Eco‐evolutionary partitioning metrics: assessing the importance of ecological and evolutionary contributions to population and community change

Interest in eco‐evolutionary dynamics is rapidly increasing thanks to ground‐breaking research indicating that evolution can occur rapidly and can alter the outcome of ecological processes. A key challenge in this sub‐discipline is establishing how important the contribution of evolutionary and ecological processes and their interactions are to observed shifts in population and community characteristics. Although a variety of metrics to separate and quantify the effects of evolutionary and ecological contributions to observed trait changes have been used, they often allocate fractions of observed changes to ecology and evolution in different ways. We used a mathematical and numerical comparison of two commonly used frameworks – the Price equation and reaction norms – to reveal that the Price equation cannot partition genetic from non‐genetic trait change within lineages, whereas the reaction norm approach cannot partition among‐ from within‐lineage trait change. We developed a new metric that combines the strengths of both Price‐based and reaction norm metrics, extended all metrics to analyse community change and also incorporated extinction and colonisation of species in these metrics. Depending on whether our new metric is applied to populations or communities, it can correctly separate intraspecific, interspecific, evolutionary, non‐evolutionary and interacting eco‐evolutionary contributions to trait change.     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

The importance of the timescale of the fitness metric for estimates of selection on phenotypic traits during a period of demographic change

Although fitness is central to the evolutionary process, metrics vary by timescale. Different timescales may give rise to different estimates of selection, especially during demographic transitions caused by rapid environmental and socioeconomic change. In this study, we used a dataset of a human population in Finland from 1775 to 1950 to compare two fitness metrics and their estimates of selection pressures, before and during a demographic transition. Both metrics, lifetime reproductive success and an annual metric of individual performance, declined while selection on the ages at first and last reproduction remained nearly constant, favouring individuals with wider reproductive windows. The ability to partition the annual metric into contributions from reproduction and survival revealed the short‐term effects of a famine and the reversal of selection pressure via the survival component of annual fitness. Although the metrics generally agreed, the annual metric detected the effects of environmental variation and demographic change occurring within a generation.     

Niche construction and the environmental term of the price equation: How natural selection changes when organisms alter their environments

Organisms construct their own environments and phenotypes through the adaptive processes of habitat choice, habitat construction, and phenotypic plasticity. We examine how these processes affect the dynamics of mean fitness change through the environmental change term of the Price Equation. This tends to be ignored in evolutionary theory, owing to the emphasis on the first term describing the effect of natural selection on mean fitness (the additive genetic variance for fitness of Fisher's Fundamental Theorem). Using population genetic models and the Price Equation, we show how adaptive niche constructing traits favorably alter the distribution of environments that organisms encounter and thereby increase population mean fitness. Because niche-constructing traits increase the frequency of higher-fitness environments, selection favors their evolution. Furthermore, their alteration of the actual or experienced environmental distribution creates selective feedback between niche constructing traits and other traits, especially those with genotype-by-environment interaction for fitness. By altering the distribution of experienced environments, niche constructing traits can increase the additive genetic variance for such traits. This effect accelerates the process of overall adaption to the niche-constructed environmental distribution and can contribute to the rapid refinement of alternative phenotypic adaptations to different environments. Our findings suggest that evolutionary biologists revisit and reevaluate the environmental term of the Price Equation: owing to adaptive niche construction, it contributes directly to positive change in mean fitness; its magnitude can be comparable to that of natural selection; and, when there is fitness G × E, it increases the additive genetic variance for fitness, the much-celebrated first term.     

Measures of success in a class of evolutionary models with fixed population size and structure

We investigate a class of evolutionary models, encompassing many established models of well-mixed and spatially structured populations. Models in this class have fixed population size and structure. Evolution proceeds as a Markov chain, with birth and death probabilities dependent on the current population state. Starting from basic assumptions, we show how the asymptotic (long-term) behavior of the evolutionary process can be characterized by probability distributions over the set of possible states. We then define and compare three quantities characterizing evolutionary success: fixation probability, expected frequency, and expected change due to selection. We show that these quantities yield the same conditions for success in the limit of low mutation rate, but may disagree when mutation is present. As part of our analysis, we derive versions of the Price equation and the replicator equation that describe the asymptotic behavior of the entire evolutionary process, rather than the change from a single state. We illustrate our results using the frequency-dependent Moran process and the birth–death process on graphs as examples. Our broader aim is to spearhead a new approach to evolutionary theory, in which general principles of evolution are proven as mathematical theorems from axioms.     

