Population and prehistory III: Food-dependent demography in variable environments

The population dynamics of preindustrial societies depend intimately on their surroundings, and food is a primary means through which environment influences population size and individual well-being. Food production requires labor; thus, dependence of survival and fertility on food involves dependence of a population’s future on its current state. We use a perturbation approach to analyze the effects of random environmental variation on this nonlinear, age-structured system. We show that in expanding populations, direct environmental effects dominate induced population fluctuations, so environmental variability has little effect on mean hunger levels, although it does decrease population growth. The growth rate determines the time until population is limited by space. This limitation introduces a tradeoff between population density and well-being, so population effects become more important than the direct effects of the environment: environmental fluctuation increases mortality, releasing density dependence and raising average well-being for survivors. We discuss the social implications of these findings for the long-term fate of populations as they transition from expansion into limitation, given that conditions leading to high well-being during growth depress well-being during limitation.     

Modelling animal growth in random environments: An application using nonparametric estimation

We study a stochastic differential equation growth model to describe individual growth in random environments. In particular, in this paper, we discuss the estimation of the drift and the diffusion coefficients using nonparametric methods for the case of nonequidistant data for several trajectories. We illustrate the methodology by using bovine growth data. Our goal is to assess: (i) if the parametric models (with specific functional forms for the drift and the diffusion coefficients) previously used by us to describe the evolution of bovine weight were adequate choices; (ii) whether some alternative specific parameterized functional forms of these coefficients might be suggested for further parametric analysis of this data.     

Polymorphism in random environments

A two-allele diploid model is described in which the fitnesses of the three genotypes are stationary stochastic processes. It is shown that a stable polymorphism will occur if the geometric mean fitness of the heterozygote exceeds that of both homozygotes. It is possible for the mean fitness of the population to be lower in polymorphic than in the associated monomorphic populations.     

Sex in random environments

Based on the theory of natural selection it is not obvious why sexual reproduction should evolve in Mendelian populations. Sexually reproducing organisms incur a “cost of meiosis”: an asexual lineage would grow at twice the rate of a comparable sexual lineage. A plausible and popular explanation for the widespread occurrence of sexual reproduction is that it adapts a lineage to temporal uncertainty in the environment. Computer simulation of a model introduced and partially analyzed in a companion paper (Hines & Moore,1981) suggests that under some of the hypothetical conditions, sexuality is advantageous, but the conditions are very restricted if only one or a few loci are selected. In the companion paper, to make analytical progress, it was necessary to assume small environmental effects or that the fitnesses of the homozygotes at each locus were identical in each generation, although fluctuating between generations. No such assumptions were made here. In addition the effect of an absorbing barrier was studied in the simulations.The computer model envisages from 1–4 loci, each with two alleles, selected independently. In each generation, each locus experiences one of three selection regimes chosen at random; each genotype is favored by one of the three selection regimes. The fitness of a multi-locus genotype is the product of the fitnesses of the independent loci. The sexual species produce genetically varied offspring according to Mendel's laws; the recombination frequency between all loci is 0–5. Members of the asexual species produce offspring that are genetic replicates of themselves. It is important to note that the model represents segregation and independent assortment of genes but not linkage disequilibrium.Computer simulation results were consistent with analytical results, suggesting that inferences can be extrapolated from the analysis without danger of serious error. Both the analysis and simulations reveal a dilemma for the hypothesis that sex is an adaptation to temporal uncertainty; viz., the conditions that are most favorable for sexually are somewhat antithetical (but not prohibitive) to the maintenance of genetic polymorphism in the sexual species whereas sex is useless in a monomorphic population. The dilemma is particularly apparent when only one or a few loci are selected; however, as the number of selected loci increases, the disadvantage in sexuality diminishes. Thus, environmental uncertainty may explain the adaptive significance of sex provided many loci are selected in the prescribed manner.     

Life-history evolution in uncertain environments: bet hedging in time

Many vertebrates, forest herbs, and trees exhibit both variable age at maturity and iteroparity as adaptations to uncertain environments. We analyze a stochastic model that combines these two life-history adaptations with density-dependent fertility. Results for a model with only iteroparity are consistent with previous work; environmental uncertainty favors adult survival over juvenile survival. This holds true even if there is a moderately strong convex trade-off between adult survival and fecundity, but the direction of selection can depend on which life-history trait is considered a random variable. A life history with only developmental delay favors juvenile survival in uncertain environments, consistent with previous models of seed banks. When both developmental delay and iteroparity are included in the model, both adaptations are favored in uncertain environments. Our simulations show that selection is not necessarily a runaway process in which either developmental delay or iteroparity is favored, as recently proposed by Tuljapurkar and Wiener, but rather that selection can favor both mechanisms. Invasion analysis shows that selective pressure on life-history delays increases as environmental variation increases. Reproductive delay and adult survival can be either adaptations or constraints. Natural-history studies that estimate model parameters can resolve this uncertainty.     

Regulated growth in random environments

Summary Conditions for extinction, convergence to a stationary distribution and attaining a carrying capacity are given for stochastic versions of the logistic growth process.     

