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.     

Mortality plateaus and directionality theory

Recent large scale studies of senescence in animals and humans have revealed mortality rates that levelled off at advanced ages. These empirical findings are now known to be inconsistent with evolutionary theories of senescence based on the Malthusian parameter as a measure of fitness. This article analyses the incidence of mortality plateaus in terms of directionality theory, a new class of models based on evolutionary entropy as a measure of fitness. We show that the intensity of selection, in the context of directionality theory, is a convex function of age, and we invoke this property to predict that in populations evolving under bounded growth constraints, evolutionarily stable mortality patterns will be described by rates which abate with age at extreme ages. The explanatory power of directionality theory, in contrast with the limitations of the Malthusian model, accords with the claim that evolutionary entropy, rather than the Malthusian parameter, constitutes the operationally valid measure of Darwinian fitness.     

Reproductive cycle,sexual maturity and longevity of Odontophrynus americanus (Anura: Odontophrynidae) in South Brazil

Studies on the reproductive biology and age of amphibians provide primary information about the life history and population demographic parameters of species. Here, we describe the reproductive cycle, size–fecundity relationships, reproductive effort, sexual dimorphism and sexual maturity of Odontophrynus americanus, the flood frog, from South Brazil. A total of 96 individuals were analysed. The reproductive cycles of males and females were described through morphoanatomical analysis of testis and ovary. Age at onset of sexual maturity and estimated longevity were determined by skeletochronology. Individuals of O. americanus presented a potentially continuous reproductive cycle with a peak of reproductive activity in the warmer months. Females presented a higher reproductive investment than males. Sexual maturity was reached at around one year of age for both sexes while longevity differed between the sexes, with females living up to six years and males up to ten years. No evidence of sexual size dimorphism was found. This study is among the few that have assessed age at sexual maturity and longevity in a Neotropical anuran. Basic aspects of life history are of paramount importance because they allow comparisons and test of hypotheses to be made, which can help to build generalizations about the evolutionary meaning of ecological strategies.     

Offspring fitness and the optimal propagule size in a fluctuating environment

Propagule size is an important maternal effect on offspring fitness and phenotype in birds and other oviparous animals. The performance of propagules often increases with size, but a fluctuating environment may introduce temporal variation in the optimal phenotype. Understanding these mechanisms will provide novel insights into the eco‐evolutionary dynamics of life history strategies in parental reproductive investment. We investigated the interaction between propagule size (measured as egg volume) and environmental conditions on offspring mortality and phenotype in a Norwegian house sparrow population. Increased propagule size reduced offspring mortality in early life, with more pronounced effects under heavy precipitation. However, the optimal propagule size for low offspring mortality until recruitment shifted from large to small as temperature increased. Propagule size had no significant effect on fledgling body mass and tarsus length. These results reveal a potential for eco‐evolutionary dynamics in propagule size, as populations adapt to fluctuating environmental conditions. The ultimate outcome of this dynamic process will also depend on variation in parental fitness and tradeoffs with other life‐history traits, particularly clutch size.     

Age at first reproduction and probability of reproductive failure in women

Life history theory predicts a trade-off between fitness benefits and costs of delaying age at first reproduction (AFR). In many human populations, maternal AFR has been increasingly delayed beyond sexual maturity over the past decades, raising a question of whether any fitness benefits accrued outweigh costs incurred. To investigate the cost–benefit trade-off concerning AFR in women, we construct a theoretical model and test its predictions using pedigree data from historical Finnish mothers. The model predicts that the probability of reproductive failure (no offspring produced reaching breeding) will increase with AFR if the benefit with delaying in terms of improvement to offspring quality (i.e., breeding probability) cannot offset the cost from decline in offspring quantity. The data show that offspring quantity declined significantly with delayed reproduction, while offspring quality remained initially constant before declining when AFR was delayed beyond 30. Consistent with the theoretical model's predictions, reproductive failure probability increased markedly with delaying AFR after 30, independently of maternal socioeconomic status. Our study is the first to investigate the associations between delay in AFR after sexual maturity and changes in not only offspring quantity but also offspring quality and suggest a significant evolutionary disadvantage of delayed AFR beyond 30 for lineage persistence in a predemographic transition society.     

