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

When the going gets tough, the tough get going: Effect of extreme climate on an Antarctic seabird's life history

Individuals differ in many ways. Most produce few offspring; a handful produce many. Some die early; others live to old age. It is tempting to attribute these differences in outcomes to differences in individual traits, and thus in the demographic rates experienced. However, there is more to individual variation than meets the eye of the biologist. Even among individuals sharing identical traits, life history outcomes (life expectancy and lifetime reproduction) will vary due to individual stochasticity, that is to chance. Quantifying the contributions of heterogeneity and chance is essential to understand natural variability. Interindividual differences vary across environmental conditions, hence heterogeneity and stochasticity depend on environmental conditions. We show that favourable conditions increase the contributions of individual stochasticity, and reduce the contributions of heterogeneity, to variance in demographic outcomes in a seabird population. The opposite is true under poor conditions. This result has important consequence for understanding the ecology and evolution of life history strategies.

Building integral projection models with nonindependent vital rates

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co-vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs and include cases where the processes co-vary as a function of time (temporal variation), co-vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population-level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life-history evolution.

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.

The performance of permutations and exponential random graph models when analyzing animal networks

Social network analysis is a suite of approaches for exploring relational data. Two approaches commonly used to analyze animal social network data are permutation-based tests of significance and exponential random graph models. However, the performance of these approaches when analyzing different types of network data has not been simultaneously evaluated. Here we test both approaches to determine their performance when analyzing a range of biologically realistic simulated animal social networks. We examined the false positive and false negative error rate of an effect of a two-level explanatory variable (e.g., sex) on the number and combined strength of an individual’s network connections. We measured error rates for two types of simulated data collection methods in a range of network structures, and with/without a confounding effect and missing observations. Both methods performed consistently well in networks of dyadic interactions, and worse on networks constructed using observations of individuals in groups. Exponential random graph models had a marginally lower rate of false positives than permutations in most cases. Phenotypic assortativity had a large influence on the false positive rate, and a smaller effect on the false negative rate for both methods in all network types. Aspects of within- and between-group network structure influenced error rates, but not to the same extent. In "grouping event-based" networks, increased sampling effort marginally decreased rates of false negatives, but increased rates of false positives for both analysis methods. These results provide guidelines for biologists analyzing and interpreting their own network data using these methods.

Estimation of Genetic Variance in Fitness, and Inference of Adaptation, When Fitness Follows a Log-Normal Distribution

Additive genetic variance in relative fitness (σA2(w)) is arguably the most important evolutionary parameter in a population because, by Fisher’s fundamental theorem of natural selection (FTNS; Fisher RA. 1930. The genetical theory of natural selection. 1st ed. Oxford: Clarendon Press), it represents the rate of adaptive evolution. However, to date, there are few estimates of σA2(w) in natural populations. Moreover, most of the available estimates rely on Gaussian assumptions inappropriate for fitness data, with unclear consequences. “Generalized linear animal models” (GLAMs) tend to be more appropriate for fitness data, but they estimate parameters on a transformed (“latent”) scale that is not directly interpretable for inferences on the data scale. Here we exploit the latest theoretical developments to clarify how best to estimate quantitative genetic parameters for fitness. Specifically, we use computer simulations to confirm a recently developed analog of the FTNS in the case when expected fitness follows a log-normal distribution. In this situation, the additive genetic variance in absolute fitness on the latent log-scale (σA2(l)) equals (σA2(w)) on the data scale, which is the rate of adaptation within a generation. However, due to inheritance distortion, the change in mean relative fitness between generations exceeds σA2(l) and equals (exp⁡(σA2(l))−1). We illustrate why the heritability of fitness is generally low and is not a good measure of the rate of adaptation. Finally, we explore how well the relevant parameters can be estimated by animal models, comparing Gaussian models with Poisson GLAMs. Our results illustrate 1) the correspondence between quantitative genetics and population dynamics encapsulated in the FTNS and its log-normal-analog and 2) the appropriate interpretation of GLAM parameter estimates.

