Directionality theory and the evolution of body size

Directionality theory, a dynamic theory of evolution that integrates population genetics with demography, is based on the concept of evolutionary entropy, a measure of the variability in the age of reproducing individuals in a population. The main tenets of the theory are three principles relating the response to the ecological constraints a population experiences, with trends in entropy as the population evolves under mutation and natural selection. (i) Stationary size or fluctuations around a stationary size (bounded growth): a unidirectional increase in entropy; (ii) prolonged episodes of exponential growth (unbounded growth), large population size: a unidirectional decrease in entropy; and (iii) prolonged episodes of exponential growth (unbounded growth), small population size: random, non-directional change in entropy. We invoke these principles, together with an allometric relationship between entropy, and the morphometric variable body size, to provide evolutionary explanations of three empirical patterns pertaining to trends in body size, namely (i) Cope's rule, the tendency towards size increase within phyletic lineages; (ii) the island rule, which pertains to changes in body size that occur as species migrate from mainland populations to colonize island habitats; and (iii) Bergmann's rule, the tendency towards size increase with increasing latitude. The observation that these ecotypic patterns can be explained in terms of the directionality principles for entropy underscores the significance of evolutionary entropy as a unifying concept in forging a link between micro-evolution, the dynamics of gene frequency change, and macro-evolution, dynamic changes in morphometric variables.     

Directionality theory: an empirical study of an entropic principle in life-history evolution

Understanding the relationship between ecological constraints and life-history properties constitutes a central problem in evolutionary ecology. Directionality theory, a model of the evolutionary process based on demographic entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn, provides an analytical framework for addressing this problem. The theory predicts that in populations that spend the greater part of their evolutionary history in the stationary growth phase (equilibrium species), entropy will increase. Equilibrium species will be characterized by high iteroparity and strong demographic stability. In populations that spend the greater part of their evolutionary history in the exponential growth phase (opportunistic species), entropy will decrease when population size is large, and will undergo random variation when population size is small. Opportunistic species will be characterized by weak iteroparity and weak demographic stability when population size is large, and random variations in these attributes when population size is small. This paper assesses the validity of these predictions by employing a demographic dataset of 66 species of perennial plants. This empirical analysis is consistent with directionality theory and provides support for its significance as an explanatory and predictive model of life-history evolution.     

Directionality theory: a computational study of an entropic principle in evolutionary processes

Analytical studies of evolutionary processes based on the demographic parameter entropy-a measure of the uncertainty in the age of the mother of a randomly chosen newborn-show that evolutionary changes in entropy are contingent on environmental constraints and can be characterized in terms of three tenets: (i) a unidirectional increase in entropy for populations subject to bounded growth constraints; (ii) a unidirectional decrease in entropy for large populations subject to unbounded growth constraints; (iii) random, non-directional change in entropy for small populations subject to unbounded growth constraints. This article aims to assess the robustness of these analytical tenets by computer simulation. The results of the computational study are shown to be consistent with the analytical predictions. Computational analysis, together with complementary empirical studies of evolutionary changes in entropy underscore the universality of the entropic principle as a model of the evolutionary process.     

Evolutionary ecology of human life history

The human life history is characterized by several unusual features, including large babies, late puberty and menopause, and the fact that there is a strong cultural influence on reproductive decisions throughout life. In this review I examine human life history from an evolutionary ecological perspective. I first review the evidence for life history trade-offs between fertility and mortality in humans. Patterns of growth, fertility and mortality across the life span are then discussed and illustrated with data from a traditional Gambian population. After outlining the stages of the human life course, I discuss two phenomena of particular interest in evolutionary anthropology, both of which are apparently unique to humans and neither yet fully understood. First, I discuss the evolution of menopause, the curtailing of female reproduction long before death. The evidence that this evolved because investment in existing children's future reproductive success is more important than continuing child bearing into old age is reviewed, along with data relating to the biological constraints that may be operating. Second, I discuss the demographic transition. Declining fertility at a time of increasingly abundant resources represents a serious challenge to an evolutionary view of human life history and behaviour, and is thus examined in detail. Parental investment in children in competition with each other may be key to understanding both of these unusual human phenomena. Copyright 2000 The Association for the Study of Animal Behaviour.     