Grafen,the Price equations,fitness maximization,optimisation and the fundamental theorem of natural selection

This paper is a commentary on the focal article by Grafen and on earlier papers of his on which many of the results of this focal paper depend. Thus it is in effect a commentary on the “formal Darwinian project”, the focus of this sequence of papers. Several problems with this sequence are raised and discussed. The first of these concerns fitness maximization. It is often claimed in these papers that natural selection leads to a maximization of fitness and that this view is claimed in Fisher’s “fundamental theorem of natural selection”. These claims are refuted, and various incorrect statements about the meaning and interpretation of the fundamental theorem of natural selection, in this sequence and in other papers by other authors, are discussed. Next, much of the work in this sequence rests on the first Price equation. In the deterministic (infinite population) case this equation is no more than the standard classical equation relating to changes in gene frequencies. In the stochastic case the equation gives the change in gene frequencies as the sum of two terms (the second of which vanishes in the deterministic case). These two terms are of essentially equal importance in the situation considered in the focal article, yet one of Grafen’s results ignores the second term in the stochastic analysis. This is associated with a wavering between deterministic and stochastic analyses and the use of the Price fitness concept and the classical fitness concept. These comments cast doubts on Grafen’s optimization theory.     

Variation in Allee effects: evidence,unknowns, and directions forward

Allee effects, positive effects of population size or density on per-capita fitness, are of broad interest in ecology and conservation due to their importance to the persistence of small populations and to range boundary dynamics. A number of recent studies have highlighted the importance of spatiotemporal variation in Allee effects and the resulting impacts on population dynamics. These advances challenge conventional understanding of Allee effects by reframing them as a dynamic factor affecting populations instead of a static condition. First, we synthesize evidence for variation in Allee effects and highlight potential mechanisms. Second, we emphasize the “Allee slope,” i.e., the magnitude of the positive effect of density on the per-capita growth rate, as a metric for demographic Allee effects. The more commonly used quantitative metric, the Allee threshold, provides only a partial picture of the underlying forces acting on population growth despite its implications for population extinction. Third, we identify remaining unknowns and strategies for addressing them. Outstanding questions about variation in Allee effects fall broadly under three categories: (1) characterizing patterns of natural variability; (2) understanding mechanisms of variation; and (3) implications for populations, including applications to conservation and management. Future insights are best achieved through robust interactions between theory and empiricism, especially through mechanistic models. Understanding spatiotemporal variation in the demographic processes contributing to the dynamics of small populations is a critical step in the advancement of population ecology.     

Natural selection, fitness entropy, and the dynamics of coevolution

The coevolutionary dynamics of interacting populations were studied by combining continuous time Lotka-Volterra models of population growth with single-locus genetic models of weak selection. The effects of natural selection on population growth were evaluated using Ginzburg's fitness entropy function as a measure of the deviation of a population's initial allele frequencies from their polymorphic equilibrium values. This entropy measure was used to relate the dynamics of a community composed of evolving populations to the dynamics of a "reference community" whose populations are initially in genetic equilibrium. Specifically, a quantity called the "selective difference area" was defined as the total difference between the population size trajectories of a reference and evolving population. The selective difference area represents the amount of extra life a species would realize if the entire community were at genetic equilibrium. It was shown that this selective difference area is a simple linear function of the initial fitness entropies of each species. This prediction is independent of the strength of selection and holds for any arbitrary set of initial population densities. Numerical examples were presented to illustrate the results. Under the assumption of weak selection, a generalization for arbitrary population growth models was outlined.     

Stochastic sampling of interaction partners versus deterministic payoff assignment

Evolutionary game dynamics describes how successful strategies spread in a population. In well-mixed populations, the usual assumption, e.g. underlying the replicator dynamics, is that individuals obtain a payoff from interactions with a representative sample of the population. This determines their fitness. Here, we analyze a situation in which payoffs are obtained through a single interaction, so that individuals of the same type can have different payoffs. We show analytically that for weak selection, this scenario is identical to the usual approach in which an individual interacts with the whole population. For strong selection, however, differences arise that are reflected in the fixation probabilities and lead to deviating evolutionary dynamics.     

Extinction, colonization, and species occupancy in tidepool fishes

Despite the increasing sophistication of ecological models with respect to the size and spatial arrangement of habitat, there is relatively little empirical documentation of how species dynamics change as a function of habitat size and the fraction of habitat occupied. In an assemblage of tidepool fishes, I used maximum-likelihood estimation to test whether models which included habitat size provided a better fit to empirical data on extinction and colonization probabilities than models that assumed constant probabilities over all habitats. I found species differences in how extinction and colonization probabilities scaled with habitat size (and hence local population size). However, there was little evidence for a relationship between extinction and colonization probabilities and the fraction of occupied tidepools, as assumed in simple metapopulation models. Instead, colonization and extinction were independent of the fraction of occupied tidepools, favoring a MacArthur-Wilson island-mainland model. When I incorporated declines in extinction probability with tidepool volume in a simple simulation model, I found that predicted occupancy could change greatly, especially when colonization was low. However, the predicted fraction of occupied patches in the simulation model changed little when I incorporated the range of values reported here for extinction and colonization and the rate at which they scale with habitat size. Quantifying extinction and colonization patterns of natural populations is fundamental to understanding how species are distributed spatially and whether metapopulation models of species occupancy provide explanatory power for field populations. Received: 14 March 1997 / Accepted: 21 September 1997     

