations.

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To determine whether there were significant differences in parameter sets between populations, we 208 followed the approach described by Marn and collegaues (2019): we compared the fit of the model to the 209 data when using the population-specific ("best") parameters with that when using a null-model parameter 210 set. We compared the "best" parameters with two null models: "null 1", which was the parameter set of 211 the alternative ecotype from the same stream (e.g. LP Yarra vs HP Yarra); and "null 2", which was the  (Table 4).

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Despite substantial differences in parameter values by data level, the different parameter sets were able 235 to reproduce how standard length, mass, and cumulative reproductive output changed as a function of 236 age and food level (Fig. 2), as well as predicting age and dry weight at birth (at high and low food) and 237 maximum length (Table S2). The overall fits of the models to the data, as quantified by the mean relative 238 Table 4: Estimates of dynamic energy budget model parameters vary depending on the type and amount of data used to fit the models. We estimated parameters using three levels of data availability (see Table 3). Parameters are shown for four populations of Trinidadian guppy: the high-predation (HP) and low-predation (LP) ecotypes from the Oropuche and Yarra rivers. Parameters which were fixed and therefore not estimated during model fitting are denoted with (n. e.). Parameters that were fixed across all data levels were: the maximum specific searching rate {Ḟ  Table 3). error, were poorest for models fit with data level 1, and were reasonable (MRE<0.1) and comparable 239 between models fit at data levels 2 and 3 (Table 4).

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Ecotype-specific parameter differences 241 Our initial assessment of ecotype-specific differences in DEB parameters considered two ecotype pairs (four 242 populations) for which level 3 data were available. In general, parameter sets were significantly different 243 between populations and ecotypes: the population-specific parameter sets gave a significantly better fit to 244 the data compared to parameter sets from the other population (different ecotype) within the same river 245 systems, or the from the same ecotype from a different river system (Table S3). There was one exception: 246 for data from the low-predation Oropuche population, there was no significant difference in fit when using 247 the population-specific parameter set, or the parameter set from the low-predation Yarra population (  Figure 3: Percentage differences in DEB parameter values of low-predation (LP) relative to highpredation (HP). Differences between ecotypes from the Oropuche are given in blue; those from the Yarra are given in yellow. Parameters are categorised into three groups: (A) Parameters differ between ecotypes, and the direction of the effect is consistent between streams; (B) Parameters differ between ecotypes, and the direction and/or magnitude of the effect differs between streams; and (C) Parameters do not differ between ecotypes or streams. Dotted lines indicate a difference of plus or minus 20%, representing the threshold used to categorise parameters as falling in A, B, or C. and use resources: we found that DEB parameters differed between ecotype pairs, and that these differences 251 were often consistent between independent evolutionary origins of ecotype pairs in the Oropuche river and 252 Yarra rivers. (Table 4, Fig. 3). Six parameters varied consistently between ecotypes: for both rivers, 253 compared to the high-predation ecotype, low-predation guppies had lower maximum assimilation rates 254 ({ṗAm}) and assimilation efficiencies (κX and κ X low ), allocated a greater fraction of available energy to 255 somatic work (κ), had a longer delay period at the onset of development (t0), and had higher values for 256 the Gompertz stress coefficient (SG) (Fig. 3A).

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The magnitude of ecotype differences were inconsistent between streams for somatic maintenance costs  For five parameters, there were negligible differences between ecotypes, and this was consistent between 261 streams. These parameters were the maturity maintenance coefficient (kJ ), energy conductance (v), the 262 energetic cost of structure ([EG]) the shape coefficient (δm), and the zoom factor z (Fig. 3C). 263 We then fit DEB models at level 1 data availability for these four populations, plus an additional twelve Note that to account for parameter variation due to differences in maximum body size between species, values for E b H and E p H are multiplied by z 3 (Kooijman, 2010). Axes are on the log-scale, except for the y-axis in (A). Filled points are parameter values obtained for Trinidadian guppies in this study, using data availability at level 1 (squares), level 2 (triangles) and level 3 (circles). For details on data levels, see Table 3. Empty circles are parameter estimates for 59 species from 7 families within the order Cyprinodontiformes, obtained from the AmP online database (AmP, 2020). . assimilation rates than the high-predation ecotype (Fig. 4). Using the parameter sets for each population, 268 we predicted basal metabolic rate in terms of dioxygen consumption rates. Note that metabolic rate data 269 was not used to fit models at data level 1. The low-predation ecotype was predicted to have lower rates 270 of oxygen consumption than the high-predation ecotype (Fig. 4C)  to fit models at level 3 in this study.

Intra-and interspecific variation
We compared the intraspecific variation in six DEB parameters reported in this study with the interspecific 276 variation reported within the order Cyprinodontiformes (AmP, 2020) (Fig. 5)  including data on metabolic rate and daily food availability halved estimates of the maximum rate at which 296 energy is assimilated ({ṗAm}); estimates of κ varied such that guppies in one population were predicted 297 to allocate as much as 70% of available energy to somatic work, or as little as 40%, depending on the type 298 of data used to fit the models (Table 4). Do these fish invest more energy in reproduction, or in somatic 299 growth and maintenance? Had we used a single level of data availability when fitting our models, we may 300 have felt confident in our answer. That confidence would have been misplaced: when fitting models with 301 different types of data, our results gave conflicting answers to this basic question of energy allocation.

