Models of speciation by sexual selection on polygenic traits

The joint evolution of female mating preferences and secondary sexual characters of males is modeled for polygamous species in which males provide only genetic material to the next generation and females have many potential mates to choose among. Despite stabilizing natural selection on males, various types of mating preferences may create a runaway process in which the outcome of phenotypic evolution depends critically on the genetic variation parameters and initial conditions of a population. Even in the absence of genetic instability, rapid evolution can result from an interaction of natural and sexual selection with random genetic drift along lines of equilibria. The models elucidate genetic mechanisms that can initiate or contribute to rapid speciation by sexual isolation and divergence of secondary sexual characters.

Genetics and demography in biological conservation

Predicting the extinction of single populations or species requires ecological and evolutionary information. Primary demographic factors affecting population dynamics include social structure, life history variation caused by environmental fluctuation, dispersal in spatially heterogeneous environments, and local extinction and colonization. In small populations, inbreeding can greatly reduce the average individual fitness, and loss of genetic variability from random genetic drift can diminish future adaptability to a changing environment. Theory and empirical examples suggest that demography is usually of more immediate importance than population genetics in determining the minimum viable sizes of wild populations. The practical need in biological conservation for understanding the interaction of demographic and genetic factors in extinction may provide a focus for fundamental advances at the interface of ecology and evolution.

Efficiency of marker-assisted selection in the improvement of quantitative traits

Molecular genetics can be integrated with traditional methods of artificial selection on phenotypes by applying marker-assisted selection (MAS). We derive selection indices that maximize the rate of improvement in quantitative characters under different schemes of MAS combining information on molecular genetic polymorphisms (marker loci) with data on phenotypic variation among individuals (and their relatives). We also analyze statistical limitations on the efficiency of MAS, including the detectability of associations between marker loci and quantitative trait loci, and sampling errors in estimating the weighting coefficients in the selection index. The efficiency of artificial selection can be increased substantially using MAS following hybridization of selected lines. This requires initially scoring genotypes at a few hundred molecular marker loci, as well as phenotypic traits, on a few hundred to a few thousand individuals; the number of marker loci scored can be greatly reduced in later generations. The increase in selection efficiency from the use of marker loci, and the sample sizes necessary to achieve them, depend on the genetic parameters and the selection scheme.

The maintenance of genetic variability by mutation in a polygenic character with linked loci

It is assumed that a character under stabilizing selection is determined genetically bynlinked, mutable loci with additive effects and a range of many possible allelic effects at each locus. A general qualitative feature of such systems is that the genetic variance for the character is independent of the linkage map of the loci, provided linkage is not very tight. A particular detailed model shows that certain aspects of the genetic system are moulded by stabilizing selection while others are selectively neutral. With reference to experimental data on characters ofDrosophilaflies, maize, and mice, it is concluded that large amounts of genetic variation can be maintained by mutation in polygenic characters even when there is strong stabilizing selection. The properties of the model are compared with those of heterotic models with linked loci.

THE GENETIC COVARIANCE BETWEEN CHARACTERS MAINTAINED BY PLEIOTROPIC MUTATIONS

A statistical genetic model of a multivariate phenotype i s derived to investigate the covariation of pleiotropic mutations with additive effects under the combined action of phenotypic selection, linkage and the mating system. Equilibrium formulas for large, randomly mating populations demonstrate that, when selection on polygenic variation is much smaller than twice the harmonic mean recombination rate between loci with interacting fitnesses, linkage disequilibrium is negligible and pleiotropy is the main cause of genetic correlations between characters. Under these conditions, approximate expressions of or the dynamics of the genetic covariances due to pleiotropic mutations are obtained. Patterns of genetic covariance between characters and their evolution are discussed with reference to data on polygenic mutation, chromosomal organization and morphological integration.

The minimum number of genes contributing to quantitative variation between and within populations

A procedure is outlined for estimating the minimum number of freely segregating genetic factors, nE, contributing to the difference in a quantitative character between two populations that have diverged by artificial or natural selection. If certain simple criteria are satisfied approximately on an appropriate scale of measurement, nE can be estimated by comparing the phenotypic means and variances in the two parental populations and in their F1 and F2 hybrids (and backcrosses). This generalizes the method of Wright to genetically heterogeneous (or wild) parental populations, as well as inbred lines. Standard errors of the estimates are derived for large samples. The minimum number of genes involved in producing a large difference between populations in a quantitative trait is typically estimated to be about 5 or 10, with occasional values up to 20. This strongly supports the neo-Darwinian theory that large evolutionary changes usually occur by the accumulation of multiple genetic factors with relatively small effects.