Population growth in random environments

This paper reviews some recent advances in single population stochastic differential equation growth models. They are a natural way to model population growth in a randomly varying environment. The question of which calculus, Itô or Stratonovich, is preferable is addressed. The two calculi coincide when the noise term is linear, if we take into account the differences in the interpretation of the parameters. This clarifies, among other things, the controversy on the theory of niche limiting similarity proposed by May and MacArthur. The effects of correlations in the environmental fluctuations and statistical methods for estimating parameters and for prediction based on a single population trajectory are mentioned. Applications to fisheries, wildlife management and particularly to environmental impact assessment are now becoming possible and are proposed in this paper.     

Evolution of delayed reproduction in uncertain environments: a life-history perspective

Environmental uncertainty alone can select for delayed reproduction; however, its relative role in the evolution of delayed reproduction across life histories is not known. Along a life-history spectrum from low-survival/high-fertility species to high-survival/low-fertility species, we show that the latter are more likely to evolve delayed reproduction if fertility varies over time. By contrast, if survival varies over time, low-survival life histories are more likely to evolve delays. If there is variation in both survival and fertility, and if this variation is positively associated, the evolutionarily stable reproductive delay is decreased (relative to independent variation in survival and fertility). Conversely, if variation in survival and fertility is negatively associated, the evolutionarily stable reproductive delay is increased. We further show that environmental uncertainty can drive the evolution of delayed reproduction in an iteroparous organism but only in the special case where juvenile survival is greater than adult survival. For common iteroparous life histories (adult survival > juvenile survival), environmental uncertainty does not select for delayed reproduction. Thus, any benefits that delayed reproduction might have on reproduction or survival could be especially important in explaining the common observation of delayed reproduction in many vertebrates and perennial plants.     

Androgens in the demography of male life course--a review

While the basics of testosterone production, effects and metabolism have been known for decades, there has been a flow of novel insights in the genomics of testosterone action on a molecular and cellular level, as well as in the clinical effects from modern clinical trials, improving the understanding of the role of testosterone in male life course. Androgens are produced under the control of an endocrine cascade from GnRH via gonadotropins to the testicular Leydig cells. In some organs, testosterone is reduced to 5alpha-dihydrotestosterone prior to the receptor binding by the 5alpha reductase. The androgen receptor gene is located on the X chromosome in the q11-12 region, each mutation in the gene will induce phenotypic manisfestations. In the first stage of the male life course, testosterone moderates the male embryonic development under the control of a complex molecular genetic network. The next important phase of male maturation is the puberty, in which testosterone levels increase and induce the development of somatic and psychological characteristics of male sexuality. In the adult male, testosterone maintains sexual functions and fertility. In aging men, testosterone levels decrease slowly. Testosterone supplementation in the aging male is able to restore the function of androgen target organs only in part.     

Variable effort fishing models in random environments

We study the growth of populations in a random environment subjected to variable effort fishing policies. The models used are stochastic differential equations and the environmental fluctuations may either affect an intrinsic growth parameter or be of the additive noise type. Density-dependent natural growth and fishing policies are of very general form so that our results will be model independent. We obtain conditions on the fishing policies for non-extinction and for non-fixation at the carrying capacity that are very similar to the conditions obtained for the corresponding deterministic model. We also obtain conditions for the existence of stationary distributions (as well as expressions for such distributions) very similar to conditions for the existence of an equilibrium in the corresponding deterministic model. The results obtained provide minimal requirements for the choice of a wise density-dependent fishing policy.     

Persistence of structured populations in random environments

Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded” dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.     

Extinction and exponential growth in random environments.

The influence of randomly varying environments on unrestricted population growth and extinction is analyzed by means of branching processes with random environments (BPRE). A main theme is the interplay between environmental and sampling (or “demographic”) variability. If the two sources of variationg are of comparable magnitude, the environmental variation will dominate except as regards the event of extinction.A diffusion approximation of BPRE is proposed to study the situation of a large population with small environmental variance and mean offspring size near one.Comments on the ecological literature as well as on the relation of the results to previous work involving stochastic differential equations are also given.     

Invariant distributions for multi-population models in random environments

We obtain the existence of a solution and invariant distribution for systems of stochastic differential equations which represent populations in random environments. The method used is a stochastic Lyapunov function, based on a theorem of Kushner. The method is applied to a system of two populations exchainging individuals through migration, and to a generalized n-dimensional Lotka-Volterra system.     