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.     

A Review for Life-history Traits Variation in Frogs Especially for Anurans in China

Environmental variation can promote differentiation in life-history traits in species of anurans. Increased environmental stress usually results in larger age at sexual maturity, older mean age, longer longevity, slower growth, larger body size, and a shift in reproductive allocation from offspring quantity to quality, and a stronger trade-off between offspring size and number. However, previous studies have suggested that there are inconsistent geographical variations in life-history traits among anuran species in China. Hence, we here review the intraspecific patterns and differences in life-history traits(i.e., egg size, clutch size, testes size, sperm length, age at sexual maturity, longevity, body size and sexual size dimorphism) among different populations within species along geographical gradients for anurans in China in recent years. We also provide future directions for studying difference in sperm performance between longer and shorter sperm within a species through transplant experiments and the relationships between metabolic rate and brain size and life-history.     

Life-history phenotypes in populations of Brachyrhaphis episcopi (Poeciliidae) with different predator communities

Variation among populations in extrinsic mortality schedules selects for different patterns of investment in key life-history traits. We compared life-history phenotypes among 12 populations of the live-bearing fish Brachyrhaphis episcopi. Five populations co-occurred with predatory fish large enough to prey upon adults, while the other seven populations lacked these predators. At sites with large predatory fish, both sexes reached maturity at a smaller size. Females of small to average length that co-occurred with predators had higher fecundity and greater reproductive allotment than those from populations that lacked predators, but the fecundity and reproductive allotment of females one standard deviation larger than mean body length did not differ among sites. In populations with large predatory fish, offspring mass was significantly reduced. In each population, fecundity, offspring size and reproductive allotment increased with female body size. When controlling for maternal size, offspring mass and number were significantly negatively correlated, indicating a phenotypic trade-off. This trade-off was non-linear, however, because reproductive allotment still increased with brood size after controlling for maternal size. Similar differences in life-history phenotypes among populations with and without large aquatic predators have been reported for Brachyrhaphis rhabdophora in Costa Rica and Poecilia reticulata (a guppy) in Trinidad. This may represent a convergent adaptation in life-history strategies attributable to predator-mediated effects or environmental correlates of predator presence.     

Competition as a selective mechanism for larger offspring size in guppies

Highly competitive environments are predicted to select for larger offspring. Guppies Poecilia reticulata from low-predation populations have evolved to make fewer, larger offspring than their counterparts from high-predation populations. As predation co-varies with the strength of competition in natural guppy populations, here I present two laboratory experiments that evaluate the role of competition in selecting for larger offspring size. In the first experiment, paired groups of large and small newborns from either a high- or a low-predation population were reared in mesocosms under a high- or a low-competition treatment. While large newborns retained their size advantage over small newborns in both treatments, newborn size increased growth only in the high-competition treatment. Moreover, the increase in growth with size was greater in guppies derived from the low-predation population. In the second experiment, pairs of large and small newborns were reared in a highly competitive environment until reproductive maturity. Small size at birth delayed maturation and the effect of birth size on male age of maturity was greater in the low-predation population. These results support the importance of competition as a selective mechanism in offspring size evolution.     

BODY SIZE AND SEXUAL SIZE DIMORPHISM IN MARINE IGUANAS FLUCTUATE AS A RESULT OF OPPOSING NATURAL AND SEXUAL SELECTION: AN ISLAND COMPARISON

