Habitat selection in a variable environment

A Monte Carlo simulation scheme was utilized to determine optimal strategies of habitat utilization in a variable environment. The model allows for differences in quality among habitats at any one time and for varying levels of environmental variance and autocorrelation. When habitats are on the average equal in quality, tracking of temporal fluctuations in environment through variable habitat selection is universally advantageous with the gain in fitness limited by environmental variance, autocorrelation, and number of available habitats. Average differences in quality among habitats will restrict the advantage of variable habitat utilization (over complete usage of the average better habitat) to cases of high environmental autocorrelation or high ratios of enviromental variance to mean habitat separation. Extending an earlier prediction of Levins (1965), the average heterozygosity per individual in a natural population should increase with increasing environmental variance.     

Evolution of a plastic quantitative trait in an age-structured population in a fluctuating environment

We analyze weak fluctuating selection on a quantitative character in an age-structured population not subject to density regulation. We assume that early in the first year of life before selection, during a critical state of development, environments exert a plastic effect on the phenotype, which remains constant throughout the life of an individual. Age-specific selection on the character affects survival and fecundity, which have intermediate optima subject to temporal environmental fluctuations with directional selection in some age classes as special cases. Weighting individuals by their reproductive value, as suggested by Fisher, we show that the expected response per year in the weighted mean character has the same form as for models with no age structure. Environmental stochasticity generates stochastic fluctuations in the weighted mean character following a first-order autoregressive model with a temporally autocorrelated noise term and stationary variance depending on the amount of phenotypic plasticity. The parameters of the process are simple weighted averages of parameters used to describe age-specific survival and fecundity. The "age-specific selective weights" are related to the stable distribution of reproductive values among age classes. This allows partitioning of the change in the weighted mean character into age-specific components.     

The interaction of genetic drift and mutation with selection in a fluctuating environment

The interaction of genetic drift, mutation, and selection in a random environment is investigated using an asymptotic analysis based on assumptions of weak mutation and strong selection. It is shown that genetic drift can be a potent force for removing variation from the population when the random environment tends to occasionally push alleles down to low frequencies.     

An analysis of age-and size-dependent flowering: A critical-production model

Three critical phenomena of flowering can be recognized in nature: critical age, critical initial size and critical switchover size. In order to understand the ecological significance of these flowering phenomena from the viewpoint of matter production, a simple model of flowering phenomean (critical-production model) was studied, assuming that plant flowering is controlled by the productive capacity of the plant (critical-production model, under the condition that plants forecast environmental conditions affecting matter production. Thus, we concluded that all three critical phenomena are various manifestation of the same critical-production principle. Then, using the model simulation, the reliability of each critical phenomenon for securing a given critical production was investigated in relation to the photosynthetic productivity of the habitat. The main predictions obtained from the simulation were as follows: 1) Only annual and biennial plants will show critical age phenomena, and most biennials will be facultative. 2) Among perennials, the critical initial size phenomenon will appear in low productive habitats, whereas in high productive habitats the critical switchover size phenomenon will be observed.     

The dynamics of the rec-system in variable environments: haploid selection in a cyclical two-state environment

The dynamics of a 3-locus infinite population with non-overlapping generations and panmixia was studied. Loci are di-allelic: two loci affect fitness under cyclical symmetric haploid selection while the third one is a modifier of recombination (rec-modifier). Selection favors alternatively haplotypes AB and ab or Ab and aB. It has been proven that under alternating selection (when period of selection consists of two generations) a dominant suppressor of recombination is displaced and the allele for non-zero recombination becomes fixed within the population. For populations with inversion heterozygosity within the selective system (i.e. with zero recombination in heterozygote for rec-modifier and non-zero for homozygotes) fixation of one of the alleles (depending on the initial point) at the rec-modifier locus is predicted. For other values of recombination parameters, the behavior of the system was studied numerically. A full bifurcation picture of parameters was obtained. Many of the results related to the case of a two-generation period hold also in the case of longer period lengths.     

The effects of a fluctuating environment on the water relations of larval Lepidoptera

Abstract. New techniques for haemolymph analysis under field conditions have permitted studies of short-term changes in the body fluid concentrations of insects, in association with ambient conditions.
The haemolymph of four species of caterpillar changes in relation to the prevailing relative humidity, but the magnitude of these changes was correlated with the degree of exposure to the environment characteristic of each species and instar. In larvae habitually fully exposed to ambient conditions, haemolymph concentrations normally changed predictably through a day in relation to the humidity. However, osmoregulatory mechanisms operated to keep the increments in osmolality within acceptable limits. For those larvae which inhabit protected microenvironments with constant high humidity, either in association with plants or in conspecific aggregations, ambient humidity had little effect on the blood when this was sampled in situ. But when removed from such habitats, blood osmolality increases were large and rapid, and the larvae often succumbed to desiccation.
The role of biochemical, physiological, behavioural and ecological strategies in establishing the water balance of an insect in its natural surroundings are considered in the light of these findings.     

