Separating intrinsic and environmental contributions to growth and their population consequences

Spatiotemporal variation in size-dependent growth rates in small isolated populations of Arctic charr (Salvelinus alpinus)

As a key life-history trait, growth rates are often used to measure individual performance and to inform parameters in demographic models. Furthermore, intraspecific trait variation generates diversity in nature. Therefore, partitioning out and understanding drivers of spatiotemporal variation in growth rate is of fundamental interest in ecology and evolution. However, this has rarely been attempted owing to the amount of individual-level data required through both time and space, and issues with missing data in important covariates. Here, we implemented a Bayesian state-space model using individual-level data from 20 populations of Arctic charr (Salvelinus alpinus) across 15 capture occasions, which allowed us to: (i) integrate over the uncertainty of missing recapture records; (ii) robustly estimate size-dependence; and (iii) include a covariate (water temperature) that contained missing data. Interestingly, although there was substantial spatial, temporal and spatiotemporal variation in growth rate, this was only weakly associated with variation in water temperature and almost entirely independent of size, suggesting that spatiotemporal variation in other environmental conditions affected individuals across sizes similarly. This fine-scale spatiotemporal variation emphasizes the importance of local conditions and highlights the potential for spatiotemporal variation in a size-dependent life-history trait, even when environmental conditions are apparently very similar.

Accounting for temporal and individual variation in the estimation of Von Bertalanffy growth curves

Growth and growth limitation are important indicators of density dependence and environmental limitation of populations. Estimating individual growth trajectories is therefore an important aspect of understanding and predicting the life history and dynamics of a population. Variation in individual growth trajectories arises due to variation in the environmental factors limiting individual growth. This environmental limitation can vary over time, between cohorts and between individuals within a cohort. For a complete and accurate understanding of individual growth in a population, it is important to include all these sources of variation. So far, statistical models only accounted for a subset of these factors or required an extensive growth history of individuals. Here, we present a novel model describing the growth curves of cohorts in a population. This model is derived from a stochastic form of the Von Bertalanffy growth equation describing individual growth. The model is specifically tailored for use on length-at-age data in which the growth trajectory of an individual is unknown and every individual is only measured once. The presented method can also be used if growth limitation differs strongly between age or length classes. We demonstrate the use of the model for length-at-age data of North Sea plaice (Pleuronectes platessa) from the last 30 years. Fitting this model to length-at-age data can provide new insights in the dynamics of the environmental factors limiting individual growth and provides a useful tool for ecological research and management.

Effects of genetics and early-life mild hypoxia on size variation in farmed gilthead sea bream (Sparus aurata)

The present study evaluated, in an 18-month gilthead sea bream trial, the time course effects of genetics on individual size variation and growth compensation processes in families selected by heritable growth in the PROGENSA^® breeding program. Families categorized as fast, intermediate, and slow growing had different growth trajectories with a more continuous growth in fast growth families. This feature was coincident with a reduced size variation at the beginning of the trial that clustered together the half-sib families sharing the same father. Regression analysis evidenced that the magnitude of compensatory growth was proportional to the initial size variation with no rescaling of families at this stage. By contrast, the finishing growth depensation process can mask, at least partially, the previous size convergence. This reflects the different contribution across the production cycle of genetics in growth. How early-life experiences affect growth compensation at juvenile stages was also evaluated in a separate cohort, and intriguingly, a first mild-hypoxia pulse at 60-81 days post-hatching (dph) increased survival rates by 10%, preventing growth impairment when fish were exposed to a second hypoxia episode (112-127 dph). The early hypoxia experience did not have a negative impact on growth compensatory processes at juvenile stages. By contrast, a diminished capacity for growth compensation was found with repeated or late hypoxia experiences. All this reinforces the use of size variation as a main criterion for improving intensive fish farming and selective breeding.