Demographic models of the northern spotted owl (Strix occidentalis caurina)

Calassical demographic methods applied to life history data on the northern spotted owl yield and estimate of the annual geometric rate of increase for the population of λ=0.96±0.03, which is not significantly different from that for a stable population (λ=1.00). Sensitivity analysis indicates that adult annual survivorship has by far the largest influence on λ, followed by the probability that juveniles survive dispersal, and the adult annual fecundity. Substantial temporal fluctuations in demographic parameters have little effect on the long-run growth rate of the population because of the long adult life expectancy. A model of dispersal and territory occupancy that assumes demographic equilibrium is evaluated using data on the amount of old forest habitat remaining in the Pacific Northwest and the current occupancy of this habitat by northern spotted owls. This model is employed to predict the effect of future habitat loss and fragmentation on the population, implying that extinction will result if the old forest is reduced to less than a proportion 0.21±0.02 of the total area in a large region. The estimated minimum habitat requirement for the population is greater than that allowed in management plants by the USDA Forest Service.

Evolution of genetic variability in a spatially heterogeneous environment: effects of genotype-environment interaction

Classical population genetic models show that disruptive selection in a spatially variable environment can maintain genetic variation. We present quantitative genetic models for the effects of disruptive selection between environments on the genetic covariance structure of a polygenic trait. Our models suggest that disruptive selection usually does not alter the equilibrium genetic variance, although transient changes are predicted. We view a quantitative character as a set ofcharacter states, each expressed in one environment. The genetic correlation between character states expressed in different environments strongly affects the evolution of the genetic variability. (1) If the genetic correlation between character states is not ± 1, then the mean phenotype expressed in each environment will eventually attain the optimum value for that environment; this is the evolution of phenotypic plasticity (Via & Lande, 1985). At the joint phenotypic optimum, there is no disruptive selection between environments and thus no increase in the equilibrium genetic variability over that maintained by a balance between mutation and stabilizing selection within each environment. (2) If, however, the genetic correlation between character states is ± 1, the mean phenotype will not evolve to the joint phenotypic optimum and a persistent force of disruptive selection between environments will increase the equilibrium genetic variance. (3) Numerical analyses of the dynamic equations indicate that the mean phenotype can usually be perturbed several phenotypic standard deviations from the optimum without producing transient changes of more than a few per cent in the genetic variances or correlations. It may thus be reasonable to assume a roughly constant covariance structure during phenotypic evolution unless genetic correlations among character states are extremely high or populations are frequently perturbed. (4) Transient changes in the genetic correlations between character states resulting from disruptive selection act to constrain the evolution of the mean phenotype rather than to facilitate it.

Chiasma interference as a function of genetic distance

For many organisms, meiotic double crossing over is less frequent than expected on the assumption that exchanges occur at random with respect to each other. This "interference," which can be almost total for nearby intervals, diminishes as the intervals in which the double crossovers are scored are moved farther apart. Most models for interference have assumed, at least implicitly, that the intensity of interference depends inversely on the physical distance separating the intervals. However, several observations suggest that interference depends on genetic distance (Morgans) rather than physical distance (base pairs or micrometers). Accordingly, we devise a model in which interference is related directly to genetic distance. Its central feature is that recombinational intermediates (C's) have two fates--they can be resolved with crossing over (Cx) or without (Co). We suppose that C's are distributed at random with respect to each other (no interference); interference results from constraints on the resolution of C's. The basic constraint is that each pair of neighboring Cx's must have between them a certain number of Co's. The required number of intervening Co's for a given organism or chromosome is estimated from the fraction of gene conversions that are unaccompanied by crossover of flanking markers. The predictions of the model are compared with data from Drosophila and Neurospora.

Vaccine- and antigen-dependent type 1 and type 2 cytokine induction after primary vaccination of infants with whole-cell or acellular pertussis vaccines