Fluctuating selection and its (elusive) evolutionary consequences in a wild rodent population

Temporal fluctuations in the strength and direction of selection are often proposed as a mechanism that slows down evolution, both over geological and contemporary timescales. Both the prevalence of fluctuating selection and its relevance for evolutionary dynamics remain poorly understood however, especially on contemporary timescales: unbiased empirical estimates of variation in selection are scarce, and the question of how much of the variation in selection translates into variation in genetic change has largely been ignored. Using long-term individual-based data for a wild rodent population, we quantify the magnitude of fluctuating selection on body size. Subsequently, we estimate the evolutionary dynamics of size and test for a link between fluctuating selection and evolution. We show that, over the past 11 years, phenotypic selection on body size has fluctuated significantly. However, the strength and direction of genetic change have remained largely constant over the study period; that is, the rate of genetic change was similar in years where selection favoured heavier vs. lighter individuals. This result suggests that over shorter timescales, fluctuating selection does not necessarily translate into fluctuating evolution. Importantly however, individual-based simulations show that the correlation between fluctuating selection and fluctuating evolution can be obscured by the effect of drift, and that substantially more data are required for a precise and accurate estimate of this correlation. We identify new challenges in measuring the coupling between selection and evolution, and provide methods and guidelines to overcome them.

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.

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.

Bigger Is Fitter? Quantitative Genetic Decomposition of Selection Reveals an Adaptive Evolutionary Decline of Body Mass in a Wild Rodent Population

In natural populations, quantitative trait dynamics often do not appear to follow evolutionary predictions. Despite abundant examples of natural selection acting on heritable traits, conclusive evidence for contemporary adaptive evolution remains rare for wild vertebrate populations, and phenotypic stasis seems to be the norm. This so-called “stasis paradox” highlights our inability to predict evolutionary change, which is especially concerning within the context of rapid anthropogenic environmental change. While the causes underlying the stasis paradox are hotly debated, comprehensive attempts aiming at a resolution are lacking. Here, we apply a quantitative genetic framework to individual-based long-term data for a wild rodent population and show that despite a positive association between body mass and fitness, there has been a genetic change towards lower body mass. The latter represents an adaptive response to viability selection favouring juveniles growing up to become relatively small adults, i.e., with a low potential adult mass, which presumably complete their development earlier. This selection is particularly strong towards the end of the snow-free season, and it has intensified in recent years, coinciding which a change in snowfall patterns. Importantly, neither the negative evolutionary change, nor the selective pressures that drive it, are apparent on the phenotypic level, where they are masked by phenotypic plasticity and a non causal (i.e., non genetic) positive association between body mass and fitness, respectively. Estimating selection at the genetic level enabled us to uncover adaptive evolution in action and to identify the corresponding phenotypic selective pressure. We thereby demonstrate that natural populations can show a rapid and adaptive evolutionary response to a novel selective pressure, and that explicitly (quantitative) genetic models are able to provide us with an understanding of the causes and consequences of selection that is superior to purely phenotypic estimates of selection and evolutionary change.

A population of snow voles provides a rare example of contemporary adaptive evolution in the wild, but without a quantitative genetic perspective this genetic change, and the selective pressure that underlies it, would have gone undetected.

Biologists struggle to demonstrate adaptive evolution in wild populations: while they routinely observe natural selection on heritable traits, in only a handful of cases could they demonstrate an evolutionary response. Although various explanations for this paradox have been proposed, comprehensive empirical tests are lacking. Over the past years, we have therefore studied an alpine population of snow voles. Following all individuals throughout their lives, we found that body mass is heritable and that heavy voles have a higher fitness. Nevertheless, mean body mass did not increase. To resolve this, we disentangled the role of genes and the environment in shaping body mass. This revealed that the population did evolve, but that this was masked by environmental variation. Furthermore, although the genetic change was adaptive, it was opposite to our initial expectation: the population evolved to become lighter, not heavier. This was because although heavy voles have the highest fitness, their mass does not cause high fitness. Instead, it is the voles with the genes for being light that do best, especially when the first winter snow arrives early. This shows that populations can evolve rapidly, but that without a genetic perspective, this, and its underlying mechanism, may go undetected.

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.