Body size is often assumed to represent the outcome of conflicting selection pressures of natural and sexual selection. Marine iguana (Amblyrhynchus cristatus) populations in the Galápagos exhibit 10-fold differences in body mass between island populations. There is also strong sexual size dimorphism, with males being about twice as heavy as females. To understand the evolutionary processes shaping body size in marine iguanas, we analyzed the selection differentials on body size in two island populations (max. male mass 900 g in Genovesa, 3500 g in Santa Fé). Factors that usually confound any evolutionary analysis of body sizes—predation, interspecific food competition, reproductive role division—are ruled out for marine iguanas. We show that, above hatchlings, mortality rates increased with body size in both sexes to the same extent. This effect was independent of individual age. The largest animals (males) of each island were the first to die once environmental conditions deteriorated (e.g., during El Niños). This sex-biased mortality was the result of sexual size dimorphism, but at the same time caused sexual size dimorphism to fluctuate. Mortality differed between seasons (selection differentials as low as –1.4) and acted on different absolute body sizes between islands. Both males and females did not cease growth when an optimal body size for survival was reached, as demonstrated by the fact that individual adult body size phenotypically increased in each population under favorable environmental conditions beyond naturally selected limits. But why did marine iguanas grow “too large” for survival? Due to lek mating, sexual selection constantly favored large body size in males (selection differentials up to +0.77). Females only need to reach a body size sufficient to produce surviving offspring. Thereafter, large body size of females was less favored by fertility selection than large size in males. Resulting from these different selection pressures on male and female size, sexual size dimorphism was mechanistically caused by the fact that females matured at an earlier age and size than males, whereafter they constantly allocated resources into eggs, which slowed growth. The observed allometric increase in sexual size dimorphism is explained by the fact that the difference between these selective processes becomes larger as energy abundance in the environment increases. Because body size is generally highly heritable, these selective processes are expected to lead to genetic differences in body size between islands. We propose a common-garden experiment to determine the influence of genetic factors and phenotypic reaction norms of final body size.     

Effects of population size and pollen diversity on reproductive success and offspring size in the narrow endemic Cochlearia bavarica (Brassicaceae)

In small, fragmented populations of self-incompatible plant species, genetic drift and increasingly close relationships between plants may restrict the number of genetically different pollen donors, the availability of compatible mates, and the opportunity for pollen competition and selection. These restrictions may reduce the siring success or increase the probability of inbreeding depression in the offspring. To test if this was the case, we hand-pollinated maternal plants in small and large populations of the rare, endemic plant Cochlearia bavarica (Brassicaceae) with pollen from one, three, or nine donors from the same population or with nine donors from a different population. In one additional population of intermediate size, maternal plants were hand-pollinated with ten donors located at a distance of 1, 10, 100, or 1000 m. We then recorded seed and offspring characters. On average, offspring from small populations were smaller than normal and fewer survived to maturity. Increasing the number of pollen donors had a positive effect on reproductive success in small and large populations, but at the highest pollen diversity this occurred at the expense of slightly reduced offspring fitness. Because the total amount of transferred pollen was held constant, these effects could not be attributed to increasing pollen load. Rather, the increasing pollen diversity may have increased the chances of selecting a particularly "good" donor for fertilization-an example of a sampling effect of diversity. Pollen from outside a population or from 10-100 m away resulted in higher reproductive success and greater offspring size. Effects of population size and pollination treatments on reproductive success and offspring fitness were additive. Apparently, there is no obvious size threshold above which the potential of inbreeding depression can be ignored in C. bavarica.     

THE EVOLUTION OF FEMALE-BIASED SEXUAL SIZE DIMORPHISM: A POPULATION-LEVEL COMPARATIVE STUDY IN HORNED LIZARDS (PHRYNOSOMA)

Female-biased sexual size dimorphism is uncommon among vertebrates and traditionally has been attributed to asymmetric selective pressures favoring large fecund females (the fecundity-advantage hypothesis) and/or small mobile males (the small-male advantage hypothesis). I use a phylogenetically based comparative method to address these hypotheses for the evolution and maintenance of sexual size dimorphism among populations of three closely related lizard species (Phrynosoma douglasi, P. ditmarsi, and P. hernandezi). With independent contrasts I estimate evolutionary correlations among female body size, male body size, and sexual size dimorphism (SSD) to determine whether males have become small, females have become large, or both sexes have diverged concurrently in body size during the evolutionary Xhistory of this group. Population differences in degree of SSD are inversely correlated with average male body size, but are not correlated with average female body size. Thus, variation in SSD among populations has occurred predominantly through changes in male size, suggesting that selective pressures on small males may affect degree of SSD in this group. I explore three possible evolutionary mechanisms by which the mean male body size in a population could evolve: changes in size at maturity, changes in the variance of male body sizes, and changes in skewness of male body size distributions. Comparative analyses indicate that population differentiation in male body size is achieved by changes in male size at maturity, without changes in the variance or skewness of male and female size distributions. This study demonstrates the potential of comparative methods at lower taxonomic levels (among populations and closely related species) for studying microevolutionary processes that underlie population differentiation.     

