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.     

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.     

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.     

An uncertain life: demography in random environments

This paper concisely reviews the demography of populations with random vital rates, highlights examples and techniques which yield insight into population dynamics, summarizes the state of significant applications of the theory, and points to open problems. The central picture in this theory is of a time-varying but statistically stationary equilibrium for population, sharply distinct from the notions of classical demography. The deepest biological insights from the theory reveal the temporal structure of life histories to be a rich arena for natural selection.     

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.     

Polymorphism maintenance in populations with mixed random mating and apomixis subjected to stabilizing and cyclical selection

We analysed a diploid population model with a mixed breeding system that includes panmixia and apomixis. Each individual produces a part (ss) of its progeny by random mating, the remainder (1-ss) being a result of precise copying (vegetative reproduction or apomixis) of the parental genotype. Both constant and periodically varying selection regimes were considered. In the main model, the selected trait was controlled by two diallelic additive or semidominant loci, A/a and B/b, whereas the parameter of breeding system (ss) was genotype-independent. A numerical iteration of the evolutionary equations were used to evaluate the proportion (V) of population trajectories converging to internal (polymorphic) fixed points. The results were the following. (a) A complex pattern of dependence of polymorphism stability on interaction among the breeding system, recombination rate, and the genetic architecture of the selected trait emerged. (b) The recombination provided some advantage to sex at intermediate period lengths and strong-to-moderate selection intensities. (c) The complex limiting behavior (CLB) was quite compatible with sexual reproduction, at least within the framework of pure genetic (not including variations in population density) models of multilocus varying selection.     

Polymorphism in heterogeneous environments,evolution of habitat selection and sympatric speciation: Soft and hard selection models

Summary The adaptation to a variable environment has been studied within soft and hard selection frameworks. It is shown that an epistatically determined habitat preference, following a Markovian process, always leads to the maintenance of an adaptive polymorphism, in a soft selection context. Although local mating does not alter the conditions for polymorphism maintenance, it is shown that, in that case, habitat selection also leads to the evolution of isolated reproductive units within each available habitat. Habitat selection, however, cannot evolve in the total absence of adaptive polymorphism. This represents a theoretical problem for all models assuming habitat selection to be an initially fixed trait, and means that within a soft selection framework, all the available habitats will be exploited, even the less favourable ones.On the other hand, polymorphism cannot be maintained when selection is hard, even when all individuals select their habitat. Here, the evolution of habitat selection does not need any prerequisite polymorphism, and always leads to the exploitation of only one habitat by the most specialized genotype. It appears then that hard selection can account for the existence of empty habitat and for an easier evolution of habitat specialization.     

Statistical properties of estimators for continuous time Markov branching processes with varying and random environments

Asymptotic properties are established for estimators of time dependent intensities in Markov branching processes with varying and random environments. For the varying environment model, the estimators are shown to be uniformly strongly consistent on bounded intervals as the initial population size X₀ → ∞, and, when considered as empirical stochastic processes, to converge weakly to Gaussian processes with independent increments. For random environments, the estimators are shown to be asymptotically normal as t → ∞, where t is the time parameter.     

Polymorphism in allergens

Allergens are antigens that elicit an IgE-mediated immune response; they originate from diverse sources such as pollens, mites, molds, mammal exudates, insects and food. Allergenic molecules can contain several antigenic determinants, termed epitopes. Allergenic proteins have been discovered with polymorphisms, i.e., a mixture of similar molecules with minor variations in their amino acid sequences. These are called isoallergens or allergenic variants depending on the degree of similarity. Polymorphism may be defined by the presence of several alleles of the same gene or as families of related genes. Polymorphisms can have an important effect on the epitopes recognized by T lymphocytes, monoclonal antibodies and IgE of allergic patients. Individual polymorphisms can affect the basal level of allergenicity as well as the cross-reactivity with other allergens. The use of isoforms with low or total absence of IgE binding capacity but with high capacity to stimulate T cell response has been suggested as an alternative to the conventional immunotherapy for allergic diseases. Standardization of allergenic compounds can be affected by the differing proportions of isoforms in allergenic sources from different regions.     

Polymorphism in Pomatoceros

Allelic variation at 13 sites for the intertidal Pomatoceros lamarckii (Quatrefages) and at six sites for the sublittoral P. triqueter (L.) in North-West Europe, when examined at 19 metabolic enzyme loci, showed significant differences between sites in the frequencies of the various enzyme morphs. There was no readily interpretable geographic or environmental trend. The Hardy-Weinberg equilibrium was maintained at almost all loci and all sites. The genetic distance between populations was very small in comparison with the difference between the two species.
Colour morphs of P. triqueter showed a clear latitudinal cline with blue and brown morphs predominating at more northerly latitudes, and grey, orange and red morphs at more southerly latitudes.
Interlocality variations in allele frequency, though statistically significant, were never sufficient to alter the order of frequency of the two or three commonest alleles, so that the frequency of all but rare alleles showed a consensus throughout the ranges studied for each species. Accounting for local genetic patchiness in gene frequencies in species with pelagic larvae raises problems if the alleles are selectively neutral; accounting for wide geographic uniformity raises problems if alleles are selected for or against by environmental factors.     

Polymorphism in myristoylpalmitoylphosphatidylcholine

This study focuses on the mixed-chain lipid myristoylpalmitoylphosphatidylcholine (MPPC) near full hydration. The lipid, synthesized according to the procedure of (Mason et al., 1981a, has a low degree of acyl chain migration. When MPPC is temperature-jumped (T-jumped) from the L alpha phase (T = 38 degrees C) to T = 20 degrees C or below, a subgel phase forms; this formation takes less than 1 h at a temperature below T = 12 degrees C. The subgel remains stable up to T = 29 degrees C. When MPPC is T-jumped from the L alpha phase to T = 24 degrees C or above, a ripple phase forms with coexisting ripple wavelengths of 240 A and 130 A. In contrast, when MPPC is melted from the subgel phase, the ripple phase is characterized by bilayers having a single ripple wavelength of 130 A. In agreement with earlier studies (Stumpel et al., 1983; Serrallach et al., 1984. Structure and thermotropic properties of mixed-chain phosphatidylcholine bilayer membranes. Biochemistry 23:713-720.), no stable gel phase was observed. Instead, an ill-defined low-angle X-ray pattern is initially observed, which gradually transforms into the subgel phase below 20 degrees C, or into the ripple phase above 24 degrees C. In the wide-angle X-ray diffraction, a single peak is observed, similar to the ripple phase wide-angle pattern, that either persists above 24 degrees C or transforms into a multi-peaked subgel wide-angle pattern below 20 degrees C. The absence of a gel phase can be understood phenomenologically as the relative dominance of the subgel phase in mixed-chain PCs compared to same-chain PCs. The subgel structure and molecular interactions responsible for this comparative behavior are interesting open issues.     

Polymorphism in mouse and human class I H-2 and HLA genes is not the result of random independent point mutations

Sufficient mouse H-2 and human HLA class I gene sequences have become available to make a statistical analysis of nucleotide variations within the multigene families possible. In the H-2 and HLA families, a group of four H-2K allelic sequences and three HLA-A sequences were compared with a group of four non-H-2 and three non-HLA-A sequences, respectively. Simple calculations show that nucleotide variations in each group do not occur in a random independent fashion. It is therefore possible that a number of mutations are concerted between the subgroups. Interestingly, these concerted mutations are clustered and distributed almost exclusively in the 5 end of H-2 and HLA genes, which is very rich in GC nucleotides, and where the dinucleotide CpG is particularly frequent. The general concept of unequal repair is proposed as the basis of a model which is supported by these observations.