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.     

The evolution of fitness in life-history theory

Theory concerning the evolution of life history (the schedule of reproduction and survival) focuses on describing the life history which maximises fitness. Although there is an intuitive link between life history and fitness, there are in fact several measures of the 'black box' concept of fitness. There has been a debate in the bio-mathematical literature on the predictive difference between the two most commonly used measures; intrinsic rate of increase r and net reproductive ratio R0. Although both measures aim to describe fitness, models using one of the measures may predict the opposite of similar models using the other measure, which is clearly undesirable. Here, I review the evolution of these fitness measures over the last four decades, the predictive differences between these measures and the resulting shift of the fitness concept. I focus in particular on some recent developments, which have solved the dilemma of predictive differences between these fitness measures by explicitly acknowledging the game-theoretical nature of life-history evolution.     

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.     

The fast–slow continuum and mammalian life-history patterns: an empirical evaluation

The fast–slow continuum hypothesis has been proposed to explain the diversity of life-history patterns exhibited by biological populations, but the quantification and population-dynamic consequences of the continuum has remained unclear. I used the ratio of fertility rate to age at first reproduction (F/α ratio) to quantify the tempo of life-history of 138 populations of mammals, and investigated the life-history and population-dynamic consequences of being “fast” or “slow”. “Fast” mammals (F/α>0.60) were characterized by early maturity, short lifespans, low survival rates, and high fertility and projected population growth rate (λ) compared to “slow” (F/α<0.15) mammals. In “fast” populations, λ was overwhelmingly most sensitive to changes in reproductive parameters (age at first reproduction and fertility rates) and relatively insensitive to changes in survival rates. In “slow” populations, λ was very sensitive to changes in juvenile or adult survival rates, and relatively insensitive to changes in reproductive parameters. The pattern of relationships between the F/α ratio and life-history variables, λ, and elasticity of λ to changes in life-history variables persisted even after the effects of body size and phylogeny were statistically removed. These results suggest that fast–slow continuum in mammalian life-history is independent of body size or phylogeny, that the F/α ratio adequately quantifies the position of a population along a fast–slow continuum, and that the tempo of life- histories has substantial population-dynamic consequences.

Zusammenfassung

Die r-K-Kontinuum-Hypothese wurde aufgestellt, um die Diversität von ,,life-history“-Mustern biologischer Populationen zu erklären, aber die Quantifizierung und die Kosnsequenzen für die Populationsdynamik des Kontinuums blieben unklar. Ich benutze das verhältnis der Fortpflanzungsrate zum Fortpflanzungsalter (F/α-Verhältnis) um die Geschwindigkeit der ,,life-history“ von 138 Populationen von Säugetieren zu quantifizieren und untersuchte die Konsequenzen fur die Lebensweise sowie die Populationsdynamik des,,schnell“oder,,langsam “-Seins. ,,Schnelle“Säugetiere (F/α>0.60) waren durch eine frühe Reife, kurze Lebenszeiten, geringe Überlebensraten sowie durch eine große Fertilität und hochgerechnete Populationswachstumsrate (λ) im Vergleich zu ,,langsamen“(F/α<0.15) Säugetieren charakterisiert. In ,,schnellen“ Population reagierte (λ) überwältigend sensibel auf Änderungen in den Fortpflanzungsparametern (Fortpflanzunsalter und Fertilitätsrate) und relativ gering auf Veräanderungen in der Überlebensrate. In ,,langsamen“ Populationen reagierte (λ) sehr sensibel auf Veräanderungen in den reproduktiven Parametern. Das Muster der Beziehung zwischen dem (F/α-Verhältnis) und den Variablen der ,,life-history“,λ, und die Elastizität von λ gegenüber Veränderungen in den variablen der Lebensweise bliev sogar bestehen, nachdem die Effekte von Körpergröße und Phylogenese statistisch eliminiert wurden. Diese Ergebnisse lassen vermuten, dass das r-K-Kontinuum in der ,,life-history“der Säugetiere unabhängig von der Körpergröße und Phylogenie ist, dass das F/α-Verhältnis die Position einer Population im r-K-Kontinuum quantifiziert und dass die Geschwindigkeit der,,life-history“beachtliche konsequenzen fur die Populationsdynamik hat.     