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.     

Field estimates of parentage reveal sexually antagonistic selection on body size in a population of Anolis lizards

Sexual dimorphism evolves when selection favors different phenotypic optima between the sexes. Such sexually antagonistic selection creates intralocus sexual conflict when traits are genetically correlated between the sexes and have sex‐specific optima. Brown anoles are highly sexually dimorphic: Males are on average 30% longer than females and 150% heavier in our study population. Viability selection on body size is known to be sexually antagonistic, and directional selection favors large male size whereas stabilizing selection constrains females to remain small. We build on previous studies of viability selection by measuring sexually antagonistic selection using reproductive components of fitness over three generations in a natural population of brown anoles. We estimated the number of offspring produced by an individual that survived to sexual maturity (termed RS^V), a measure of individual fitness that includes aspects of both individual reproductive success and offspring survival. We found directional selection on male body size, consistent with previous studies of viability selection. However, selection on female body size varied among years, and included periods of positive directional selection, quadratic stabilizing selection, and no selection. Selection acts differently in the sexes based on both survival and reproduction and sexual conflict appears to be a persistent force in this species.     

Variations in age and size at maturity of female Nile tilapia, Oreochromis niloticus, populations from man-made lakes of Côte d'Ivoire

The reproductive characteristics of Oreochromis niloticus females were studied in two large hydroelectric dams and 6 small agropastoral reservoirs of Côte d'Ivoire, selected for their diversity of environmental conditions and sizes (6 to 80000 ha). Comparative analysis of age and size at maturity revealed large differences between the populations with early maturity, late maturity, and intermediate situations. All the populations matured in their first year, between 5.6 and 10 months. Age and size at maturity were positively correlated with the reservoir area. The range of variation in age at maturity between populations was far greater than that of size at maturity. However, size at maturity also appears to be very plastic as intra-population variations of 2 to 3 cm were found between consecutive years. A comparison of age at maturity for a population in 1994 and 1996 showed that this trait is also likely to vary significantly at the intra-population level. Environmental factors which could potentially affect age and size at maturity are discussed. Growth differences are the probable explanation for the observed patterns of variation between populations. Rapid changes in age and size at maturity at inter or intra-population levels suggest that the observed variations might be explained by differences in environmental variables (phenotypic plasticity) rather than by genetic differences.     

Spatial and temporal variation in a suite of life-history traits in two species of wolf spider

Abstract.  1. Life-history traits and density were assayed in seven populations of two sympatric species of wolf spider for three consecutive years. The goal of the study was to quantify population dynamics and its relation to spatial and temporal life-history variation.
2. Adult female body size and fecundity varied significantly, among field sites and among years, in both species. Female spiders of both species differed in mean relative reproductive effort among sites, but not among years. The size of offspring was invariable, with no significant differences due to site or year.
3. All populations of both species tended to either decrease or increase in density during a given year and this was tightly correlated with changes in prey consumption rates.
4. Since life-history patterns are determined primarily by selection, it is concluded that size at sexual maturity for females is phenotypically plastic and responds to changes in prey availability. Offspring size however is not plastic and it is likely that other selection forces have determined offspring size. Temporal fluctuations in population size are correlated over a large area relative to dispersal capabilities for these species and conservation efforts for invertebrates must take this into consideration.     