Cytokine profiles were examined 1 month after primary vaccination of infants with a whole-cell pertussis vaccine (wP) (Connaught) or either of two acellular pertussis vaccines, aP-Chiron Biocine (aP-CB) or aP-SmithKline Beecham (aP-SB), each combined with diphtheria-tetanus toxoids (DT), in Bordetella pertussis antigen-stimulated or unstimulated peripheral blood mononuclear cells (PBMC). Pertussis toxin (PT), filamentous hemagglutinin (FHA), and pertactin (PRN) were used as antigens, and the children were defined as responsive when their PBMC proliferated in response to these antigens. The controls were either children who received only DT or children who received pertussis vaccine but whose PBMC did not proliferate upon stimulation with B. pertussis antigens (unresponsive children). Antigen-stimulated PBMC of responsive wP recipients were characterized by an elevated production of T-helper-cell type 1 cytokines gamma interferon (IFN-gamma) and interleukin 2 (IL-2), low to minimal production of IL-5, and no production of IL-4. The PBMC of aP vaccine-responsive recipients showed, in addition to the elevated IFN-gamma production, a consistent, antigen-dependent production of type 2 cytokines (IL-4 and IL-5), with PRN being the most and PT being the least effective antigen. Type 2 cytokine induction was more pronounced in aP-SB than in aP-CB recipients, as shown by the presence of IL-4 mRNA transcripts and higher IL-5 production in the former (161.6 +/- 36 and 47.9 +/- 44 pg/ml [mean +/- standard error for five subjects each], respectively, after PRN stimulation). Appreciable, antigen-unstimulated (constitutive) IFN-gamma production was also detected in PBMC cultures of all vaccinees. However, this spontaneous IFN-gamma production was, in most vaccinees, significantly lower than the antigen-driven cytokine production. In contrast, no constitutive type 2 cytokine production was ever observed in any vaccine group. PBMC from the two control groups (either DT or pertussis vaccine recipients) did not show any type 2 cytokine production, while IFN-gamma production was comparable in both antigen-stimulated and unstimulated conditions. Absence of type 2 cytokines and low levels of constitutive IFN-gamma production were also seen in prevaccination children. Thus, pertussis vaccines induce in infants a basically type 1 cytokine profile, which is, however, accompanied by some production of type 2 cytokines. The latter are more expressed by aP-SB than by aP-CB recipients, and with PRN than with other antigens, and they are minimally expressed in wP recipients and with PT as antigen. Our data also highlight a constitutive IFN-gamma production in infancy, which might reflect natural immunization and/or the burden of concomitant vaccinations and which may have an impact on T-helper-cell cytokine pattern polarization consequent to pertussis vaccination.

The fixation of chromosomal rearrangements in a subdivided population with local extinction and colonization

The fixation of major chromosomal rearrangements with a heterozygote disadvantage is modelled as a simple example of Wright's shifting balance process of evolution in a strongly subdivided population. Chromosomal mutations with an inferior heterozygote become fixed in a local population (or deme) by random genetic drift and spread by migration and colonization. Wright postulated a process of selective diffusion in which the numbers of emigrants and colonizers dispersed from a deme increase with the mean fitness of individuals in it. The present models show that interdeme selection during the spread of a mutation depends more on the capacity of the mutant to invade and become established in other demes than on selective diffusion, unless there is rapid local extinction and colonization. The intensity of interdeme selection is reduced by random local extinction and colonization, and when these processes are rapid (with no selective diffusion) the expected fixation rate of spontaneous mutations with a heterozygote disadvantage approaches that in a single isolated deme. Local extinction and colonization, and selection on the homozygotes, accelerate the spread of chromosomal mutations which are destined to be fixed.

Evolution of mating preference and sexual dimorphism

A quantitative genetic model of the joint evolution of female mating preferences and sexual dimorphism in homologous characters of the sexes is described for polygamous species with no male parental effort, such that mating preferences are selectively neutral and evolve only by indirect selection on genetically correlated characters. The male character and the homologous female character are each under stabilizing natural selection toward an optimum phenotype. At an evolutionary equilibrium the female character under natural selection is at its optimum, whereas there is a line of possible equilibria between female mating preferences and the male character. The line of equilibria may be stable or unstable, depending on the intensity of natural selection, the type of mating preferences, and the inheritance of the characters. Various mechanisms for maladaptive evolution of mating preferences and sexual dimorphism are discussed.

The evolution of self-fertilization and inbreeding depression under pollen discounting and pollen limitation

We model the evolution of plant mating systems under the joint effects of pollen discounting and pollen limitation, using a dynamic model of inbreeding depression, allowing for partial purging of recessive lethal mutations by selfing. Stable mixed mating systems occur for a wide range of parameter values with pollen discounting alone. However, when typical levels of pollen limitation are combined with pollen discounting, stable selfing rates are always high but less than 1 (0.9<s<1 in most cases); in this situation, complete selfing does not evolve because pollen discounting becomes very large at high selfing rates, so that the automatic advantage of selfing changes to a disadvantage. These results suggest that mixed mating systems with high selfing rates can be maintained by selection, whereas mixed mating systems with low to moderate selfing rates are more likely attributable to unavoidable geitonogamous selfing.

