Allele frequencies and selection coefficients in locally adapted populations.

Understanding the role of natural selection in driving evolutionary change requires accurate estimates of the strength of selection acting at the genetic level in the wild. This is challenging to achieve but may be easier in the case of populations in migration-selection balance. When two populations are at equilibrium under migration-selection balance, there exist loci whose alleles are selected different ways in the two populations. Such loci can be identified from genome sequencing by their high values of FST. This raises the question of what is the strength of selection on locally-adaptive alleles. To answer this question we analyse a 1-locus 2-allele model of a population distributed between two niches. We show by simulation of selected cases that the outputs from finite-population models are essentially the same as those from deterministic infinite-population models. We then derive theory for the infinite-population model showing the dependence of selection coefficients on equilibrium allele frequencies, migration rates, dominance and relative population sizes in the two niches. An Excel spreadsheet is provided for the calculation of selection coefficients and their approximate standard errors from observed values of population parameters. We illustrate our results with a worked example, with graphs showing the dependence of selection coefficients on equilibrium allele frequencies, and graphs showing how FST depends on the selection coefficients acting on the alleles at a locus. Given the extent of recent progress in ecological genomics, we hope our methods may help those studying migration-selection balance to quantify the advantages conferred by adaptive genes.

Multiple environmental controls explain global patterns in soil animal communities.

Soil animals play important roles in ecosystem functioning and stability, but the environmental controls on their communities are not fully understood. In this study, we compiled a dataset of soil animal communities for which the abundance and body mass of multiple soil animal groups were recorded. The mass-abundance scaling relationships were then used to investigate multiple environmental controls on soil animal community composition. The data reveal latitudinal shifts from high abundances of small soil animals at high latitudes to greater relative abundances of large soil animals at low latitudes. A hierarchical linear mixed effects model was applied to reveal the environmental variables shaping these latitudinal trends. The final hierarchical model identified mean annual temperature, soil pH and soil organic carbon content as key environmental controls explaining global mass-abundance scaling relationships in soil animal communities (R2c = 0.828, Ngroup = 117). Such relationships between soil biota with climate and edaphic conditions have been previously identified for soil microbial, but not soil animal, communities at a global scale. More comprehensive global soil community datasets are needed to better understand the generality of these relationships over a broader range of global ecosystems and soil animal groups.

The importance of including habitat-specific behaviour in models of butterfly movement.

Dispersal is a key process affecting population persistence and major factors affecting dispersal rates are the amounts, connectedness and properties of habitats in landscapes. We present new data on the butterfly Maniola jurtina in flower-rich and flower-poor habitats that demonstrates how movement and behaviour differ between sexes and habitat types, and how this effects consequent dispersal rates. Females had higher flight speeds than males, but their total time in flight was four times less. The effect of habitat type was strong for both sexes, flight speeds were ~ 2.5 × and ~ 1.7 × faster on resource-poor habitats for males and females, respectively, and flights were approximately 50% longer. With few exceptions females oviposited in the mown grass habitat, likely because growing grass offers better food for emerging caterpillars, but they foraged in the resource-rich habitat. It seems that females faced a trade-off between ovipositing without foraging in the mown grass or foraging without ovipositing where flowers were abundant. We show that taking account of habitat-dependent differences in activity, here categorised as flight or non-flight, is crucial to obtaining good fits of an individual-based model to observed movement. An important implication of this finding is that incorporating habitat-specific activity budgets is likely necessary for predicting longer-term dispersal in heterogeneous habitats, as habitat-specific behaviour substantially influences the mean (> 30% difference) and kurtosis (1.4 × difference) of dispersal kernels. The presented IBMs provide a simple method to explicitly incorporate known activity and movement rates when predicting dispersal in changing and heterogeneous landscapes.

Taking error into account when fitting models using Approximate Bayesian Computation.

Stochastic computer simulations are often the only practical way of answering questions relating to ecological management. However, due to their complexity, such models are difficult to calibrate and evaluate. Approximate Bayesian Computation (ABC) offers an increasingly popular approach to this problem, widely applied across a variety of fields. However, ensuring the accuracy of ABC's estimates has been difficult. Here, we obtain more accurate estimates by incorporating estimation of error into the ABC protocol. We show how this can be done where the data consist of repeated measures of the same quantity and errors may be assumed to be normally distributed and independent. We then derive the correct acceptance probabilities for a probabilistic ABC algorithm, and update the coverage test with which accuracy is assessed. We apply this method, which we call error-calibrated ABC, to a toy example and a realistic 14-parameter simulation model of earthworms that is used in environmental risk assessment. A comparison with exact methods and the diagnostic coverage test show that our approach improves estimation of parameter values and their credible intervals for both models.

