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Statistical associations between phenotypic traits often result from shared developmental processes and include both covariation between the trait values and more complex associations between higher moments of the joint distribution of traits. In this article, an analytical technique for calculating the covariance between traits is presented on the basis of (1) the distribution of underlying genetic and environmental variation that jointly influences the traits and (2) the mechanics of how these underlying factors influence the development of each trait. It is shown that epistasis can produce patterns of covariation between traits that are not seen in additive models. Applying this approach to a trait in parents and the same trait in their offspring allows us to study the consequences of epistasis for the evolution of additive genetic variance and heritability. This analysis is then extended to the study of more complicated associations between traits. It is shown that even traits that are not correlated may exhibit developmental associations that influence their joint evolution.

Abstract Background Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. Results I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Conclusion Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general prospective evolution equation compliments the Price equation and shows that the influence of stochastic processes on directional evolution is more diverse than has generally been recognized.

Reciprocity is characterized by individuals actively making it beneficial for others to cooperate by responding to them. This makes it a particularly powerful generator of mutual interest, because the benefits accrued by an individual can be redistributed to another. However, reciprocity is a composite biological function, entailing at least two subfunctions: (i) a behavioral ability to provide fitness benefits to others and (ii) a cognitive ability to evaluate the benefits received from others. For reciprocity to evolve, these two subfunctions must appear together, which raises an evolutionary problem of bootstrapping. In this article, I develop mathematical models to study the necessary conditions for the gradual emergence of reciprocity in spite of this bootstrapping problem. I show that the evolution of reciprocity is based on three conditions. First, there must be some variability in behavior. Second, cooperation must pre-evolve for reasons independent of reciprocity. Third, and most significantly, selection favors conditional cooperation only if the cooperation expressed by others is already conditional, that is, if some reciprocity is already present in the first place. In the discussion, I show that these three conditions help explain the specific features of the instances in which reciprocity does occur in the wild. For instance, it accounts for the role of spatial symmetry (as in ungulate allogrooming), the importance of synergistic benefits (as in nuptial gifts), the facilitating role of collective actions (as in many instances of human cooperation), and the potential role of kinship (as in primate grooming). [ABSTRACT FROM AUTHOR]

The allocation of resources between growth, storage, and reproduction is a key trade-off in the life-history strategies of organisms. A central dichotomy is between capital breeders and income breeders. Capital breeders build reserves that allow them to spawn at a later time independently of food availability, while income breeders allocate ingested food directly to reproduction. Motivated by copepod studies, we use an analytical model to compare the fitness of income with capital breeding in a deterministic seasonal environment. We analyze how the fitness of breeding strategies depend on feeding season duration and size at maturity. Small capital breeders perform better in short feeding seasons but fall behind larger individuals when the length of the feeding season increases. Income breeding favors smaller individuals as their short generation time allows for multiple generations within a year and thereby achieve a high annual growth rate, outcompeting capital breeders in long feeding seasons. Therefore, we expect to find a dominance of small income breeders in temperate waters, while large capital breeders should dominate high latitudes where the spring is short and intense. This pattern is evident in nature, particularly in organisms with a generation time of a year or less. [ABSTRACT FROM AUTHOR]

Environmental change, if severe, can drive a population extinct unless the population succeeds in adapting to the new conditions. How likely is a population to win the race between population decline and adaptive evolution? Assuming that environmental degradation progresses across a habitat, we analyze the impact of several ecological factors on the probability of evolutionary rescue. Specifically, we study the influence of population structure and density- dependent competition as well as the speed and severity of environmental change. We also determine the relative contribution of standing genetic variation and new mutations to evolutionary rescue. To describe population structure, we use a generalized island model, where islands are affected by environmental deterioration one after the other. Our analysis is based on the mathematical theory of timeinhomogeneous branching processes and complemented by computer simulations. We find that in the interplay of various, partially antagonistic effects, the probability of evolutionary rescue can show nontrivial and unexpected dependence on ecological characteristics. In particular, we generally observe a nonmonotonic dependence on the migration rate between islands. Counterintuitively, under some circumstances, evolutionary rescue can occur more readily in the face of harsher environmental shifts, because of the reduced competition experienced by mutant individuals. Similarly, rescue sometimes occurs more readily when the entire habitat degrades rapidly, rather than progressively over time, particularly when migration is high and competition strong. [ABSTRACT FROM AUTHOR]