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Nevertheless, despite these large data-type-dependent differences among parameter sets, the net combi-303 nation of parameter values reproduced remarkably similar patterns of growth and reproduction, reasonably 304 fitting the observed data (Fig 2). This is an example of getting the right answer for the wrong reasons. But 305 which reason is least wrong? The nature of a balanced energy budget means that, for example, a decrease 306 in somatic maintenance costs must be balanced by, say, a decrease in assimilation efficiency, if patterns of 307 growth are to remain fixed. The interactive and parameter-rich structure of the DEB model allows many 308 possible routes through which this balance can manifest, but those routes become increasingly constrained 309 as more different types of data are used to fit the models.
When we included data on dioxygen consumption and daily food availability, estimates of several 311 parameters changed substantially, and these changes were consistent across all four populations tested: 312 maximum assimilation rate, the fraction of energy allocated to somatic work, and somatic maintenance 313 costs all decreased, while the maturity threshold at which the adult stage is met increased (Table 4).

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Respectively, this meant that: less energy was entering the system from the environment; less was allocated 315 to somatic growth; somatic overheads were reduced; and more energy was invested in attaining, and also 316 in maintaining maturity. This happened because initial fits (without using dioxygen consumption data) 317 generated parameter sets that overestimated metabolic rate by about a half (Table S2). When the fitting 318 process was forced to account for the measured rates of dioxygen consumption, the total dissipation power 319 had to decrease: data on growth and reproduction constrained this to decreases in energy assimilation 320 rates, with more investment in non-somatic work balanced by decreases in somatic maintenance costs, 321 and increases in the costs of maturation. As such, in the absence of dioxygen consumption data, we 322 overestimated the energetic costs of somatic maintenance by a factor of around 2, resulting in overestimation 323 of basal metabolic rate. We suspect that somatic and maturity maintenance costs are generally poorly 324 determined by data on reproduction and growth alone.

Biological variation and DEB parameters 326
Because the data-type-dependency of parameter estimates was consistent across the four populations that 327 we tested, we argue that relative biological differences can be assessed when comparing DEB parameter 328 sets fit with the same types of data. Our aim here was to determine whether the DEB approach could 16 populations, representing five independent evolutionary origins of the low-predation ecotype (Fig. 4).

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For the four populations that we were able to fit at higher levels of data availability, we also found that 345 the low-predation ecotype were less efficient at assimilating energy (lower values of κX ) than their high-346 predation counterparts (Fig. 3). Population-specific parameter sets gave significantly better fits to the data than parameter sets from the other ecotype, indicating that these parameter differences reflect biological 348 differences between ecotypes.

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Apart from predicting the patterns of growth and reproduction used to fit the models, how do these

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To improve model fits, we introduced two additional parameters to the standard DEB model. First, 368 we included a second assimilation efficiency parameter, specific to the low food treatment (κ X low ). As-369 similation efficiencies were consistently higher in the low food treatment than they were in the high food 370 treatment. This could indicate that in the high food treatment not all of the daily food ration was con-371 sumed, meaning that we overestimated the amount of food eaten by individuals in this group. However, a 372 daily record of whether each fish had consumed it's full ration was kept for these experiments: failure to 373 eat the full ration was rare, and there was no systematic tendency for fish in the high food treatment to 374 not consume full rations. A more plausible explanation is that our DEB model failed to capture how total 375 energetic flux changed as a function of food availability. One empirical measure of energetic flux -standard 376 metabolic rate -has been shown to increase at higher food levels . Although this should 377 be captured in the DEB model -reserve density should be greater, and therefore every process downstream 378 of the assimilation flux ( For four parameters, the magnitude of ecotype differences varied considerably between streams (Fig. 3B).

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Because each stream represents an independent evolutionary origin of the low-predation ecotype, these 388 differences may reflect alternative mechanisms through which adaptation to competitive, resource-limited 389 environments has occurred. The distinction between guppy ecotypes is well characterised ( there are multiple mechanistic routes through which the low-predation ecotype can evolve.

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One of the strengths of the DEB approach -that models can be fit with a wide range of commonly 398 available data -may come at a cost in terms of the reliability of comparisons of parameters across species.

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Although the sensitivity of parameter estimation to the types of data used to fit DEB models has been of data-type-dependent variation is truly systematic, as it appears to be in this study, then correcting for 407 data type could improve the ability to detect such broad-scale patterns of life-history strategies.

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When we considered only parameter sets fit with the same types of data, we identified intraspecific 409 variation in DEB parameters. DEB theory predicts that closely related species should share more similar 410 parameter values, and our results support this: guppy parameters (when fit with the same data types) 411 tended to cluster together when compared to interspecific variation in parameters (Fig. 5), and intraspecific 412 variation in guppies was significantly lower than the variation seen within the family Poeciliidae. However, 413 in our system, ecotype pairs (i.e. high-predation and low-predation ecotypes) within a stream are more 414 closely genetically related than two populations of the same ecotype, yet DEB parameters were more similar 415 within ecotypes than between. Our results suggest that convergent evolution can result in similarity of 416 DEB parameters that do not reflect genetic relatedness.

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Our study demonstrates that variation among sets of DEB parameters can result not only from biolog-418 ical differences (i.e. between individuals, populations, or species), but also from artefacts of the parameter 419 estimation process. Different parameter sets can generate the same biological patterns. In some instances 420 this may not matter: for example, if the goal is to predict a biological process based on limited data.

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In our study, DEB models predicted dioxygen consumption rates with quite impressive accuracy, given that the models were fit using data only on age, weight, length, and number of offspring. However, the 423 goal of mechanistic modelling is to determine the causal relationships among interacting components of