Biological and statistical interpretation of size-at-age, mixed-effects models of growth

The differences in life-history traits and processes between organisms living in the same or different populations contribute to their ecological and evolutionary dynamics. We developed mixed-effect model formulations of the popular size-at-age von Bertalanffy and Gompertz growth functions to estimate individual and group variation in body growth, using as a model system four freshwater fish populations, where tagged individuals were sampled for more than 10 years. We used the software Template Model Builder to estimate the parameters of the mixed-effect growth models. Tests on data that were not used to estimate model parameters showed good predictions of individual growth trajectories using the mixed-effects models and starting from one single observation of body size early in life; the best models had R 2 > 0.80 over more than 500 predictions. Estimates of asymptotic size from the Gompertz and von Bertalanffy models were not significantly correlated, but their predictions of size-at-age of individuals were strongly correlated (r > 0.99), which suggests that choosing between the best models of the two growth functions would have negligible effects on the predictions of size-at-age of individuals. Model results pointed to size ranks that are largely maintained throughout the lifetime of individuals in all populations.

Resurgence of an apex marine predator and the decline in prey body size

Recent recoveries of marine mammal populations worldwide have heightened concerns for their potential impacts on global fisheries. While predator-induced reductions in prey abundance have been documented, trait-mediated changes in life-history characteristics are rarely considered. Here we provide a striking example of the impact of a resurging apex marine predator on a commercially important fish species through changes in prey life-history traits. We find that widespread declines in the body size of Chinook salmon over the past 50 y can be explained by intensified predation by growing populations of resident killer whales that selectively feed on large Chinook salmon, thus revealing a potential conflict between salmon fisheries and marine mammal conservation objectives.

In light of recent recoveries of marine mammal populations worldwide and heightened concern about their impacts on marine food webs and global fisheries, it has become increasingly important to understand the potential impacts of large marine mammal predators on prey populations and their life-history traits. In coastal waters of the northeast Pacific Ocean, marine mammals have increased in abundance over the past 40 to 50 y, including fish-eating killer whales that feed primarily on Chinook salmon. Chinook salmon, a species of high cultural and economic value, have exhibited marked declines in average size and age throughout most of their North American range. This raises the question of whether size-selective predation by marine mammals is generating these trends in life-history characteristics. Here we show that increased predation since the 1970s, but not fishery selection alone, can explain the changes in age and size structure observed for Chinook salmon populations along the west coast of North America. Simulations suggest that the decline in mean size results from the selective removal of large fish and an evolutionary shift toward faster growth and earlier maturation caused by selection. Our conclusion that intensifying predation by fish-eating killer whales contributes to the continuing decline in Chinook salmon body size points to conflicting management and conservation objectives for these two iconic species.

Density dependence governs when population responses to multiple stressors are magnified or mitigated

Population endangerment typically arises from multiple, potentially interacting anthropogenic stressors. Extensive research has investigated the consequences of multiple stressors on organisms, frequently focusing on individual life stages. Less is known about population-level consequences of exposure to multiple stressors, especially when exposure varies through life. We provide the first theoretical basis for identifying species at risk of magnified effects from multiple stressors across life history. By applying a population modeling framework, we reveal conditions under which population responses from stressors applied to distinct life stages are either magnified (synergistic) or mitigated. We find that magnification or mitigation critically depends on the shape of density dependence, but not the life stage in which it occurs. Stressors are always magnified when density dependence is linear or concave, and magnified or mitigated when it is convex. Using Bayesian numerical methods, we estimated the shape of density dependence for eight species across diverse taxa, finding support for all three shapes.

Individual heterogeneity and early life conditions shape growth in a freshwater top predator

Body size can have profound impacts on survival, movement, and reproductive schedules shaping individual fitness, making growth a central process in ecological and evolutionary dynamics. Realized growth is the result of a complex interplay between life history schedules, individual variation, and environmental influences. Integrating all of these aspects into growth models is methodologically difficult, depends on the availability of repeated measurements of identifiable individuals, and consequently represents a major challenge in particular for natural populations. Using a unique 30-yr time series of individual length measurements inferred from scale year rings of wild brown trout, we develop a Bayesian hierarchical model to estimate individual growth trajectories in temporally and spatially varying environments. We reveal a gradual decrease in average juvenile growth, which has carried over to adult life and contributed to decreasing sizes observed at the population level. Commonly studied environmental drivers like temperature and water flow did not explain much of this trend and overall persistent and among-year individual variation dwarfed temporal variation in growth patterns. Our model and results are relevant to a wide range of questions in ecology and evolution requiring a detailed understanding of growth patterns, including conservation and management of many size-structured populations.