Tracking a fluctuating environment: a study of sampling

The problem of how animals keep track of unpredictable changes in the profitability of foraging sites was studied. An optimality model was used to predict the frequency with which a forager should sample a foraging site in which the probability of reward fluctuates randomly between high and low. The alternative foraging site is stable and offers an intermediate probability of reward. The model was tested with pigeons in a shuttle-box the two ends of which represented the two foraging sites. The pigeons succeeded in tracking the changes in the fluctuating site and the payoff attained was close to the optimum. Variations in the frequency of sampling between experimental treatments were in qualitative agreement with the model for some treatments but not others. The quantitative details of sampling behaviour were not as predicted by the optimality model, but many features could be accounted for by a mechanistic model of choice. The pigeons' choice rule, although different from that of the optimality model, is one that produces near-optimal payoffs under the conditions of this experiment.     

Evolution of phenotypic plasticity and environmental tolerance of a labile quantitative character in a fluctuating environment

Quantitative genetic models of evolution of phenotypic plasticity are used to derive environmental tolerance curves for a population in a changing environment, providing a theoretical foundation for integrating physiological and community ecology with evolutionary genetics of plasticity and norms of reaction. Plasticity is modelled for a labile quantitative character undergoing continuous reversible development and selection in a fluctuating environment. If there is no cost of plasticity, a labile character evolves expected plasticity equalling the slope of the optimal phenotype as a function of the environment. This contrasts with previous theory for plasticity influenced by the environment at a critical stage of early development determining a constant adult phenotype on which selection acts, for which the expected plasticity is reduced by the environmental predictability over the discrete time lag between development and selection. With a cost of plasticity in a labile character, the expected plasticity depends on the cost and on the environmental variance and predictability averaged over the continuous developmental time lag. Environmental tolerance curves derived from this model confirm traditional assumptions in physiological ecology and provide new insights. Tolerance curve width increases with larger environmental variance, but can only evolve within a limited range. The strength of the trade‐off between tolerance curve height and width depends on the cost of plasticity. Asymmetric tolerance curves caused by male sterility at high temperature are illustrated. A simple condition is given for a large transient increase in plasticity and tolerance curve width following a sudden change in average environment.     

Advantage of storage in a fluctuating environment

We will elaborate the evolutionary course of an ecosystem consisting of a population in a chemostat environment with periodically fluctuating nutrient supply. The organisms that make up the population consist of structural biomass and energy storage compartments. In a constant chemostat environment a species without energy storage always out-competes a species with energy reserves. This hinders evolution of species with storage from those without storage. Using the adaptive dynamics approach for non-equilibrium ecological systems we will show that in a fluctuating environment there are multiple stable evolutionary singular strategies (ss's): one for a species without, and one for a species with energy storage. The evolutionary end-point depends on the initial evolutionary state. We will formulate the invasion fitness in terms of Floquet multipliers for the oscillating non-autonomous system. Bifurcation theory is used to study points where due to evolutionary development by mutational steps, the long-term dynamics of the ecological system changes qualitatively. To that end, at the ecological time scale, the trait value at which invasion of a mutant into a resident population becomes possible can be calculated using numerical bifurcation analysis where the trait is used as the free parameter, because it is just a bifurcation point. In a constant environment there is a unique stable equilibrium for one species following the "competitive exclusion" principle. In contrast, due to the oscillatory dynamics on the ecological time scale two species may coexist. That is, non-equilibrium dynamics enhances biodiversity. However, we will show that this coexistence is not stable on the evolutionary time scale and always one single species survives.     

Advantage of storage in a fluctuating environment

We will elaborate the evolutionary course of an ecosystem consisting of a population in a chemostat environment with periodically fluctuating nutrient supply. The organisms that make up the population consist of structural biomass and energy storage compartments. In a constant chemostat environment a species without energy storage always out-competes a species with energy reserves. This hinders evolution of species with storage from those without storage. Using the adaptive dynamics approach for non-equilibrium ecological systems we will show that in a fluctuating environment there are multiple stable evolutionary singular strategies (ss's): one for a species without, and one for a species with energy storage. The evolutionary end-point depends on the initial evolutionary state. We will formulate the invasion fitness in terms of Floquet multipliers for the oscillating non-autonomous system. Bifurcation theory is used to study points where due to evolutionary development by mutational steps, the long-term dynamics of the ecological system changes qualitatively. To that end, at the ecological time scale, the trait value at which invasion of a mutant into a resident population becomes possible can be calculated using numerical bifurcation analysis where the trait is used as the free parameter, because it is just a bifurcation point. In a constant environment there is a unique stable equilibrium for one species following the “competitive exclusion” principle. In contrast, due to the oscillatory dynamics on the ecological time scale two species may coexist. That is, non-equilibrium dynamics enhances biodiversity. However, we will show that this coexistence is not stable on the evolutionary time scale and always one single species survives.     