Measuring marine fishes biodiversity: temporal changes in abundance, life history and demography

Patterns in marine fishes biodiversity can be assessed by quantifying temporal variation in rate of population change, abundance, life history and demography concomitant with long-term reductions in abundance. Based on data for 178 populations (62 species) from four north-temperate oceanic regions (Northeast Atlantic and Pacific, Northwest Atlantic, North mid-Atlantic), 81% of the populations in decline prior to 1992 experienced reductions in their rate of loss thereafter; species whose rate of population decline accelerated after 1992 were predominantly top predators such as Atlantic cod (Gadus morhua), sole (Solea solea) and pelagic sharks. Combining population data across regions and species, marine fishes have declined 35% since 1978 and are currently less than 70% of recorded maxima; demersal species are generally at historic lows, pelagic species are generally stable or increasing in abundance. Declines by demersal species have been associated with substantive increases in pelagic species, a pattern consistent with the hypothesis that increases in the latter may be largely attributable to reduced predation mortality. There is a need to determine the consequences to population growth effected by the reductions in age and size at maturity, and in mean age and size of spawners, concomitant with population decline. We conclude that reductions in the rate of population decline, in the absence of targets for population increase, will be insufficient to effect a recovery of marine fishes biodiversity, and that great care must be exercised when interpreting multi-species patterns in abundance. Of fundamental importance is the need to explain the geographical, species-specific and habitat biases that pervade patterns of marine fishes recovery and biodiversity.     

Variation in life history and demography of the American black bear

Variation in life history and demography across a species' range informs researchers about regional adaptations and affects whether managers can borrow information from other populations in decision-making. The American black bear (Ursus americanus) is a long-lived game species whose continued persistence depends on management of harvest and removal of habituated bears that come into conflict with humans. Understanding the demography of black bears guides efforts at management and conservation, yet detailed knowledge of many populations is typically lacking. I performed a hierarchical Bayesian meta-analysis of black bear demographic studies across the geographic range of the species to explore how vital rates vary across the range, what information they give us about population growth, and whether managers can justify borrowing information from other studies to inform management decisions. Cub, yearling, and adult survival and fecundity varied between eastern and western North America, whereas subadult survival did not show geographic structuring. Adult survival and fecundity appeared to trade off, with higher survival in the western portions of bears' range and higher fecundity in the east. Although adult survival had the highest elasticity, differences in reproduction drove differences in population growth rate. Mean population growth rate was higher in the east (0.99; 95% credible interval [CrI]: 0.96, 1.03) than the west (0.97; 95%CrI: 0.93, 1.01). Despite declining trends in the west, 34% of the distribution of population growth rate was >1, compared to 55% in the east. Further work needs to be done to address the cause of the apparent trade-off between adult survival and fecundity and explore how the estimated growth rates are likely to affect population status of black bears. Because population growth rates are close to 1 and small deviations could impact whether a population is considered increasing or decreasing, managers need to employ caution in borrowing vital rates from other populations. © 2011 The Wildlife Society.     

Timescales of population rarity and commonness in random environments

This is a mathematical study of the interactions between non-linear feedback (density dependence) and uncorrelated random noise in the dynamics of unstructured populations. The stochastic non-linear dynamics are generally complex, even when the deterministic skeleton possesses a stable equilibrium. There are three critical factors of the stochastic non-linear dynamics; whether the intrinsic population growth rate (lambda) is smaller than, equal to, or greater than 1; the pattern of density dependence at very low and very high densities; and whether the noise distribution has exponential moments or not. If lambda < 1, the population process is generally transient with escape towards extinction. When lambda > or = 1, our quantitative analysis of stochastic non-linear dynamics focuses on characterizing the time spent by the population at very low density (rarity), or at high abundance (commonness), or in extreme states (rarity or commonness). When lambda >1 and density dependence is strong at high density, the population process is recurrent: any range of density is reached (almost surely) in finite time. The law of time to escape from extremes has a heavy, polynomial tail that we compute precisely, which contrasts with the thin tail of the laws of rarity and commonness. Thus, even when lambda is close to one, the population will persistently experience wide fluctuations between states of rarity and commonness. When lambda = 1 and density dependence is weak at low density, rarity follows a universal power law with exponent -3/2. We provide some mathematical support for the numerical conjecture [Ferriere, R., Cazelles, B., 1999. Universal power laws govern intermittent rarity in communities of interacting species. Ecology 80, 1505-1521.] that the -3/2 power law generally approximates the law of rarity of 'weakly invading' species with lambda values close to one. Some preliminary results for the dynamics of multispecific systems are presented.     

Dynamic decision-making in uncertain environments II. Allais paradox in human behavior

In both animal and human behavioral repertoires, classical expected utility theory is considered a fundamental element of decision making under conditions of uncertainty. This theory has been widely applied to problems of animal behavior and evolutionary game theory, as well as to human economic behavior. The Allais paradox hinges on the expression of avoidance of bankruptcy by humans, or death by starvation in animals. This paradox reveals that human behavioral patterns are often inconsistent with predictions under the classical expected utility theory as formulated by von Neumann and Morgenstern. None of the many attempts to reformulate utility theory has been entirely successful in resolving this paradox with rigorous logic. We present a simple, but novel approach to the theory of decision making, in which utility is dependent on current wealth, and in which losses are more heavily weighted than gains. Our approach resolves the Allais paradox in a manner that is consistent with how humans formulate decisions under uncertainty. Our results indicate that animals, including humans, are in principle risk-averse. Our restructuring of dynamic utility theory presents a basic optimization scheme for sequential or dynamic decisions in both animals and humans.