Is bigger really better? Relative and absolute body size influence individual growth rate under competition

Models suggest that the mechanism of competition can influence the growth advantage associated with being large (in absolute body size or relative to other individuals in the population). Large size is advantageous under interference, but disadvantageous under exploitative competition. We addressed this prediction in a laboratory experiment on Rana temporaria tadpoles competing for limited food. There were 166 target individuals spanning a 10‐fold range in body mass reared for 3 days with three other individuals that were either the same size, half as large, or twice as large as the target. Relative growth rate (proportion per day) declined with size, and absolute growth rate (mass per day) reached a peak at intermediate size and declined thereafter. Tadpoles grew slowly if they were large relative to their competitors, although relative body size was less important than absolute size. As a result, size variation declined in groups that were initially composed of individuals of variable size. Thus, bigger was not better under exploitative competition. Our results help connect individual‐level behavior with individual growth and the size distribution of the population.

Individual, spatial and inter-sex variation in somatic growth: a study of Piaractus mesopotamicus (Characiformes: Serrasalmidae), a long-distance freshwater Neotropical migratory fish

ABSTRACT Growth is a fundamental biological process, driven by multiple endogenous (intra-individual) and exogenous (environmental) factors that maintain individual fitness and population stability. The current study aims to assess whether individual, spatial (headwaters and floodplains) and inter-sex variation occurs in the growth of Piaractus mesopotamicus in the Cuiabá River basin. Samples were collected monthly from July 2006 to July 2007, at two areas in the Cuiabá River basin (headwaters and floodplain). Three growth models (individuals; individuals and sex factors; individuals and areas factors) were developed and compared the fish growth parameters using Akaike information criterion (AIC). The best fit to the length-at-age data was obtained by a model that considered individual variation and sex. The theoretical maximum average length ( L∞ ) was 64.99 cm for females, and 63.23 cm for males. Females showed a growth rate (k) of 0.230 yr-1and males of 0.196 yr-1. Thus, could be concluded that individual variability and sex were the main sources of variation in P. mesopotamicus somatic growth parameters.

Trade-offs between accuracy and interpretability in von Bertalanffy random-effects models of growth

Better understanding of variation in growth will always be an important problem in ecology. Individual variation in growth can arise from a variety of processes; for example, individuals within a population vary in their intrinsic metabolic rates and behavioral traits, which may influence their foraging dynamics and access to resources. However, when adopting a growth model, we face trade-offs between model complexity, biological interpretability of parameters, and goodness of fit. We explore how different formulations of the von Bertalanffy growth function (vBGF) with individual random effects and environmental predictors affect these trade-offs. In the vBGF, the growth of an organism results from a dynamic balance between anabolic and catabolic processes. We start from a formulation of the vBGF that models the anabolic coefficient (q) as a function of the catabolic coefficient (k), a coefficient related to the properties of the environment (γ) and a parameter that determines the relative importance of behavior and environment in determining growth (ψ). We treat the vBGF parameters as a function of individual random effects and environmental variables. We use simulations to show how different functional forms and individual or group variability in the growth function's parameters provide a very flexible description of growth trajectories. We then consider a case study of two fish populations of Salmo marmoratus and Salmo trutta to test the goodness of fit and predictive power of the models, along with the biological interpretability of vBGF's parameters when using different model formulations. The best models, according to AIC, included individual variability in both k and γ and cohort as predictor of growth trajectories, and are consistent with the hypothesis that habitat selection is more important than behavioral and metabolic traits in determining lifetime growth trajectories of the two fish species. Model predictions of individual growth trajectories were largely more accurate than predictions based on mean size-at-age of fish. Our method shares information across individuals, and thus, for both fish populations investigated, allows using a single measurement early in the life of individual fish or cohort to obtain accurate predictions of lifetime individual or cohort size-at-age.