Fundamental insights into ontogenetic growth from theory and fish.

The fundamental features of growth may be universal, because growth trajectories of most animals are very similar, but a unified mechanistic theory of growth remains elusive. Still needed is a synthetic explanation for how and why growth rates vary as body size changes, both within individuals over their ontogeny and between populations and species over their evolution. Here, we use Bertalanffy growth equations to characterize growth of ray-finned fishes in terms of two parameters, the growth rate coefficient, K, and final body mass, m∞. We derive two alternative empirically testable hypotheses and test them by analyzing data from FishBase. Across 576 species, which vary in size at maturity by almost nine orders of magnitude, K scaled as [Formula: see text]. This supports our first hypothesis that growth rate scales as [Formula: see text] as predicted by metabolic scaling theory; it implies that species that grow to larger mature sizes grow faster as juveniles. Within fish species, however, K scaled as [Formula: see text]. This supports our second hypothesis, which predicts that growth rate scales as [Formula: see text] when all juveniles grow at the same rate. The unexpected disparity between across- and within-species scaling challenges existing theoretical interpretations. We suggest that the similar ontogenetic programs of closely related populations constrain growth to [Formula: see text] scaling, but as species diverge over evolutionary time they evolve the near-optimal [Formula: see text] scaling predicted by metabolic scaling theory. Our findings have important practical implications because fish supply essential protein in human diets, and sustainable yields from wild harvests and aquaculture depend on growth rates.

Metabolic theory predicts whole-ecosystem properties.

Understanding the effects of individual organisms on material cycles and energy fluxes within ecosystems is central to predicting the impacts of human-caused changes on climate, land use, and biodiversity. Here we present a theory that integrates metabolic (organism-based bottom-up) and systems (ecosystem-based top-down) approaches to characterize how the metabolism of individuals affects the flows and stores of materials and energy in ecosystems. The theory predicts how the average residence time of carbon molecules, total system throughflow (TST), and amount of recycling vary with the body size and temperature of the organisms and with trophic organization. We evaluate the theory by comparing theoretical predictions with outputs of numerical models designed to simulate diverse ecosystem types and with empirical data for real ecosystems. Although residence times within different ecosystems vary by orders of magnitude-from weeks in warm pelagic oceans with minute phytoplankton producers to centuries in cold forests with large tree producers-as predicted, all ecosystems fall along a single line: residence time increases linearly with slope = 1.0 with the ratio of whole-ecosystem biomass to primary productivity (B/P). TST was affected predominantly by primary productivity and recycling by the transfer of energy from microbial decomposers to animal consumers. The theory provides a robust basis for estimating the flux and storage of energy, carbon, and other materials in terrestrial, marine, and freshwater ecosystems and for quantifying the roles of different kinds of organisms and environments at scales from local ecosystems to the biosphere.

Energetics, lifestyle, and reproduction in birds.

Theoretical and empirical studies of life history aim to account for resource allocation to the different components of fitness: survival, growth, and reproduction. The pioneering evolutionary ecologist David Lack [(1968) Ecological Adaptations for Breeding in Birds (Methuen and Co., London)] suggested that reproductive output in birds reflects adaptation to environmental factors such as availability of food and risk of predation, but subsequent studies have not always supported Lack's interpretation. Here using a dataset for 980 bird species (Dataset S1), a phylogeny, and an explicit measure of reproductive productivity, we test predictions for how mass-specific productivity varies with body size, phylogeny, and lifestyle traits. We find that productivity varies negatively with body size and energetic demands of parental care and positively with extrinsic mortality. Specifically: (i) altricial species are 50% less productive than precocial species; (ii) species with female-only care of offspring are about 20% less productive than species with other methods of parental care; (iii) nonmigrants are 14% less productive than migrants; (iv) frugivores and nectarivores are about 20% less productive than those eating other foods; and (v) pelagic foragers are 40% less productive than those feeding in other habitats. A strong signal of phylogeny suggests that syndromes of similar life-history traits tend to be conservative within clades but also to have evolved independently in different clades. Our results generally support both Lack's pioneering studies and subsequent research on avian life history.

The maximum rate of mammal evolution.