Cumulative benefit games: achieving cooperation when players discount the future

The science of thermodynamics is concerned with understanding the properties of inanimate matter in so far as they are determined by changes in temperature. The Second Law asserts that in irreversible processes there is a uni-directional increase in thermodynamic entropy, a measure of the degree of uncertainty in the thermal energy state of a randomly chosen particle in the aggregate. The science of evolution is concerned with understanding the properties of populations of living matter in so far as they are regulated by changes in generation time. Directionality theory, a mathematical model of the evolutionary process, establishes that in populations subject to bounded growth constraints, there is a uni-directional increase in evolutionary entropy, a measure of the degree of uncertainty in the age of the immediate ancestor of a randomly chosen newborn. This article reviews the mathematical basis of directionality theory and analyses the relation between directionality theory and statistical thermodynamics. We exploit an analytic relation between temperature, and generation time, to show that the directionality principle for evolutionary entropy is a non-equilibrium extension of the principle of a uni-directional increase of thermodynamic entropy. The analytic relation between these directionality principles is consistent with the hypothesis of the equivalence of fundamental laws as one moves up the hierarchy, from a molecular ensemble where the thermodynamic laws apply, to a population of replicating entities (molecules, cells, higher organisms), where evolutionary principles prevail.     

Population size,habitat fragmentation,and the nature of adaptive variation in a stream fish

Whether and how habitat fragmentation and population size jointly affect adaptive genetic variation and adaptive population differentiation are largely unexplored. Owing to pronounced genetic drift, small, fragmented populations are thought to exhibit reduced adaptive genetic variation relative to large populations. Yet fragmentation is known to increase variability within and among habitats as population size decreases. Such variability might instead favour the maintenance of adaptive polymorphisms and/or generate more variability in adaptive differentiation at smaller population size. We investigated these alternative hypotheses by analysing coding-gene, single-nucleotide polymorphisms associated with different biological functions in fragmented brook trout populations of variable sizes. Putative adaptive differentiation was greater between small and large populations or among small populations than among large populations. These trends were stronger for genetic population size measures than demographic ones and were present despite pronounced drift in small populations. Our results suggest that fragmentation affects natural selection and that the changes elicited in the adaptive genetic composition and differentiation of fragmented populations vary with population size. By generating more variable evolutionary responses, the alteration of selective pressures during habitat fragmentation may affect future population persistence independently of, and perhaps long before, the effects of demographic and genetic stochasticity are manifest.     

Genomic and phenomic analysis of island ant community assembly

Island biodiversity has long fascinated biologists as it typically presents tractable systems for unpicking the eco‐evolutionary processes driving community assembly. In general, two recurring themes are of central theoretical interest. First, immigration, diversification, and extinction typically depend on island geographical properties (e.g., area, isolation, and age). Second, predictable ecological and evolutionary trajectories readily occur after colonization, such as the evolution of adaptive trait syndromes, trends toward specialization, adaptive radiation, and eventual ecological decline. Hypotheses such as the taxon cycle draw on several of these themes to posit particular constraints on colonization and subsequent eco‐evolutionary dynamics. However, it has been challenging to examine these integrated dynamics with traditional methods. Here, we combine phylogenomics, population genomics and phenomics, to unravel community assembly dynamics among Pheidole (Hymenoptera, Formicidae) ants in the isolated Fijian archipelago. We uphold basic island biogeographic predictions that isolated islands accumulate diversity primarily through in situ evolution rather than dispersal, and population genomic support for taxon cycle predictions that endemic species have decreased dispersal ability and demography relative to regionally widespread taxa. However, rather than trending toward island syndromes, ecomorphological diversification in Fiji was intense, filling much of the genus‐level global morphospace. Furthermore, while most endemic species exhibit demographic decline and reduced dispersal, we show that the archipelago is not an evolutionary dead‐end. Rather, several endemic species show signatures of population and range expansion, including a successful colonization to the Cook islands. These results shed light on the processes shaping island biotas and refine our understanding of island biogeographic theory.     

