Modeling reproductive trajectories of roe deer females: fixed or dynamic heterogeneity?

Variety is the spice of life: nongenetic variation in life histories influences population growth and evolvability

Individual vital rates, such as mortality and birth rates, are key determinants of lifetime reproductive success, and variability in these rates shapes population dynamics. Previous studies have found that this vital rate heterogeneity can influence demographic properties, including population growth rates. However, the explicit effects of the variation within and the covariance between vital rates that can also vary throughout the lifespan on population growth remain unknown. Here, we explore the analytical consequences of nongenetic heterogeneity on long-term population growth rates and rates of evolution by modifying traditional age-structured population projection matrices to incorporate variation among individual vital rates. The model allows vital rates to be permanent throughout life ("fixed condition") or to change over the lifespan ("dynamic condition"). We reduce the complexity associated with adding individual heterogeneity to age-structured models through a novel application of matrix collapsing ("phenotypic collapsing"), showing how to collapse in a manner that preserves the asymptotic and transient dynamics of the original matrix. The main conclusion is that nongenetic individual heterogeneity can strongly impact the long-term growth rate and rates of evolution. The magnitude and sign of this impact depend heavily on how the heterogeneity covaries across the lifespan of an organism. Our results emphasize that nongenetic variation cannot simply be viewed as random noise, but rather that it has consistent, predictable effects on fitness and evolvability.

Demystifying individual heterogeneity

Among-individual variation in vital rates, such as mortality and birth rates, exists in nearly all populations. Recent studies suggest that this individual heterogeneity produces substantial life-history and fitness differences among individuals, which in turn scale up to influence population dynamics. However, our ability to understand the consequences of individual heterogeneity is limited by inconsistencies across conceptual frameworks in the field. Studies of individual heterogeneity remain filled with contradicting and ambiguous terminology that introduces risks of misunderstandings, conflicting models and unreliable conclusions. Here, we synthesise the existing literature into a single and comparatively straightforward framework with explicit terminology and definitions. This work introduces a distinction between potential vital rates and realised vital rates to develop a coherent framework that maps directly onto mathematical models of individual heterogeneity. We suggest the terms "fixed condition" and "dynamic condition" be used to distinguish potential vital rates that are permanent from those that can change throughout an individual's life. To illustrate, we connect the framework to quantitative genetics models and to common classes of statistical models used to infer individual heterogeneity. We also develop a population projection matrix model that provides an example of how our definitions are translated into precise quantitative terms.

Exploring causal components of plasticity in grey seal birthdates: Effects of intrinsic traits, demography, and climate

Change in breeding phenology is often a response to environmental forcing, but less is known of the mechanism underlying such changes and their fitness consequences. Here, we report on changes in the breeding phenology from a 27-year longitudinal study (1991-2017) of individually marked, known-aged grey seals (Halichoerus grypus) on Sable Island, Nova Scotia, Canada. We used generalized linear mixed models and a 3-step process to develop a model that includes interactions between intrinsic and extrinsic covariates and to test hypotheses about the influence of fixed factors (maternal age, parity, previous reproductive success, pup sex, colony density, Atlantic Multidecal Oscillation (AMO), North Atlantic Oscillation (NAO), and Sea Surface Temperature) and a random factor (female identity) on parturition dates. We also examined the consequences of the shift in birthdates on maternal energy allocation in offspring as measured by pup weaning mass. Birthdates were known for 2,768 pups of 660 known-age females. For 494 females with ≥2 parturition dates, repeatability as measured by the intraclass correlation was high (mean = 0.66). 87% of the variation in birthdates was explained by a mixed-effects model that included intrinsic and extrinsic fixed effects. Most of the explained variation was associated with the random effect of female identity. Parity was the most important intrinsic fixed effect, with inexperienced mothers giving birth later in the season than multiparous females. Over almost 3 decades, mean birthdates advanced by 15 days. The mixed model with intrinsic effects and population size, the detrended AMO from the previous year and mean NAO in the previous 3 years explained 80% of the variation with 21% of variation from the fixed effects. Both primiparous and multiparous individuals responded to the climate forcing, and there was strong evidence for heterogeneity in the response. Nevertheless, the shift in birthdates did not impact pup weaning mass.