Directionality in the evolution of influenza A haemagglutinin

The evolution of haemagglutinin (HA), an important influenza virus antigen, has been the subject of intensive research for more than two decades. Many characteristics of HA's sequence evolution are captured by standard Markov chain substitution models. Such models assign equal fitness to all accessible amino acids at a site. We show, however, that such models strongly underestimate the number of homoplastic amino acid substitutions during the course of HA's evolution, i.e. substitutions that repeatedly give rise to the same amino acid at a site. We develop statistics to detect individual homoplastic events and find that they preferentially occur at positively selected epitopic sites. Our results suggest that the evolution of the influenza A HA, including evolution by positive selection, is strongly affected by the long-term site-specific preferences for individual amino acids.     

Siblicide and life-history evolution in parasitoids

Parasitoid wasps exhibit a stark dichotomy in larval behaviorand developmental mode. In gregarious species, siblings developingtogether tolerate each other; hence more than one individualcan successfully complete development. In contrast, solitaryspecies have intolerant larvae that will engage in siblicide,leading to only one individual successfully completing development.Previous theoretical and empirical work has suggested that females from species with intolerant larvae should reduce theirrelative investment in reproduction. We tested this predictionby measuring investment in survival and reproduction in a pairof sister species from the genus Aphaereta (Hymenoptera: Braconidae).With increasing body size, divergent patterns of investmentexist in the two species. Females of the solitary A. genevensisallocate additional resources almost exclusively toward greaterfat reserves, resulting in enhanced longevity. Females of thegregarious A. pallipes invest relatively more in reproductionand hence have lower fat reserves, reduced longevity, and greater egg loads than A. genevensis. These differences reflect a trend toward greater investment in survival relative to reproductionin the solitary species, as predicted. We discuss the implicationsof these findings for the development of sibling rivalry andlife-history theory.     

Carotenoids and life-history evolution in animals

Animals must allocate finite resources amongst competing demands. A suite of such trade-offs is thought to occur in the deployment of carotenoids, being widely responsible for sexual coloration and also important in antioxidant and immune defences. Experimental manipulation of dietary carotenoid availability is a useful approach for elucidating the mechanistic bases of carotenoid allocation trade-offs. Recent work using birds has shown that both sexual display and immune defences can be limited by carotenoid availability, providing support for the hypothesis that males allocating greater amounts of carotenoids to sexual coloration are advertising their superior health. Carotenoid availability has also been shown to limit egg-laying capacity in birds, although it remains to be seen whether carotenoid display in females advertises reproductive potential. More experiments are required to ascertain the importance of direct (material) and indirect (genetic) benefits accruing through choosing to mate with individuals that have greater carotenoid display.     

A century of life-history evolution in grayling

Synchronic and allochronic data sets consisting of phenotypic values of various life-history traits from five grayling Thymallus thymallus populations with common ancestors were analysed for the purpose of estimating evolution and divergence rates. The synchronic data contained both juvenile and adult traits from populations that have been segregated for 44–88 years (9–22 generations). The allochronic time series contained growth- and maturation data spanning 95 years (16 generations). Estimated evolution and divergence rates were high compared with other life-history studies on the same temporal scale (0.002–1.008 haldanes, 10–30, 500 darwins). The divergence of adult traits were most probably caused by differential mortalities induced by variation in fishing intensity. For the population with allochronic data, 48 years (eight generations) of intense and consistent size-selective gill-net fishing resulted in a constant reduction in age (–0.33 years pr 10 year) and length (–18mm pr 10 year) at maturity. Length-at-age for ages one to five also decreased during the same period. When gill-net fishing was relaxed, age and length at maturity and length-at-age increased. Divergence rates for juvenile traits derived from a common-garden experiment were high, and standardized selection differentials (s) were high, especially for yolk-sac volume (s=2.6). We also document that low divergence rates for juvenile traits were lower between populations having similar spawning/nursery habitats (running water) than populations having relatively different habitats (running water v.s. still water). We suggest that the major part of the observed phenotypic divergence is mostly due to adaptive evolution, although microsatellite data indicate that genetic drift also has occurred.     

Ecological determinants of life-history evolution.

Density-dependent natural selection has been studied, empirically with laboratory populations of Drosophila melanogaster. Populations kept at very high and low population density have become differentiated with respect to important fitness-related traits. There is now some understanding of the behavioural and physiological basis of these differences. These studies have identified larval competitive ability and efficiency of food utilization as traits that are negatively correlated with respect to effects on fitness. Theory that illuminates and motivates additional research with this experimental system has been lacking. Current research has focused on models that incorporate many details of Drosophila ecology in laboratory environments.     