Darwinian fitness, evolutionary entropy and directionality theory

Two recent articles provide computational and empirical validation of the following analytical fact: the outcome of competition between an invading genotype and that of a resident population is determined by the rate at which the population returns to its original size after a random perturbation. This phenomenon can be quantitatively described in terms of the demographic parameter termed "evolutionary entropy", a measure of the variability in the age at which individuals produce offspring and die. The two articles also validate certain predictions of directionality theory, an evolutionary model that integrates demography and ecology with population genetics. In particular, directionality theory predicts that in populations that spend the greater part of their life cycle in the stationary growth phase, evolution will result in an increase in entropy. These species will be described by a late age of sexual maturity, small progeny sets and a broad reproductive time-span. In populations that undergo large fluctuations in size, however, the evolutionary outcome will be different. When the average size is large, evolution will result in a decrease in entropy-these populations will be described by early age of sexual maturity, large numbers of offspring and narrow reproductive span but when the average size is small, the evolutionary outcome will be random and non-directional.     

Sustainability of culture-driven population dynamics

We consider models of the interactions between human population dynamics and cultural evolution, asking whether they predict sustainable or unsustainable patterns of growth. Phenomenological models predict either unsustainable population growth or stabilization in the near future. The latter prediction, however, is based on extrapolation of current demographic trends and does not take into account causal processes of demographic and cultural dynamics. Most existing causal models assume (or derive from simplified models of the economy) a positive feedback between cultural evolution and demographic growth, and predict unlimited growth in both culture and population. We augment these models taking into account that: (1) cultural transmission is not perfect, i.e., culture can be lost; (2) culture does not always promote population growth. We show that taking these factors into account can cause radically different model behavior, such as population extinction rather than stability, and extinction rather than growth. We conclude that all models agree that a population capable of maintaining a large amount of culture, including a powerful technology, runs a high risk of being unsustainable. We suggest that future work must address more explicitly both the dynamics of resource consumption and the cultural evolution of beliefs implicated in reproductive behavior (e.g., ideas about the preferred family size) and in resource use (e.g., environmentalist stances).     

The evolution of cooperative breeding in birds: kinship,dispersal and life history

The evolution of cooperation among animals has posed a major problem for evolutionary biologists, and despite decades of research into avian cooperative breeding systems, many questions about the evolution of their societies remain unresolved. A review of the kin structure of avian societies shows that a large majority live in kin-based groups. This is consistent with the proposed evolutionary routes to cooperative breeding via delayed dispersal leading to family formation, or limited dispersal leading to kin neighbourhoods. Hypotheses proposed to explain the evolution of cooperative breeding systems have focused on the role of population viscosity, induced by ecological/demographic constraints or benefits of philopatry, in generating this kin structure. However, comparative analyses have failed to generate robust predictions about the nature of those constraints, nor differentiated between the viscosity of social and non-social populations, except at a coarse level. I consider deficiencies in our understanding of how avian dispersal strategies differ between social and non-social species, and suggest that research has focused too narrowly on population viscosity and that a broader perspective that encompasses life history and demographic processes may provide fresh insights into the evolution of avian societies.     

Group versus population level demographics: An analysis of comparability using long term data on wild white‐faced capuchin monkeys (Cebus capucinus imitator)

Primates have long been used as indicator species for assessing overall ecosystem health. However, area‐wide census methods are time consuming, costly, and not always feasible under many field conditions. Therefore, it is important to establish whether monitoring a subset of a population accurately reflects demographic changes occurring in the population at large. Over the past 35 years, we have conducted 15 area‐wide censuses in Sector Santa Rosa, Costa Rica. These efforts have revealed important trends in population growth patterns of capuchin monkeys following the protection and subsequent regeneration of native forests. During this same period, we have also intensively studied a subset of the capuchin groups. Comparing these two datasets, we investigate whether the population structures of the closely monitored groups are reliable indicators of area‐wide demographic patterns. We compare the overall group size and the individual age/sex class compositions of study groups and nonstudy groups (i.e., those contacted during area‐wide censuses only). Our study groups contained more individuals overall with a larger proportion of infants, and there were indications that the proportion of adult and subadult males was lower. These differences can be ascribed either to sampling errors or real differences attributable to human presence and/or better habitat quality for the study groups. No other sex/age classes differed, and major demographic changes were simultaneously evident in both study and nonstudy groups. This study suggests that the Santa Rosa capuchin population is similarly impacted by large‐scale ecological patterns observable within our study groups.     