How fast can a mammal evolve from the size of a mouse to the size of an elephant? Achieving such a large transformation calls for major biological reorganization. Thus, the speed at which this occurs has important implications for extensive faunal changes, including adaptive radiations and recovery from mass extinctions. To quantify the pace of large-scale evolution we developed a metric, clade maximum rate, which represents the maximum evolutionary rate of a trait within a clade. We applied this metric to body mass evolution in mammals over the last 70 million years, during which multiple large evolutionary transitions occurred in oceans and on continents and islands. Our computations suggest that it took a minimum of 1.6, 5.1, and 10 million generations for terrestrial mammal mass to increase 100-, and 1,000-, and 5,000-fold, respectively. Values for whales were down to half the length (i.e., 1.1, 3, and 5 million generations), perhaps due to the reduced mechanical constraints of living in an aquatic environment. When differences in generation time are considered, we find an exponential increase in maximum mammal body mass during the 35 million years following the Cretaceous-Paleogene (K-Pg) extinction event. Our results also indicate a basic asymmetry in macroevolution: very large decreases (such as extreme insular dwarfism) can happen at more than 10 times the rate of increases. Our findings allow more rigorous comparisons of microevolutionary and macroevolutionary patterns and processes.

How body mass and lifestyle affect juvenile biomass production in placental mammals.

In mammals, the mass-specific rate of biomass production during gestation and lactation, here called maternal productivity, has been shown to vary with body size and lifestyle. Metabolic theory predicts that post-weaning growth of offspring, here termed juvenile productivity, should be higher than maternal productivity, and juveniles of smaller species should be more productive than those of larger species. Furthermore because juveniles generally have similar lifestyles to their mothers, across species juvenile and maternal productivities should be correlated. We evaluated these predictions with data from 270 species of placental mammals in 14 taxonomic/lifestyle groups. All three predictions were supported. Lagomorphs, perissodactyls and artiodactyls were very productive both as juveniles and as mothers as expected from the abundance and reliability of their foods. Primates and bats were unproductive as juveniles and as mothers, as expected as an indirect consequence of their low predation risk and consequent low mortality. Our results point the way to a mechanistic explanation for the suite of correlated life-history traits that has been called the slow-fast continuum.

Patterns of maximum body size evolution in Cenozoic land mammals: eco-evolutionary processes and abiotic forcing.

There is accumulating evidence that macroevolutionary patterns of mammal evolution during the Cenozoic follow similar trajectories on different continents. This would suggest that such patterns are strongly determined by global abiotic factors, such as climate, or by basic eco-evolutionary processes such as filling of niches by specialization. The similarity of pattern would be expected to extend to the history of individual clades. Here, we investigate the temporal distribution of maximum size observed within individual orders globally and on separate continents. While the maximum size of individual orders of large land mammals show differences and comprise several families, the times at which orders reach their maximum size over time show strong congruence, peaking in the Middle Eocene, the Oligocene and the Plio-Pleistocene. The Eocene peak occurs when global temperature and land mammal diversity are high and is best explained as a result of niche expansion rather than abiotic forcing. Since the Eocene, there is a significant correlation between maximum size frequency and global temperature proxy. The Oligocene peak is not statistically significant and may in part be due to sampling issues. The peak in the Plio-Pleistocene occurs when global temperature and land mammal diversity are low, it is statistically the most robust one and it is best explained by global cooling. We conclude that the macroevolutionary patterns observed are a result of the interplay between eco-evolutionary processes and abiotic forcing.

Effects of allometry, productivity and lifestyle on rates and limits of body size evolution.

Body size affects nearly all aspects of organismal biology, so it is important to understand the constraints and dynamics of body size evolution. Despite empirical work on the macroevolution and macroecology of minimum and maximum size, there is little general quantitative theory on rates and limits of body size evolution. We present a general theory that integrates individual productivity, the lifestyle component of the slow-fast life-history continuum, and the allometric scaling of generation time to predict a clade's evolutionary rate and asymptotic maximum body size, and the shape of macroevolutionary trajectories during diversifying phases of size evolution. We evaluate this theory using data on the evolution of clade maximum body sizes in mammals during the Cenozoic. As predicted, clade evolutionary rates and asymptotic maximum sizes are larger in more productive clades (e.g. baleen whales), which represent the fast end of the slow-fast lifestyle continuum, and smaller in less productive clades (e.g. primates). The allometric scaling exponent for generation time fundamentally alters the shape of evolutionary trajectories, so allometric effects should be accounted for in models of phenotypic evolution and interpretations of macroevolutionary body size patterns. This work highlights the intimate interplay between the macroecological and macroevolutionary dynamics underlying the generation and maintenance of morphological diversity.

Shifts in metabolic scaling, production, and efficiency across major evolutionary transitions of life.