Drivers of Diversification in Individual Life Courses

Heterogeneity in life courses among individuals of a population influences the speed of adaptive evolutionary processes, but it is less clear how biotic and abiotic environmental fluctuations influence such heterogeneity. We investigate principal drivers of variability in sequence of stages during an individual's life in a stage-structured population. We quantify heterogeneity by measuring population entropy of a Markov chain, which computes the rate of diversification of individual life courses. Using individual data of a primate population, we show that density regulates the stage composition of the population but that its entropy and the generating moments of heterogeneity are independent of density. This lack of influence of density on heterogeneity is due to neither low year-to-year variation in entropy nor differences in survival among stages but is rather due to differences in stage transitions. Our analysis thus shows that well-known classical ecological selective forces, such as density regulation, are not linked to potential selective forces governing heterogeneity through underlying stage dynamics. Despite evolution acting heavily on individual variability in fitness components, our understanding is poor whether observed heterogeneity is adaptive and how it evolves and is maintained. Our analysis illustrates how entropy represents a more integrated measure of diversity compared to the population structural composition, giving us new insights about the underlying drivers of individual heterogeneity within populations and potential evolutionary mechanisms.

From early life to senescence: individual heterogeneity in a long-lived seabird

Although population studies have long assumed that all individuals of a given sex and age are identical, ignoring among‐individual differences may strongly bias our perception of eco‐evolutionary processes. Individual heterogeneity, often referred to as individual quality, has received increasing research attention in the last decades. However, there are still substantial gaps in our current knowledge. For example, there is little information on how individual heterogeneity influences various life‐history traits simultaneously, and studies describing individual heterogeneity in wild populations are generally not able to jointly identify possible sources of this variation. Here, based on a mark–recapture data set of 9,685 known‐aged Wandering Albatrosses (Diomedea exulans), we investigated the existence of individual quality over the entire life cycle of this species, from early life to senescence. Using finite mixture models, we investigated the expression of individual heterogeneity in various demographic traits, and examined the origin of these among‐individual differences by considering the natal environmental conditions. We found that some individuals consistently outperformed others during most of their life. In old age, however, the senescence rate was stronger in males that showed high demographic performance at younger ages. Variation in individual quality seemed strongly affected by extrinsic factors experienced during the ontogenetic period. We found that individuals born in years with high population density tended to have lower performances during their lifespan, suggesting delayed density dependence effects through individual quality. Our study showed that among‐individual differences could be important in structuring individual life history trajectories, with substantial consequences at higher ecological levels such as population dynamics.

Drivers of Diversification in Individual Life Courses

Heterogeneity in life courses among individuals of a population influences the speed of adaptive evolutionary processes, but it is less clear how biotic and abiotic environmental fluctuations influence such heterogeneity. We investigate principal drivers of variability in sequence of stages during an individual's life in a stage-structured population. We quantify heterogeneity by measuring population entropy of a Markov chain, which computes the rate of diversification of individual life courses. Using individual data of a primate population, we show that density regulates the stage composition of the population but that its entropy and the generating moments of heterogeneity are independent of density. This lack of influence of density on heterogeneity is due to neither low year-to-year variation in entropy nor differences in survival among stages but is rather due to differences in stage transitions. Our analysis thus shows that well-known classical ecological selective forces, such as density regulation, are not linked to potential selective forces governing heterogeneity through underlying stage dynamics. Despite evolution acting heavily on individual variability in fitness components, our understanding is poor whether observed heterogeneity is adaptive and how it evolves and is maintained. Our analysis illustrates how entropy represents a more integrated measure of diversity compared to the population structural composition, giving us new insights about the underlying drivers of individual heterogeneity within populations and potential evolutionary mechanisms.