Evolution of complex dynamics in spatially structured populations

Dynamics of populations depend on demographic parameters which may change during evolution. In simple ecological models given by one-dimensional difference equations, the evolution of demographic parameters generally leads to equilibrium population dynamics. Here we show that this is not true in spatially structured ecological models. Using a multi-patch metapopulation model, we study the evolutionary dynamics of phenotypes that differ both in their response to local crowding, i.e. in their competitive behaviour within a habitat, and in their rate of dispersal between habitats. Our simulation results show that evolution can favour phenotypes that have the intrinsic potential for very complex dynamics provided that the environment is spatially structured and temporally variable. These phenotypes owe their evolutionary persistence to their large dispersal rates. They typically coexist with phenotypes that have low dispersal rates and that exhibit equilibrium dynamics when alone. This coexistence is brought about through the phenomenon of evolutionary branching, during which an initially uniform population splits into the two phenotypic classes.     

A metabolic view of the diversity-stability relationship

A theoretical analysis of the “portfolio effect” expressed in metabolic terms indicates that the coefficient of variation of total biomass in the ecosystem is influenced by three factors: metabolic diversity, total population size and organism biomass (body mass). The contribution of these factors to ecosystem stability depends on the power scaling of population size to its temporal variance: the Tilman's z. In natural populations, 1<z<2 both from a theoretical and an empirical background, and so a higher metabolic diversity, a larger population size and a bigger body mass are expected to increase ecosystem stability. The maximization of any of these factors will enhance ecosystem stability both at ecological (successional) and evolutionary timescales, which could explain a number of trends observed in ecosystems and in the history of life.     

Social bonds in birds are associated with brain size and contingent on the correlated evolution of life‐history and increased parental investment

In birds, large brains are associated with a series of population‐level phenomena, including invasion success, species richness, and resilience to population decline. Thus, they appear to open up adaptive opportunities through flexibility in foraging and anti‐predator behaviour. The evolutionary pathway leading to large brain size has received less attention than behavioural and ecological correlates. Using a comparative approach, we show that, independent of previously recognized associations with developmental constraints, relative brain size in birds is strongly related to biparental care, pair‐bonding, and stable social relationships. We also demonstrate correlated evolution between large relative brain size and altricial development, and that the evolution of both traits is contingent on biparental care. Thus, biparental care facilitates altricial development, which permits the evolution of large relative brain size. Finally, we show that large relative brain size is associated with pair‐bond strength, itself a likely consequence of cooperation and negotiation between partners under high levels of parental investment. These analyses provide an evolutionary model for the evolution of and prevalence of biparental care, altricial development, and pair‐bonding in birds. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 100 , 111–123.     

Multidisciplinary population monitoring when demographic data are sparse: a case study of remote trout populations

The potential of genetic, genomic, and phenotypic metrics for monitoring population trends may be especially high in isolated regions, where traditional demographic monitoring is logistically difficult and only sporadic sampling is possible. This potential, however, is relatively underexplored empirically. Over eleven years, we assessed several such metrics along with traditional ecological knowledge and catch data in a socioeconomically important trout species occupying a large, remote lake. The data revealed largely stable characteristics in two populations over 2–3 generations, but possible contemporary changes in a third population. These potential shifts were suggested by reduced catch rates, reduced body size, and changes in selection implied at one gene‐associated single nucleotide polymorphism. A demographic decline in this population, however, was ambiguously supported, based on the apparent lack of temporal change in effective population size, and corresponding traditional knowledge suggesting little change in catch. We illustrate how the pluralistic approach employed has practicality for setting future monitoring efforts of these populations, by guiding monitoring priorities according to the relative merits of different metrics and availability of resources. Our study also considers some advantages and disadvantages to adopting a pluralistic approach to population monitoring where demographic data are not easily obtained.     