Interpopulation variation in life-history traits of Poeciliopsis prolifica: implications for the study of placental evolution

Placental reproduction is widespread across vertebrate taxa, but little is known about its life-history correlates and putative adaptive value. We studied variation in life-history traits in two populations of the placental poeciliid fish Poeciliopsis prolifica to determine whether differences in post-fertilization maternal provisioning to embryos have a genetic basis and how food availability affects reproduction. Life histories were characterized for wild-caught females and for second-generation lab-born females raised under two levels of food availability. We found that the two populations did not differ significantly in the wild for any life-history traits except for the lipid dry weight in females and in embryos at an advanced stage of development. When environmental effects were experimentally controlled, however, populations exhibited significant differences in several traits, including the degree of maternal provisioning to embryos. Food availability significantly affected female size at first parturition, brood size and offspring dry weight at birth. Altogether, these results demonstrate that population differences in maternal provisioning and other life-history traits have a genetic basis and show a plastic response to food availability. We infer that phenotypic plasticity may mask population differences in the field. In addition, when comparing life-history patterns in these two populations with known patterns in placental and non-placental poeciliids, our results support the hypotheses that placentation is an adaptive reproductive strategy under high-resource conditions but that it may represent a cost under low-food conditions. Finally, our results highlight that age at maturity and reproductive allotment may be key life-history traits accompanying placental evolution.     

Hamilton goes empirical: estimation of inclusive fitness from life-history data

Hamilton's theory of kin selection is one of the most important advances in evolutionary biology since Darwin. Central to the kin-selection theory is the concept of inclusive fitness. However, despite the importance of inclusive fitness in evolutionary theory, empirical estimation of inclusive fitness has remained an elusive task. Using the concept of individual fitness, I present a method for estimating inclusive fitness and its components for diploid organisms with age-structured life histories. The method presented here: (i) allows empirical estimation of inclusive fitness from life-history data; (ii) simultaneously considers all components of fitness, including timing and magnitude of reproduction; (iii) is consistent with Hamilton's definition of inclusive fitness; and (iv) adequately addresses shortcomings of existing methods of estimating inclusive fitness. I also demonstrate the application of this new method for testing Hamilton's rule.     

Contributions of genomics to life-history theory

Life-history theory seeks to understand the factors that produce variation in life histories that are found both among and within species. At the organismal level there is a well developed mathematical framework, and an important focus of the current research is determining the biological underpinnings of this framework, with particular attention to the causal mechanisms that underlie trade-offs. Genomic approaches are proving useful in addressing this issue.     

A new view of avian life-history evolution tested on an incubation paradox

Viewing life-history evolution in birds based on an age-specific mortality framework can explain broad life-history patterns, including the long incubation periods in southern latitudes documented here. I show that incubation periods of species that are matched phylogenetically and ecologically between Argentina and Arizona are longer in Argentina. Long incubation periods have mystified scientists because they increase the accumulated risk of time-dependent mortality to young without providing a clear benefit. I hypothesize that parents of species with low adult mortality accept increased risk of mortality to their young from longer incubation if this allows reduced risk of mortality to themselves. During incubation, songbird parents can reduce risk of mortality to themselves by reducing nest attentiveness (percentage of time on the nest). Here I show that parents of species with lower adult mortality exhibit reduced nest attentiveness and that lower attentiveness is associated with longer incubation periods. However, the incubation period is also modified by juvenile mortality. Clutch size variation is also strongly correlated with age-specific mortality. Ultimately, adult and juvenile mortality explain variation in incubation and other life-history traits better than the historical paradigm.     

Mammal life-history evolution: a comparative test of Charnov's model

We present a comparative test of Charnov's recent theoretical model of mammalian life-history evolution. Phylogenetic analysis of life-table data from 64 species, ranging across nine orders. supports all of Charnov's assumptions and most of his predictions. The allometries of time from independence to maturity (a), annual fecundity, and adult and juvenile mortality rates are in agreement with previous work and with the theory, as are the signs of the relationships among these traits when body size is controlled for. As predicted, the non-dimensional products of a and each of the other three traits are independent of adult body size, as is survivorship to maturity. However, we find that the ratio of weaning weight to adult weight (δ) is correlated with adult weight, in contradiction with the theory, and we do not find the predicted relationships between δ and the three non-dimensional products. The discrepancies could be because we have equated independence with weaning, or because the model assumes determinate growth: they could arise if large mammals have relatively longer periods of post-weaning care, or continue to grow after starting to reproduce. There is some evidence that δ is influenced by the nature of mortality around independence (density-dependent or density-independent), and we suggest this as a possible area for further work. In general, the areas of agreement between Charnov's theory and the data are more impressive than the differences, indicating that it could be a major breakthrough in understanding the evolution of life histories in placental mammals.     