Intralocus sexual conflict,adaptive sex allocation,and the heritability of fitness

Intralocus sexual conflict arises when selection favours alternative fitness optima in males and females. Unresolved conflict can create negative between‐sex genetic correlations for fitness, such that high‐fitness parents produce high‐fitness progeny of their same sex, but low‐fitness progeny of the opposite sex. This cost of sexual conflict could be mitigated if high‐fitness parents bias sex allocation to produce more offspring of their same sex. Previous studies of the brown anole lizard (Anolis sagrei) show that viability selection on body size is sexually antagonistic, favouring large males and smaller females. However, sexual conflict over body size may be partially mitigated by adaptive sex allocation: large males sire more sons than daughters, whereas small males sire more daughters than sons. We explored the evolutionary implications of these phenomena by assessing the additive genetic (co)variance of fitness within and between sexes in a wild population. We measured two components of fitness: viability of adults over the breeding season, and the number of their progeny that survived to sexual maturity, which includes components of parental reproductive success and offspring viability (RS^V). Viability of parents was not correlated with adult viability of their sons or daughters. RS^V was positively correlated between sires and their offspring, but not between dams and their offspring. Neither component of fitness was significantly heritable, and neither exhibited negative between‐sex genetic correlations that would indicate unresolved sexual conflict. Rather, our results are more consistent with predictions regarding adaptive sex allocation in that, as the number of sons produced by a sire increased, the adult viability of his male progeny increased.     

Leaf size in three generations of a dioecious tropical tree, Ocotea tenera (Lauraceae): Sexual dimorphism and changes with age

? Premise of the study: In dioecious species, selection should favor different leaf sizes in males and females whenever the sexes experience distinct environments or constraints such as different costs of reproduction. We took advantage of a long-term experimental study of Ocotea tenera (Lauraceae), a dioecious understory tree in Monteverde, Costa Rica, to explore leaf size differences between genders and age classes across generations. ? Methods: We measured leaf size in adult trees in a natural population, in their adult F(1) offspring in two experimental populations, and in their F(2) offspring at the seedling stage. Individual trees were measured at various times over 20 yr. ? Results: Leaves of female trees averaged 8% longer and 12% greater in area than those of males. Leaves were sexually dimorphic at reproductive maturity. Leaf size declined during the lifetime of most trees. Heritability estimates for leaf length were positive although not statistically significant (h(2) = 0.63, SE = 0.48, P = 0.095). ? Conclusions: We ruled out the ecological causation hypothesis for sexual dimorphism in leaf size because male and female trees co-occurred in the same habitats. Sexual dimorphism appeared not to result from genetic or phenotypic correlations with other traits such as height or flower size. Rather, females appear to compensate for higher costs of reproduction and diminished photosynthetic capacity by producing larger leaves. Additive genetic variance in leaf size, a prerequisite for an evolutionary response to selection for sexual dimorphism, was suggested by positive (although only marginally significant) heritability estimates.     

Sexual selection on song and cuticular hydrocarbons in two distinct populations of Drosophila montana

Sexual selection has the potential to contribute to population divergence and speciation. Most studies of sexual selection in Drosophila have concentrated on a single signaling modality, usually either courtship song or cuticular hydrocarbons (CHCs), which can act as contact pheromones. We have examined the relationship between both signal types and reproductive success using F(1-3) offspring of wild-collected flies, raised in the lab. We used two populations of the Holarctic species Drosophila montana that represent different phylogeographic clades that have been separate for ca. 0.5 million years (MY), and differ to some extent in both traits. Here, we characterize the nature and identify the targets of sexual selection on song, CHCs, and both traits combined within the populations. Three measures of courtship outcome were used as fitness proxies. They were the probability of mating, mating latency, and the production of rejection song by females, and showed patterns of association with different traits that included both linear and quadratic selection. Courtship song predicted courtship outcome better than CHCs and the signal modalities acted in an additive rather than synergistic manner. Selection was generally consistent in direction and strength between the two populations and favored males that sang more vigorously. Sexual selection differed in the extent, strength, and nature on some of the traits between populations. However, the differences in the directionality of selection detected were not a good predictor of population differences. In addition, a character previously shown to be important for species recognition, interpulse interval, was found to be under sexual selection. Our results highlight the complexity of understanding the relationship between within-population sexual selection and population differences. Sexual selection alone cannot predict differences between populations.