Extinction dynamics of age-structured populations in a fluctuating environment

We model density-independent growth of an age- (or stage-) structured population, assuming that mortality and reproductive rates fluctuate as stationary time series. Analytical formulas are derived for the distribution of time to extinction and the cumulative probability of extinction before a certain time, which are determined by the initial age distribution, and by the infinitesimal mean and variance, mu and sigma 2, of a diffusion approximation for the logarithm of total population size. These parameters can be estimated from the average life history and the pattern of environmental fluctuations in the vital rates. We also show that the distribution of time to extinction (conditional on the event) depends on the magnitude but not the sign of mu. When the environmental fluctuations in vital rates are small or moderate, the diffusion approximation gives accurate estimates of cumulative extinction probabilities obtained from computer simulations.

The genetic correlation between characters maintained by selection, linkage and inbreeding

Mutation is modelled in two quantitative characters under separate genetic control in a large population. A bivariate pattern of selection acts to correlate the characters and, without pleiotropy, their genetic correlation is due entirely to linkage disequilibrium. Data on spontaneous mutation, the effective number of genes, and the intensity of natural selection on quantitative characters are used to evaluate the models. It is concluded that, even when selection favors a high correlation between the characters, with random mating and no linkage between loci influencing different traits the genetic correlation between characters is likely to be small in magnitude. A genetic correlation of large magnitude can be maintained only if the loci influencing different characters are tightly linked, or there is a high level of inbreeding in the population created by frequent mating between closely related individuals.

Expected time for random genetic drift of a population between stable phenotypic states

Natural selection and random genetic drift are modeled by using diffusion equations for the mean phenotype of a quantitative (polygenic) character in a finite population with two available adaptive zones or ecological niches. When there is appreciable selection, the population is likely to spend a very long time drifting around the peak in its original adaptive zone. With the mean phenotype initially anywhere near the local optimum, the expected time until a shift between phenotypic adaptive peaks increases approximately exponentially with the effective population size. In comparison, the expected duration of intermediate forms in the actual transition between adaptive peaks is extremely short, generally below the level of resolution in the fossil record, and increases approximately logarithmically with the effective population size. The evolutionary dynamics of this model conform to the pattern of current paleontological concepts of morphological "stasis" and "punctuated equilibria."

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.

Population dynamic models generating the lognormal species abundance distribution

This paper deals with a new class of stochastic species abundance models where the abundances are the points of an inhomogeneous Poisson process. These models are the result of a dynamic approach in which the changes in abundances through time are described by a multivariate diffusion and speciation constitutes a homogeneous Poisson process. In particular, the lognormal model is generated by assuming that the density regulation within each species is given by the Gompertz curve and that the environmental variances are constant. A substantial generalization is obtained by introducing a general type of interspecific density regulation and correlated environmental noise. This more general mechanism also generates the lognormal species abundance distribution.

Mitochondrial DNA variation, phylogeography and population structure of the Asian elephant

We report the first genetic analysis of free-ranging Asian elephants (Elephas maximus). We sampled 118 elephants from Sri Lanka, Bhutan/North India, and Laos/Vietnam by extracting DNA from dung, PCR amplifying and sequencing 630 nucleotides of mitochondrial DNA, including part of the variable left domain of the control region. Comparison with African elephant (Loxodonta africana) sequences indicated a relatively slow molecular clock in the Proboscidea with a sequence divergence of approximately 1%/Myr. Genetic diversity within Asian elephants was low, suggesting a small long-term effective population size. Seventeen haplotypes were identified within Asian elephants, which clustered into two well-differentiated assemblages with an estimated Pliocene divergence of 2.5-3.5 million years ago. The two assemblages showed incomplete geographical partitioning, suggesting allopatric divergence and secondary admixture. On the mainland, little genetic differentiation was observed between elephant populations of Bhutan and India or Laos and Vietnam. A significant difference in haplotype frequencies but relatively weak subdivision was observed between the regions Bhutan-India and Laos-Vietnam. Significant genetic differentiation was observed between the mainland and Sri Lanka, and between northern, mid-latitude and southern regions in Sri Lanka.

Ecological speciation by sexual selection

Quantitative genetic models are used to investigate a mechanism of speciation involving natural and sexual selection on a population with more than one ecological niche available. Female choice of mates, based on ecologically important characters, can initiate a sudden shift into a new niche. Whether males alone or both sexes make the transition depends strongly on the genetic correlation between homologous male and female characters. This mode of speciation rapidly produces premating and postmating isolating barriers, as well as ecological separation, between populations that can then coexist in the same area as distinct species.