Leishmania-sandfly interactions: an empirical field study

Phlebotomus papatasi is the sandfly vector of Leishmania major in the Jordan Valley. The objective of this study was to characterize vector-parasite relations in an active zoonotic focus. Seasonality and intensity of promastigote infection rates in female sandflies and the developmental stage of these hosts were established. On 153 trap-nights, 641 female P. papatasi were caught and examined. Of these, 48 (7.4%, range 12.9-4.8%) were infected with L. major promastigotes. Correlating the number of parasites with the gonotrophic age of the vector revealed that most infections initially are light ones, and those that survive in the vector generally prosper and proliferate. Comparing infection rates in parous and gravid flies revealed that similar proportions of gravid and parous flies are found infected. Thus, Leishmania infections do not appear to affect sandfly survival.     

Pathogen-induced rapid evolution in a vertebrate life-history trait

Anthropogenic factors, including climate warming, are increasing the incidence and prevalence of infectious diseases worldwide. Infectious diseases caused by pathogenic parasites can have severe impacts on host survival, thereby altering the selection regime and inducing evolutionary responses in their hosts. Knowledge about such evolutionary consequences in natural populations is critical to mitigate potential ecological and economic effects. However, studies on pathogen-induced trait changes are scarce and the pace of evolutionary change is largely unknown, particularly in vertebrates. Here, we use a time series from long-term monitoring of perch to estimate temporal trends in the maturation schedule before and after a severe pathogen outbreak. We show that the disease induced a phenotypic change from a previously increasing to a decreasing size at maturation, the most important life-history transition in animals. Evolutionary rates imposed by the pathogen were high and comparable to those reported for populations exposed to intense human harvesting. Pathogens thus represent highly potent drivers of adaptive phenotypic evolution in vertebrates.     

Convergent maternal provisioning and life-history evolution in echinoderms

In marine invertebrates, the frequent evolution of lecithotrophic nonfeeding development from a planktotrophic feeding ancestral developmental mode has involved the repeated, independent acquisition of a large, lipid-rich, usually buoyant egg. To investigate the mechanistic basis of egg-size evolution and the role of maternally provisioned lipids in lecithotrophic development, we identified and quantified the egg lipids in six sea urchin species and five sea star species encompassing four independent evolutionary transformations to lecithotrophy. The small eggs of species with planktotrophic development were dominated by triglycerides with low levels of wax esters, whereas the larger eggs of lecithotrophs contain measurable triglycerides but were dominated by wax ester lipids, a relatively minor egg component of planktotrophs. Comparative analysis by independent contrasts confirmed that after removing the influence of phylogeny, the evolution of a large egg by lecithotrophs was correlated with the conspicuous deposition of wax esters. Increases in wax ester abundance exceeded expectations based solely on changes in egg volume. Wax esters may have roles in providing buoyancy to the egg and for postmetamorphic provisioning. Experimentally reducing the amount of wax esters in blastula stage embryos of the lecithotroph Heliocidaris erythrogramma resulted in a viable but nonbuoyant larvae. During normal development for H. erythrogramma, wax ester biomass remained constant during development to metamorphosis (five days postfertilization), but decreased during juvenile development before complete mouth formation (12 days postfertilization) and was further reduced at 18 days postfertilization. The function of wax esters may be specific to the lecithotrophic developmental mode because there were negligible wax esters present in competent pluteus larvae of Strongylocentrotus drobachiensis, a planktotrophic species. These data suggest that this seminal evolutionary modification, the production of a large egg, has been accomplished in part by the elaboration of a preexisting oogenic component, wax esters. The modification of preexisting oogenic processes may facilitate the observed high frequency of transformations in larval mode in marine invertebrates.     

Directionality of evolution at molecular and organismic levels.

The molecular evolution theories of Eigen and Kimura are compared and their difference is explained. In terms of Eigen's theory for the evolution of macromolecules, the selection of genotypes occurs directly. The physical meaning of the neutral theory is the degeneracy of the correlation between a phenotype and a genotype at the molecular level. A model theory of evolution on a fitness landscape is proposed. The theory shows that the constraints of selection determined by the structure and dynamics of previous evolution stages increases its rate strongly.