Historical demography of a wild lemur population (Propithecus verreauxi) in southwest Madagascar

The human colonization of Madagascar is associated with the extinction of numerous lemur species. However, the degree to which humans have negatively influenced the historical population dynamics of extant lemur species is not well understood. This study employs genetic and demographic analyses to estimate demographic parameters relating to the historical population dynamics of a wild lemur population, Verreaux’s sifaka (Propithecus verreauxi). The genetic analyses are used to determine whether this population experienced a historically recent (i.e., within the last 2000 years) population bottleneck, as well as to estimate the historical population growth rate and the timing of any changes in population size in the past. In addition, a retrospective demographic analysis is used to determine sources of variation and covariation in the sifaka life cycle and how variation in life-cycle transitions contributes to variation in population growth rate. The genetic analyses indicate that the sifaka population did not experience a recent population bottleneck; however, the historical population growth rate was negative, indicating that the ancestral population size was much larger than the current size. The timing of the ancestral population decline has a point estimate of 2300 years ago, but with large credible intervals: 3611–1736 years ago. This point estimate corresponds with the first evidence for human arrival to Madagascar. Climatic variation has also likely influenced past (and current) population dynamics due to stochastic annual rainfall patterns and climatic desiccation, the latter of which began in southwestern Madagascar around 4000 years ago. Variation in the survival of 2-year-old animals as well as large adult females makes the largest contribution to variation in population growth rate. In the absence of more explicit models pertaining to historical population dynamics, it is difficult to attribute the negative population growth rate of this species solely to a single factor (e.g., hunting, habitat destruction).     

Evaluating the role and measures of juvenile growth rate: latitudinal variation in insect life histories

Latitudinal and elevational trends in body size are found in numerous animal taxa, with various adaptive explanations proposed. It is however debatable whether geographic trends in adult body size are accompanied by corresponding differences in juvenile growth rate (= mass gain per unit time). Respective studies have been complicated by conceptual and methodological problems related to defining and measuring this variable, particularly in organisms with discontinuous growth like arthropods. Using an original method for estimating differential (instantaneous) juvenile growth rates, we compared geographically distant European populations of six insect species in a common garden experiment. We found no among population differences in differential growth rate in any of the species. This result is in concert with concurrent increase in both adult size and developmental time towards the south. While opposite examples exist, we interpret our results as challenging the view that growth rate is a trait that readily responds to environmentally based selective pressures. Our results thus advocate the more classical view of growth rate maximisation within its physiological limits. We discuss the advantages of using differential (rather than integral) measures of growth rate in evolutionary ecological studies and evaluate the reasons for the detected latitudinal trends in life history traits.     

Darwinian fitness

The term Darwinian fitness refers to the capacity of a variant type to invade and displace the resident population in competition for available resources. Classical models of this dynamical process claim that competitive outcome is a deterministic event which is regulated by the population growth rate, called the Malthusian parameter. Recent analytic studies of the dynamics of competition in terms of diffusion processes show that growth rate predicts invasion success only in populations of infinite size. In populations of finite size, competitive outcome is a stochastic process--contingent on resource constraints--which is determined by the rate at which a population returns to its steady state condition after a random perturbation in the individual birth and death rates. This return rate, a measure of robustness or population stability, is analytically characterized by the demographic parameter, evolutionary entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn. This article appeals to computational and numerical methods to contrast the predictive power of the Malthusian and the entropic principles. The computational analysis rejects the Malthusian model and is consistent with of the entropic principle. These studies thus provide support for the general claim that entropy is the appropriate measure of Darwinian fitness and constitutes an evolutionary parameter with broad predictive and explanatory powers.     

The contributions of age and sex to variation in common tern population growth rate

1. The decomposition of population growth rate into contributions from different demographic rates has many applications, ranging from evolutionary biology to conservation and management. Demographic rates with low variance may be pivotal for population persistence, but variable rates can have a dramatic influence on population growth rate. 2. In this study, the mean and variance in population growth rate (lambda) is decomposed into contributions from different ages and demographic rates using prospective and retrospective matrix analyses for male and female components of an increasing common tern (Sterna hirundo) population. 3. Three main results emerged: (1) subadult return was highly influential in prospective and retrospective analyses; (2) different age-classes made different contributions to variation in lambda: older age classes consistently produced offspring whereas young adults performed well only in high quality years; and (3) demographic rate covariation explained a significant proportion of variation in both sexes. A large contribution to lambda did not imply a large contribution to its variation. 4. This decomposition strengthens the argument that the relationship between variation in demographic rates and variation in lambda is complex. Understanding this relationship and its consequences for population persistence and evolutionary change demands closer examination of the lives, and deaths, of the individuals within populations within species.