The diversification of life involved enormous increases in size and complexity. The evolutionary transitions from prokaryotes to unicellular eukaryotes to metazoans were accompanied by major innovations in metabolic design. Here we show that the scalings of metabolic rate, population growth rate, and production efficiency with body size have changed across the evolutionary transitions. Metabolic rate scales with body mass superlinearly in prokaryotes, linearly in protists, and sublinearly in metazoans, so Kleiber's 3/4 power scaling law does not apply universally across organisms. The scaling of maximum population growth rate shifts from positive in prokaryotes to negative in protists and metazoans, and the efficiency of production declines across these groups. Major changes in metabolic processes during the early evolution of life overcame existing constraints, exploited new opportunities, and imposed new constraints.

A general basis for quarter-power scaling in animals.

It has been known for decades that the metabolic rate of animals scales with body mass with an exponent that is almost always <1, >2/3, and often very close to 3/4. The 3/4 exponent emerges naturally from two models of resource distribution networks, radial explosion and hierarchically branched, which incorporate a minimum of specific details. Both models show that the exponent is 2/3 if velocity of flow remains constant, but can attain a maximum value of 3/4 if velocity scales with its maximum exponent, 1/12. Quarter-power scaling can arise even when there is no underlying fractality. The canonical "fourth dimension" in biological scaling relations can result from matching the velocity of flow through the network to the linear dimension of the terminal "service volume" where resources are consumed. These models have broad applicability for the optimal design of biological and engineered systems where energy, materials, or information are distributed from a single source.

Rensch's rule in large herbivorous mammals derived from metabolic scaling.

Rensch's rule, which states that the magnitude of sexual size dimorphism tends to increase with increasing body size, has evolved independently in three lineages of large herbivorous mammals: bovids (antelopes), cervids (deer), and macropodids (kangaroos). This pattern can be explained by a model that combines allometry, life-history theory, and energetics. The key features are that female group size increases with increasing body size and that males have evolved under sexual selection to grow large enough to control these groups of females. The model predicts relationships among body size and female group size, male and female age at first breeding, death and growth rates, and energy allocation of males to produce body mass and weapons. Model predictions are well supported by data for these megaherbivores. The model suggests hypotheses for why some other sexually dimorphic taxa, such as primates and pinnipeds (seals and sea lions), do or do not conform to Rensh's rule.

Evolution of discrimination in populations at equilibrium between selfishness and altruism.

Where there is genetically based variation in selfishness and altruism, as in man, altruists with an innate ability to recognise and thereby only help their altruistic relatives may evolve. Here we use diploid population genetic models to chart the evolution of genetically-based discrimination in populations initially in stable equilibrium between altruism and selfishness. The initial stable equilibria occur because help is assumed subject to diminishing returns. Similar results were obtained whether we used a model with two independently inherited loci, one controlling altruism the other discrimination, or a one locus model with three alleles. The latter is the opposite extreme to the first model, and can be thought of as involving complete linkage between two loci on the same chromosome. The introduction of discrimination reduced the benefits obtained by selfish individuals, more so as the number of discriminators increased, and selfishness was eventually eliminated in some cases. In others selfishness persisted and the evolutionary outcome was a stable equilibrium involving selfish individuals and both discriminating and non-discriminating altruists. Heritable variation in selfishness, altruism and discrimination is predicted to be particularly evident among full sibs. The suggested coexistence of these three genetic dispositions could explain widespread interest within human social groups as to who will and who will not help others. These predictions merit experimental and observational investigation by primatologists, anthropologists and psychologists.

Sexual imprinting leads to speciation in locally adapted populations.

Sexual imprinting is widespread in birds and other species but its existence requires explanation. Our results suggest that sexual imprinting leads to speciation in locally-adapted populations if a neutral mating cue-e.g., novel plumage coloration-arises through mutation. Importantly, the mating cue locus is not linked to adaptation loci. Local adaptation is a necessary precursor to speciation and occurs when evolution results in stable genetic polymorphisms with one allele predominating in some areas while others predominate elsewhere. Here we use a deterministic two-niche population genetic model to map the set of migration and selection rates for which polymorphic evolutionary outcomes, i.e., local adaptations, can occur. Approximate equations for the boundaries of the set of polymorphic evolutionary outcomes were derived by Bulmer (American Naturalist, 106, 254, 1972), but our results, obtained by deterministic simulation of the evolutionary process, show that one of Bulmer's equations is inaccurate except when the level of dominance is 0.5, and fails if one of the alleles is dominant. Having an accurate map of the set of migration and selection rates for which polymorphic evolutionary outcomes can occur, we then show using the model of Sibly et al. (Ecology and Evolution, 9, 13506, 2019) that local adaptation in all analyzed cases leads to speciation if a new neutral mating cue arises by mutation. We finish by considering how genome sequencing makes possible testing our model and its predictions.