Population models in a periodically fluctuating environment

Summary We investigate the behavior of population models in the presence of a periodically fluctuating environment. We consider in particular single-species models and models of interspecific competition. It is shown that the fluctuations cause constant equilibrium states to be replaced by periodic equilibrium states, with a shift in the mean value relative to the constant-environment state. It is shown also that the locations of points of exchange of stability may be changed as a result of the fluctuations.     

Gene selection: a Bayesian variable selection approach

Selection of significant genes via expression patterns is an important problem in microarray experiments. Owing to small sample size and the large number of variables (genes), the selection process can be unstable. This paper proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables to specialize the model to a regression setting and uses a Bayesian mixture prior to perform the variable selection. We control the size of the model by assigning a prior distribution over the dimension (number of significant genes) of the model. The posterior distributions of the parameters are not in explicit form and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the parameters from the posteriors. The Bayesian model is flexible enough to identify significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays where the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify a set of significant genes. The method is also applied successfully to the leukemia data. SUPPLEMENTARY INFORMATION: http://stat.tamu.edu/people/faculty/bmallick.html.     

Evolution of learning in fluctuating environments: when selection favors both social and exploratory individual learning

Cumulative cultural change requires organisms that are capable of both exploratory individual learning and faithful social learning. In our model, an organism's phenotype is initially determined innately (by its genotypic value) or by social learning (copying a phenotype from the parental generation), and then may or may not be modified by individual learning (exploration around the initial phenotype). The environment alternates periodically between two states, each defined as a certain range of phenotypes that can survive. These states may overlap, in which case the same phenotype can survive in both states, or they may not. We find that a joint social and exploratory individual learning strategy-the strategy that supports cumulative culture-is likely to spread when the environmental states do not overlap. In particular, when the environmental states are contiguous and mutation is allowed among the genotypic values, this strategy will spread in either moderately or highly stable environments, depending on the exact nature of the individual learning applied. On the other hand, natural selection often favors a social learning strategy without exploration when the environmental states overlap. We find only partial support for the "consensus" view, which holds that individual learning, social learning, and innate determination of behavior will evolve at short, intermediate, and long environmental periodicities, respectively.     

Evolution of altruism under group selection in large and small populations in fluctuating environments

A continuous, graded form of group selection which does not involve extinction of demes can effectively oppose selection on the individual level against an altruistic allele under fluctuating environments in infinitely large demes among which uniform mixing occurs every generation. Although group selection cannot alter the conditions necessary for the initial increase of altruistic alleles, group selection can significantly influence the stationary distribution of gene frequency which is attained once stochastic forces have allowed theirintroduction. Drift is a more effective source of variation than fluctuations in selection when the variance in selection is moderate to small. High numbers of demes promote polymorphism under both graded group selection and extinction group selection.     

Rainfall and flowering synchrony in a tropical shrub: Variable selection on the flowering time ofErythroxylum havanense

Summary We tested the adaptive significance of flowering synchrony by means of a quantitative analysis of selection and by flowering induction experiments with the deciduous shrubErythroxylum havanense. Temporal schedules of flower and fruit production were determined for a local population (in three sites) in a Mexican seasonal forest for 2 years (1987–1988). The consequences of natural variation in flowering time (flowering initiation day) on maternal reproductive success (fecundity) were evaluated. We observed high levels of inter- and intraindividual flowering synchrony in 1987, but not in 1988 and this contrast was related to differences in rainfall patterns between the two years. A significant proportion (15.4%) of the phenotypic variation in flowering initiation day was accounted for by environmental variance. The expression of phenotypic variance of flowering time and, consequently, the opportunity for selection to act, are controlled by annual variation in rainfall. Despite the between-year difference in flowering synchrony, we detected a relatively intense directional selection on flowering initiation day in both years, but selection coefficients were of opposite sign (standardized directional gradients were –0.326 and 0.333 for 1987 and 1988, respectively). For both years there was a significant relationship between individual relative fitness and the number of neighbouring flowering plants in a given day, suggesting positive frequency-dependent selection.     

Maintaining heritable variation via sex-limited temporally fluctuating selection: a phenotypic model accommodating non-Mendelian epigenetic effects

Using a phenotypic model, we show that significant heritable variation can be maintained in a population subjected to temporally fluctuating selection if only one sex is subject to selection. In fact, more variation is maintained with sex-limited selection at a given selection intensity than if both sexes are subject to half that selection intensity. This result is commensurate with existing population genetic models. However, genetic models may be inappropriate for sexually selected traits because many of them may be of non-genetic origin, such as maternal effects or – more likely –epigenetic effects. Phenotypic models obviate this problem by accommodating both genetic and epigenetic effects, as well as maternaleffects. Our phenotypic model of sex-limited temporally fluctuating selection shows that substantial heritable variation can be maintained and therebyprovides impetus to develop population epigenetic models.