Explaining long-term inter-individual growth variation in plant populations: persistence of abiotic factors matters

An unanswered question in ecology is whether the environmental factors driving short-term performance also determine the often observed long-term performance differences among individuals. Here, we analyze the extent to which temporal persistence of spatial heterogeneity in environmental factors can contribute to long-term inter-individual variation in stem length growth. For a natural population of a long-lived understorey palm, we first quantified the effect of several environmental factors on stem length growth and survival. We then performed individual-based simulations of growth trajectories, in which we varied, for two environmental factors: (1) the strength of the effect on stem length growth and (2) the temporal persistence. Short-term variation in stem length growth was strongly driven by light availability. Auto-correlation in light availability and soil pH increased simulated variation in stem length growth among 20-year-old palms to levels similar to the observed variation. Analyses in which we varied both the strength of the effect on stem length growth and the temporal persistence of the environmental factors revealed that a large fraction of observed long-term growth differences can be explained, as long as one of these effects is strong. This implies that environmental factors that are relatively unimportant for short-term performance can still drive long-term performance differences when the environmental variation is sufficiently persistent over time.

Trait level analysis of multitrait population projection matrices

In most matrix population projection models, individuals are characterized according to, usually, one or two traits such as age, stage, size or location. A broad theory of multitrait population projection matrices (MPPMs) incorporating larger number of traits was long held back by time and space computational complexity issues. As a consequence, no study has yet focused on the influence of the structure of traits describing a life-cycle on population dynamics and life-history evolution. We present here a novel vector-based MPPM building methodology that allows to computationally-efficiently model populations characterized by numerous traits with large distributions, and extend sensitivity analyses for these models. We then present a new method, the trait level analysis consisting in folding an MPPM on any of its traits to create a matrix with alternative trait structure (the number of traits and their characteristics) but similar asymptotic properties. Adding or removing one or several traits to/from the MPPM and analyzing the resulting changes in spectral properties, allows investigating the influence of the trait structure on the evolution of traits. We illustrate this by modeling a 3-trait (age, parity and fecundity) population designed to investigate the implications of parity-fertilitytrade-offs in a context of fecundity heterogeneity in humans. The trait level analysis, comparing models of the same population differing in trait structures, demonstrates that fertility selection gradients differ between cases with or without parity-fertility trade-offs. Moreover it shows that age-specific fertility has seemingly very different evolutionary significance depending on whether heterogeneity is accounted for. This is because trade-offs can vary strongly in strength and even direction depending on the trait structure used to model the population.

Wolf in sheep's clothing: Model misspecification undermines tests of the neutral theory for life histories

Understanding the processes behind change in reproductive state along life‐history trajectories is a salient research program in evolutionary ecology. Two processes, state dependence and heterogeneity, can drive the dynamics of change among states. Both processes can operate simultaneously, begging the difficult question of how to tease them apart in practice. The Neutral Theory for Life Histories (NTLH) holds that the bulk of variations in life‐history trajectories is due to state dependence and is hence neutral: Once previous (breeding) state is taken into account, variations are mostly random. Lifetime reproductive success (LRS), the number of descendants produced over an individual's reproductive life span, has been used to infer support for NTLH in natura. Support stemmed from accurate prediction of the population‐level distribution of LRS with parameters estimated from a state dependence model. We show with Monte Carlo simulations that the current reliance of NTLH on LRS prediction in a null hypothesis framework easily leads to selecting a misspecified model, biased estimates and flawed inferences. Support for the NTLH can be spurious because of a systematic positive bias in estimated state dependence when heterogeneity is present in the data but ignored in the analysis. This bias can lead to spurious positive covariance between fitness components when there is in fact an underlying trade‐off. Furthermore, neutrality implied by NTLH needs a clarification because of a probable disjunction between its common understanding by evolutionary ecologists and its translation into statistical models of life‐history trajectories. Irrespective of what neutrality entails, testing hypotheses about the dynamics of change among states in life histories requires a multimodel framework because state dependence and heterogeneity can easily be mistaken for each other.