Smaller, scale-free gene networks increase quantitative trait heritability and result in faster population recovery

One of the goals of biology is to bridge levels of organization. Recent technological advances are enabling us to span from genetic sequence to traits, and then from traits to ecological dynamics. The quantitative genetics parameter heritability describes how quickly a trait can evolve, and in turn describes how quickly a population can recover from an environmental change. Here I propose that we can link the details of the genetic architecture of a quantitative trait--i.e., the number of underlying genes and their relationships in a network--to population recovery rates by way of heritability. I test this hypothesis using a set of agent-based models in which individuals possess one of two network topologies or a linear genotype-phenotype map, 16-256 genes underlying the trait, and a variety of mutation and recombination rates and degrees of environmental change. I find that the network architectures introduce extensive directional epistasis that systematically hides and reveals additive genetic variance and affects heritability: network size, topology, and recombination explain 81% of the variance in average heritability in a stable environment. Network size and topology, the width of the fitness function, pre-change additive variance, and certain interactions account for ～75% of the variance in population recovery times after a sudden environmental change. These results suggest that not only the amount of additive variance, but importantly the number of loci across which it is distributed, is important in regulating the rate at which a trait can evolve and populations can recover. Taken in conjunction with previous research focused on differences in degree of network connectivity, these results provide a set of theoretical expectations and testable hypotheses for biologists working to span levels of organization from the genotype to the phenotype, and from the phenotype to the environment.     

Use of erythrocyte indicators of health and condition in vertebrate ecophysiology: a review and appraisal

We review evidence for and against the use of erythrocyte indicators of health status and condition, parasite infection level and physiological stress in free‐living vertebrates. The use of indicators that are measured directly from the blood, such as haemoglobin concentration, haematocrit and erythrocyte sedimentation rate, and parameters that are calculated from multiple measured metrics, such as mean cell volume, mean cell haemoglobin content or mean cell haemoglobin concentration is evaluated. The evidence for or against the use of any given metric is equivocal when the relevant research is considered in total, although there is sometimes strong support for using a particular metric in a particular taxon. Possibly the usefulness of these metrics is taxon, environment or condition specific. Alternatively, in an uncontrolled environment where multiple factors are influencing a metric, its response to environmental change will sometimes, but not always, be predictable. We suggest that (i) researchers should validate a metricfres utility before use, (ii) multiple metrics should be used to construct an overall erythrocyte profile for an individual or population, (iii) there is a need for researchers to compile reference ranges for free‐living species, and (iv) some metrics which are useful under controlled, clinical conditions may not have the same utility or applicability for free‐living vertebrates. Erythrocyte metrics provide useful information about health and condition that can be meaningfully interpreted in free‐living vertebrates, but their use requires careful forethought about confounding factors.     

Winning and losing with microbes: how microbially mediated fitness differences influence plant diversity

Interactions between plants and soil microbes can strongly influence plant diversity and community dynamics. Soil microbes may promote plant diversity by driving negative frequency‐dependent plant population dynamics, or may favor species exclusion by providing one species an average fitness advantage over others. However, past empirical research has focused overwhelmingly on the consequences of frequency‐dependent feedbacks for plant species coexistence and has generally neglected the consequences of microbially mediated average fitness differences. Here we use theory to develop metrics that quantify microbially mediated plant fitness differences, and show that accounting for these effects can profoundly change our understanding of how microbes influence plant diversity. We show that soil microbes can generate fitness differences that favour plant species exclusion when they disproportionately harm (or favour) one plant species over another, but these fitness differences may also favor coexistence if they trade off with competition for other resources or generate intransitive dominance hierarchies among plants. We also show how the metrics we present can quantify microbially mediated fitness differences in empirical studies, and explore how microbial control over coexistence varies along productivity gradients. In all, our analysis provides a more complete theoretical foundation for understanding how plant–microbe interactions influence plant diversity.     