Estimating density dependence from population time series using demographic theory and life-history data

For populations with a density-dependent life history reproducing at discrete annual intervals, we analyze small or moderate fluctuations in population size around a stable equilibrium, which is applicable to many vertebrate populations. Using a life history having age at maturity alpha, with stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time lags from 1 to alpha yr. Contrary to current interpretations, the coefficients corresponding to different time lags in the autoregressive dynamics are not simply measures of delayed density dependence but also depend on life-history parameters. The theory indicates that the total density dependence in a life history, D, should be defined as the negative elasticity of population growth rate per generation with respect to change in population size, [Formula: see text], where lambda is the asymptotic multiplicative growth rate per year, T is the generation time, and N is adult population size. The total density dependence in the life history, D, can be estimated from the sum of the autoregression coefficients. We estimate D in populations of seven vertebrate species for which life-history studies and unusually long time series of complete population censuses are available. Estimates of D were statistically significant and large, on the order of 1 or higher, indicating strong density dependence in five of the seven species. We also show that life history can explain the qualitative features of population autocorrelation functions and power spectra and observations of increasing empirical variance in population size with increasing length of time series.

Cell-mediated immune responses in four-year-old children after primary immunization with acellular pertussis vaccines

Cell-mediated immune (CMI) responses to Bordetella pertussis antigens (pertussis toxin [PT], pertactin [PRN], and filamentous hemagglutinin [FHA]) were assessed in 48-month-old recipients of acellular pertussis [aP] vaccines (either from Chiron-Biocine [aP-CB] or from SmithKline Beecham [aP-SB]) and compared to CMI responses to the same antigens at 7 months of age, i.e., 1 month after completion of the primary immunization cycle. None of the children enrolled in this study received any booster of pertussis vaccines or was affected by pertussis during the whole follow-up period. Overall, around 75% of 4-year-old children showed a CMI-positive response to at least one B. pertussis antigen, independently of the type of aP vaccine received, and the proportion of CMI responders were at least equal at 48 and 7 months of age. However, longitudinal examination of individual responses showed that from 20 (against PT) to 37% (against FHA) of CMI responders after primary immunization became negative at 48 months of age. This loss was more than compensated for by conversion to positive CMI responses, ranging from 36% against FHA to 69% against PRN, in other children who were CMI negative at 7 months of age. In 60 to 80% of these CMI converters, a lack of decline or even marked elevation of antibody (Ab) titers against B. pertussis antigens also occurred between 20 and 48 months of age. In particular, the frequency of seropositivity to PRN and FHA (but not to PT) was roughly three times higher in CMI converters than in nonconverters. The acquisition of CMI response to B. pertussis antigens in 48-month-old children was not associated with a greater frequency of coughing episodes lasting >/=7 days and was characterized by a prevalent type 1 cytokine profile, with high gamma interferon and low or no production of interleukin-5, reminiscent of cytokine patterns following immunization with whole-cell pertussis vaccine or natural infection. Our data imply that vaccination-induced systemic CMI may wane by 4 years of age but may be acquired or naturally boosted by symptomless or minor clinical infection by B. pertussis. This might explain, at least in part, the persistence of protection against typical pertussis in aP vaccine recipients despite a substantial waning of both Ab and CMI responses induced by the primary immunization.

On the distribution of the mean and variance of a quantitative trait under mutation-selection-drift balance

The distributions of the mean phenotype and of the genetic variance of a polygenic trait under a balance between mutation, stabilizing selection and genetic drift are investigated. This is done by stochastic simulations in which each individual and each gene are represented. The results are compared with theoretical predictions. Some aspects of the existing theories for the evolution of quantitative traits are discussed. The maintenance of genetic variance and the average dynamics of phenotypic evolution in finite populations (with Ne < 1000) are generally simpler than those suggested by some recent deterministic theories for infinite populations.

Cell-mediated immunity and antibody responses to Bordetella pertussis antigens in children with a history of pertussis infection and in recipients of an acellular pertussis vaccine

Cell-mediated immunity (CMI) and antibody responses to Bordetella pertussis antigens were assessed 4-6 years after primary infant immunization with diphtheria-tetanus tricomponent acellular pertussis (DTaP) or diphtheria-tetanus (DT) vaccine in a country with high endemicity of B. pertussis infection. CMI to the B. pertussis antigens (especially to the pertussis toxin [PT]) was more frequent and/or intense in DTaP than in DT recipients. No lymphoproliferation differences were found between those with and without a history of pertussis although the DT recipients produced very little interferon-gamma after antigen (particularly PT and filamentous hemagglutinin [FHA]) stimulation. In contrast, seropositivity to PT, but not to pertactin or FHA, was more frequent in DT recipients with history of pertussis than in all other subjects. Thus, years after disease or vaccination, CMI response to PT or circulating PT antibodies appears to be the main distinctive feature of pertussis-protected DTaP recipients or pertussis-affected DT recipients.