Determining individual variation in growth and its implication for life-history and population processes using the empirical Bayes method

The differences in demographic and life-history processes between organisms living in the same population have important consequences for ecological and evolutionary dynamics. Modern statistical and computational methods allow the investigation of individual and shared (among homogeneous groups) determinants of the observed variation in growth. We use an Empirical Bayes approach to estimate individual and shared variation in somatic growth using a von Bertalanffy growth model with random effects. To illustrate the power and generality of the method, we consider two populations of marble trout Salmo marmoratus living in Slovenian streams, where individually tagged fish have been sampled for more than 15 years. We use year-of-birth cohort, population density during the first year of life, and individual random effects as potential predictors of the von Bertalanffy growth function's parameters k (rate of growth) and (asymptotic size). Our results showed that size ranks were largely maintained throughout marble trout lifetime in both populations. According to the Akaike Information Criterion (AIC), the best models showed different growth patterns for year-of-birth cohorts as well as the existence of substantial individual variation in growth trajectories after accounting for the cohort effect. For both populations, models including density during the first year of life showed that growth tended to decrease with increasing population density early in life. Model validation showed that predictions of individual growth trajectories using the random-effects model were more accurate than predictions based on mean size-at-age of fish.

Somatic growth is a crucial determinant of ecological and evolutionary dynamics, since larger organisms often have higher survival and reproductive success. Size may be the result of intrinsic (i.e. genetic), environmental (temperature, food), and social (competition with conspecifics) factors and interaction between them. Knowing the contribution of intrinsic, environmental, and social factors will improve our understanding of individual population dynamics, help conservation and management of endangered species, and increase our ability to predict future growth trajectories of individuals and populations. The latter goal is also relevant for humans, since predicting future growth of newborns may help identify early pathologies that occur later in life. However, teasing apart the contribution of individual and environmental factors requires powerful and efficient statistical methods, as well as biological insights and the use of longitudinal data. We developed a novel statistical approach to estimate and separate the contribution of intrinsic and environmental factors to lifetime growth trajectories, and generate hypotheses concerning the life-history strategies of organisms. Using two fish populations as a case study, we show that our method predicts future growth of organisms with substantially greater accuracy than using historical information on growth at the population level, and help us identify year-class effects, probably associated with climatic vagaries, as the most important environmental determinant of growth.

A method for detecting positive growth autocorrelation without marking individuals

In most ecological studies, within-group variation is a nuisance that obscures patterns of interest and reduces statistical power. However, patterns of within-group variability often contain information about ecological processes. In particular, such patterns can be used to detect positive growth autocorrelation (consistent variation in growth rates among individuals in a cohort across time), even in samples of unmarked individuals. Previous methods for detecting autocorrelated growth required data from marked individuals. We propose a method that requires only estimates of within-cohort variance through time, using maximum likelihood methods to obtain point estimates and confidence intervals of the correlation parameter. We test our method on simulated data sets and determine the loss in statistical power due to the inability to identify individuals. We show how to accommodate nonlinear growth trajectories and test the effects of size-dependent mortality on our method's accuracy. The method can detect significant growth autocorrelation at moderate levels of autocorrelation with moderate-sized cohorts (for example, statistical power of 80% to detect growth autocorrelation ρ² = 0.5 in a cohort of 100 individuals measured on 16 occasions). We present a case study of growth in the red-eyed tree frog. Better quantification of the processes driving size variation will help ecologists improve predictions of population dynamics. This work will help researchers to detect growth autocorrelation in cases where marking is logistically infeasible or causes unacceptable decreases in the fitness of marked individuals.