Complexity, pleiotropy, and the fitness effect of mutations

One of the assumptions underlying many theoretical predictions in evolutionary biology concerns the distribution of the fitness effect of mutations. Approximations to this distribution have been derived using various theoretical approaches, of which Fisher's geometrical model is among the most popular ones. Two key concepts in this model are complexity and pleiotropy. Recent studies have proposed different methods for estimating how complexity varies across species, but their results have been contradictory. Here, we show that contradictory results are to be expected when the assumption of universal pleiotropy is violated. We develop a model in which the two key parameters are the total number of traits and the mean number of traits affected by a single mutation. We derive approximations for the distribution of the fitness effect of mutations when populations are either well-adapted or away from the optimum. We also consider drift load in a well-adapted population and show that it is independent of the distribution of the fitness effect of mutations. We show that mutation accumulation experiments can only measure the effect of the mean number of traits affected by mutations, whereas drift load only provides information about the total number of traits. We discuss the plausibility of the model.     

Cultural transmission of fitness: genes take the fast lane

Classical population genetics describes how the fate of an allele is driven by four forces: mutation, migration, selection and drift. However, these are sometimes insufficient to explain how the observed allele frequency changes and, therefore, another factor must be invoked: cultural transmission of fitness (CTF). CTF is the non-genetic transmission of any kind of behaviour that affects reproductive success. There are several clearly documented examples of CTF, and theoretical studies have shown that it affects effective population size, linkage disequilibrium and coalescent times. It is therefore a factor that must be taken into account to explain the structure of genetic diversity. In this article, we will present documented cases of how CTF affects the genetic diversity of populations and yields dramatic changes in allele frequencies.     

To aggregate or not? Capturing the spatio-temporal complexity of the thermal regime

Freshwater stream systems are under immense pressure from various anthropogenic impacts, including climate change. Stream systems are increasingly being altered by changes to the magnitude, timing, frequency, and duration of their thermal regimes, which will have profound impacts on the life-history dynamics of resident biota within their home range. Although temperature regimes have a significant influence on the biology of instream fauna, large spatio-temporal temperature datasets are often reduced to a single metric at discrete locations and used to describe the thermal regime of a system; potentially leading to a significant loss of information crucial to stream management. Models are often used to extrapolate these metrics to unsampled locations, but it is unclear whether predicting actual daily temperatures or an aggregated metric of the temperature regime best describes the complexity of the thermal regime. We fit spatial statistical stream-network models (SSNMs), random forest and non-spatial linear models to stream temperature data from the Upper Condamine River in QLD, Australia and used them to semi-continuously predict metrics describing the magnitude, duration, and frequency of the thermal regime through space and time. We compared both daily and aggregated temperature metrics and found that SSNMs always had more predictive ability than the random forest models, but both models outperformed the non-spatial linear model. For metrics describing thermal magnitude and duration, aggregated predictions were most accurate, while metrics describing the frequency of heating events were better represented by metrics based on daily predictions generated using a SSNM. A more comprehensive representation of the spatio-temporal thermal regime allows researchers to explore new spatio-temporally explicit questions about the thermal regime. It also provides the information needed to generate a suite of ecologically meaningful metrics capturing multiple aspects of the thermal regime, which will increase our scientific understanding of how organisms respond to thermal cues and provide much-needed information for more effective management actions.     

An evaluation of information content as a metric for the inference of putative conserved noncoding regions in DNA sequences using a genetic algorithms approach

In previous work, we presented GAMI, an approach to motif inference that uses a genetic algorithms search. GAMI is designed specifically to find putative conserved regulatory motifs in noncoding regions of divergent species, and is designed to allow for analysis of long nucleotide sequences. In this work, we compare GAMI's performance when run with its original fitness function (a simple count of the number of matches) and when run with information content, as well as several variations on these metrics. Results indicate that information content does not identify highly conserved regions, and thus is not the appropriate metric for this task, while variations on information content as well as the original metric succeed in identifying putative conserved regions.     

Inbreeding, heterozygosity and fitness in a reintroduced population of endangered African wild dogs (Lycaon pictus)

It is crucial to understand the genetic health and implications of inbreeding in wildlife populations, especially of vulnerable species. Using extensive demographic and genetic data, we investigated the relationships among pedigree inbreeding coefficients, metrics of molecular heterozygosity and fitness for a large population of endangered African wild dogs (Lycaon pictus) in South Africa. Molecular metrics based on 19 microsatellite loci were significantly, but modestly correlated to inbreeding coefficients in this population. Inbred wild dogs with inbreeding coefficients of ??0.25 and subordinate individuals had shorter lifespans than outbred and dominant contemporaries, suggesting some deleterious effects of inbreeding. However, this trend was confounded by pack-specific effects as many inbred individuals originated from a single large pack. Despite wild dogs being endangered and existing in small populations, findings within our sample population indicated that molecular metrics were not robust predictors in models of fitness based on breeding pack formation, dominance, reproductive success or lifespan of individuals. Nonetheless, our approach has generated a vital database for future comparative studies to examine these relationships over longer periods of time. Such detailed assessments are essential given knowledge that wild canids can be highly vulnerable to inbreeding effects over a few short generations.