Successful by Chance? The Power of Mixed Models and Neutral Simulations for the Detection of Individual Fixed Heterogeneity in Fitness Components

Heterogeneity in fitness components consists of fixed heterogeneity due to latent differences fixed throughout life (e.g., genetic variation) and dynamic heterogeneity generated by stochastic variation. Their relative magnitude is crucial for evolutionary processes, as only the former may allow for adaptation. However, the importance of fixed heterogeneity in small populations has recently been questioned. Using neutral simulations (NS), several studies failed to detect fixed heterogeneity, thus challenging previous results from mixed models (MM). To understand the causes of this discrepancy, we estimate the statistical power and false positive rate of both methods and apply them to empirical data from a wild rodent population. While MM show high false-positive rates if confounding factors are not accounted for, they have high statistical power to detect real fixed heterogeneity. In contrast, NS are also subject to high false-positive rates but always have low power. Indeed, MM analyses of the rodent population data show significant fixed heterogeneity in reproductive success, whereas NS analyses do not. We suggest that fixed heterogeneity may be more common than is suggested by NS and that NS are useful only if more powerful methods are not applicable and if they are complemented by a power analysis.

We Happy Few: Using Structured Population Models to Identify the Decisive Events in the Lives of Exceptional Individuals

In any population, some individuals make it big: they are among the few that produce many offspring, grow to large size, and so on. What distinguishes the lives of these happy few? We present three approaches for identifying what factors distinguish those "lucky" individuals who come to dominate reproduction in a population without fixed differences between individuals (genotype, site quality, etc.): comparing life-history trajectories for lucky and unlucky individuals and calculating the elasticity of the probability of becoming lucky to perturbations in demographic rates at a given size or a given age. As examples we consider published size-structured integral projection models for the tropical tree Dacrydium elatum and the semiarid shrub Artemisia ordosica and an age-size-structured matrix model for the tropical tree Cedrela ordosica. We find that good fortune (e.g., rapid growth) when small and young matters much more than good fortune when older and larger. Becoming lucky is primarily a matter of surviving while others die. For species with more variable growth (such as Cedrela and Ordosica), it is also a matter of growing fast. We focus on reproductive skew, but our methods are broadly applicable and can be used to investigate how individuals come to be exceptional in any aspect.

The survival-reproduction association becomes stronger when conditions are good

Positive covariations between survival and reproductive performance (S-R covariation) are generally interpreted in the context of fixed or dynamic demographic heterogeneity (i.e. persistent differences between individuals, or dynamic variation in resource acquisition), but the processes underlying covariations are still unknown. We used multi-event modelling to investigate how environmental and individual features influence S-R covariation patterns in a long-lived seabird, the Monteiro's storm petrel (Oceanodroma monteiroi). Our analysis reveals that a strong positive association between individual breeding success and subsequent survival occurs only when conditions are favourable to reproduction (in favourable years, in high-quality nests and in nest-faithful breeders). This finding reflects differences in the main causes of breeding failure and mortality under favourable and unfavourable conditions, which in turn lead to distinct patterns of S-R covariation. We suggest, in particular, that resource-related sources of demographic heterogeneity do not generate a strong S-R covariation, in contrast with hidden and unpredictable sources of variation.

Individual heterogeneity in reproductive rates and cost of reproduction in a long-lived vertebrate

Individual variation in reproductive success is a key feature of evolution, but also has important implications for predicting population responses to variable environments. Although such individual variation in reproductive outcomes has been reported in numerous studies, most analyses to date have not considered whether these realized differences were due to latent individual heterogeneity in reproduction or merely random chance causing different outcomes among like individuals. Furthermore, latent heterogeneity in fitness components might be expressed differently in contrasted environmental conditions, an issue that has only rarely been investigated. Here, we assessed (i) the potential existence of latent individual heterogeneity and (ii) the nature of its expression (fixed vs. variable) in a population of female Weddell seals (Leptonychotes weddellii), using a hierarchical modeling approach on a 30-year mark–recapture data set consisting of 954 individual encounter histories. We found strong support for the existence of latent individual heterogeneity in the population, with “robust” individuals expected to produce twice as many pups as “frail” individuals. Moreover, the expression of individual heterogeneity appeared consistent, with only mild evidence that it might be amplified when environmental conditions are severe. Finally, the explicit modeling of individual heterogeneity allowed us to detect a substantial cost of reproduction that was not evidenced when the heterogeneity was ignored.