A major criticism of the "overkill" theory for the late Pleistocene extinction in the Americas has been the seeming implausibility of a relatively small number of humans selectively killing off millions of large-bodied mammals. Critics argue that early Paleoindian hunters had to be extremely selective to have produced the highly size-biased extinction pattern characteristic of this event. Here, we derive a probabilistic extinction model that predicts the extinction risk of mammals at any body mass without invoking selective human harvest. The new model systematically analyzes the variability in life-history characteristics, such as the instantaneous mortality rate, age of first reproduction, and the maximum net reproductive rate. It captures the body size-biased extinction pattern in the late Pleistocene and precisely predicts the percentage of unexpectedly persisting large mammals and extinct small ones. A test with a global late Quaternary mammal database well supports the model. The model also emphasizes that quantitatively analyzing patterns of variability in ecological factors can shed light on diverse behaviors and patterns in nature. From a macro-scale conservation perspective, our model can be modified to predict the fate of biota under the pressures from both climate change and human impacts. [ABSTRACT FROM AUTHOR]

How individual-level movement decisions in response to habitat edges influence population-level patterns of persistence and spread of a species is a major challenge in spatial ecology and conservation biology. Here, we integrate novel insights into edge behavior, based on habitat preference and movement rates, into spatially explicit growth-dispersal models. We demonstrate how crucial ecological quantities (e.g., minimal patch size, spread rate) depend critically on these individual-level decisions. In particular, we find that including edge behavior properly in these models gives qualitatively different and intuitively more reasonable results than those of some previous studies that did not consider this level of detail. Our results highlight the importance of new empirical work on individual movement response to habitat edges. [ABSTRACT FROM AUTHOR]

Recent years have seen huge interest in understanding how demographic factors mediate the evolution of social behavior in viscous populations. Here we study the impact of variation in group size on the evolution of helping and harming behavior. Although variation in group size influences the degree of relatedness and the degree of competition between groupmates, we find that these effects often exactly cancel, so as to give no net impact of variation in group size on the evolution of helping and harming. Specifically, (1) obligate helping and harming are never mediated by variation in group size, (2) facultative helping and harming are not mediated by variation in group size when this variation is spatial only, (3) facultative helping and harming are mediated by variation in group size only when this variation is temporal or both spatial and temporal, and (4) when there is an effect of variation in group size, facultative helping is favored in big groups and facultative harming is favored in little groups. Moreover, we find that spatial and temporal heterogeneity in individual fecundity may interact with patch-size heterogeneity to change these predictions, promoting the evolution of harming in big patches and of helping in little patches. [ABSTRACT FROM AUTHOR]

Current theory explains accelerating invasions with increased levels of dispersal as being caused by "spatial selection." Here we argue that another selective force, strong kin competition resulting from high relatedness due to subsequent founder effects at the expanding margin, is of at least comparable importance for dispersal evolution during invasions. We test this hypothesis with individualbased simulations of a spatially structured population invading empty space. To quantify the relative contribution of kin competition to dispersal evolution, we contrast two scenarios, one including kin effects and one excluding them without influencing spatial selection. We find that kin competition is a major determinant for dispersal evolution at invasion fronts, especially under environmental conditions that favor a pronounced kin structure (i.e., small patches, low environmental stochasticity, and high patch isolation).We demonstrate the importance of kin competition and thus biotic influences on dispersal evolution during invasions. [ABSTRACT FROM AUTHOR]

Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms underlying robustness are diverse, ranging from thermodynamic stability at the RNA and protein level to behavior at the organismal level. Phenotypes can be robust either against heritable perturbations (e.g., mutations) or nonheritable perturbations (e.g., the weather). Here we primarily focus on the first kind of robustness--genetic robustness--and survey three growing avenues of research: (1) measuring genetic robustness in nature and in the laboratory; (2) understanding the evolution of genetic robustness; and (3) exploring the implications of genetic robustness for future evolution. [ABSTRACT FROM AUTHOR]

The Price equation shows that evolutionary change can be written in terms of two fundamental variables: the fitness of parents (or ancestors) and the phenotypes of their offspring (descendants). Its power lies in the fact that it requires no simplifying assumptions other than a closed population, but realizing the full potential of Price's result requires that we flesh out the mathematical representation of both fitness and offspring phenotype. Specifically, both need to be treated as stochastic variables that are themselves functions of parental phenotype. Here, I show how new mathematical tools allow us to do this without introducing any simplifying assumptions. Combining this representation of fitness and phenotype with the stochastic Price equation reveals fundamental rules underlying multivariate evolution and the evolution of inheritance. Finally, I show how the change in the entire phenotype distribution of a population, not simply the mean phenotype, can be written as a single compact equation from which the Price equation and related results can be derived as special cases. This article is part of the theme issue 'Fifty years of the Price equation'.