Universal scaling of production rates across mammalian lineages.

Over many millions of years of independent evolution, placental, marsupial and monotreme mammals have diverged conspicuously in physiology, life history and reproductive ecology. The differences in life histories are particularly striking. Compared with placentals, marsupials exhibit shorter pregnancy, smaller size of offspring at birth and longer period of lactation in the pouch. Monotremes also exhibit short pregnancy, but incubate embryos in eggs, followed by a long period of post-hatching lactation. Using a large sample of mammalian species, we show that, remarkably, despite their very different life histories, the scaling of production rates is statistically indistinguishable across mammalian lineages. Apparently all mammals are subject to the same fundamental metabolic constraints on productivity, because they share similar body designs, vascular systems and costs of producing new tissue.

Behavior underpins the predictive power of a trait-based model of butterfly movement.

Dispersal ability is key to species persistence in times of environmental change. Assessing a species' vulnerability and response to anthropogenic changes is often performed using one of two methods: correlative approaches that infer dispersal potential based on traits, such as wingspan or an index of mobility derived from expert opinion, or a mechanistic modeling approach that extrapolates displacement rates from empirical data on short-term movements.Here, we compare and evaluate the success of the correlative and mechanistic approaches using a mechanistic random-walk model of butterfly movement that incorporates relationships between wingspan and sex-specific movement behaviors.The model was parameterized with new data collected on four species of butterfly in the south of England, and we observe how wingspan relates to flight speeds, turning angles, flight durations, and displacement rates.We show that flight speeds and turning angles correlate with wingspan but that to achieve good prediction of displacement even over 10 min the model must also include details of sex- and species-specific movement behaviors.We discuss what factors are likely to differentially motivate the sexes and how these could be included in mechanistic models of dispersal to improve their use in ecological forecasting.

Mammal reproductive strategies driven by offspring mortality-size relationships.

Trade-offs have long been a major theme in life-history theory, but they have been hard to document. We introduce a new method that reveals patterns of divergent trade-offs after adjusting for the pervasive variation in rate of resource allocation to offspring as a function of body size and lifestyle. Results suggest that preweaning vulnerability to predation has been the major factor determining how female placental mammals allocate production between a few large and many small offspring within a litter and between a few large litters and many small ones within a reproductive season. Artiodactyls, perissodactyls, cetaceans, and pinnipeds, which give birth in the open on land or in the sea, produce a few large offspring, at infrequent intervals, because this increases their chances of escaping predation. Insectivores, fissiped carnivores, lagomorphs, and rodents, whose offspring are protected in burrows or nests, produce large litters of small newborns. Primates, bats, sloths, and anteaters, which carry their young from birth until weaning, produce litters of one or a few offspring because of the need to transport and care for them.

The effects of spatial and temporal heterogeneity on the population dynamics of four animal species in a Danish landscape.

BACKGROUND: Variation in carrying capacity and population return rates is generally ignored in traditional studies of population dynamics. Variation is hard to study in the field because of difficulties controlling the environment in order to obtain statistical replicates, and because of the scale and expense of experimenting on populations. There may also be ethical issues. To circumvent these problems we used detailed simulations of the simultaneous behaviours of interacting animals in an accurate facsimile of a real Danish landscape. The models incorporate as much as possible of the behaviour and ecology of skylarks Alauda arvensis, voles Microtus agrestis, a ground beetle Bembidion lampros and a linyphiid spider Erigone atra. This allows us to quantify and evaluate the importance of spatial and temporal heterogeneity on the population dynamics of the four species. RESULTS: Both spatial and temporal heterogeneity affected the relationship between population growth rate and population density in all four species. Spatial heterogeneity accounted for 23-30% of the variance in population growth rate after accounting for the effects of density, reflecting big differences in local carrying capacity associated with the landscape features important to individual species. Temporal heterogeneity accounted for 3-13% of the variance in vole, skylark and spider, but 43% in beetles. The associated temporal variation in carrying capacity would be problematic in traditional analyses of density dependence. Return rates were less than one in all species and essentially invariant in skylarks, spiders and beetles. Return rates varied over the landscape in voles, being slower where there were larger fluctuations in local population sizes. CONCLUSION: Our analyses estimated the traditional parameters of carrying capacities and return rates, but these are now seen as varying continuously over the landscape depending on habitat quality and the mechanisms of density dependence. The importance of our results lies in our demonstration that the effects of spatial and temporal heterogeneity must be accounted for if we are to have accurate predictive models for use in management and conservation. This is an area which until now has lacked an adequate theoretical framework and methodology.