田中 嘉成

A simplified ecosystem model, the Aquatic Tritrophic Ecological Risk Assessment Model (A‐TERAM), for the ecological risk assessment of chemicals is presented. The A‐TERAM comprises a linear grazer food chain with 3 trophic levels.

Here we developed an analytical means of estimating population-level effects of endocrine disruptors on Daphnia magna. Our approach was based on the fact that the endocrine-disrupting juvenile hormone analogs induce the production of male neonates if they are exposed to the analogs during a particular period in their prenatal development; the method also assumed that the abnormal production of male neonates in the sake of production of female neonates reduces population growth. We constructed a linear toxicodynamics model to elucidate the period in which D. magna neonates are sensitive to exposure to the analog and also the probability of an individual neonate changing sex under specific exposure concentrations. The proposed model was applied to D. magna reproduction test data obtained under time-varying exposure to pyriproxyfen to derive the maximum-likelihood estimates and the posterior distributions of the model parameters. To quantitatively assess the ecological risk at the population level, we conducted a population dynamics simulation under two time-varying exposure scenarios (i.e., constant or pulsed exposure) by using an age-structured population model. When the change in sex ratio was based on the time-weighted average concentration during the period of sensitivity, change in sex ratio caused approximately equivalent population-level effects as did reproductive inhibition (i.e., reduction in the total number of neonates per female parent) regardless of the exposure scenario. In contrast, when change in sex ratio was based on maximum concentration during the sensitive period, change in sex ratio caused only half the population-level effects as did reproductive inhibition under constant exposure, whereas it caused a much larger population-level effect than did reproductive inhibition under pulsed exposure.

Short-term pulsed exposure tests have been increasingly used to evaluate the ecotoxicity of pollutants of which concentrations vary over time in the field. In pulsed exposure, time-weighted average (TWA) concentration is often used as an index of exposure. However, there have been few studies to demonstrate whether TWA concentration can be used to evaluate the effect of endocrine-disrupting chemicals on the daphnids. Pyriproxyfen is one of the juvenile hormone analogs that induces daphnids to produce male offspring. To evaluate whether peak or TWA concentration can explain the effects of pyriproxyfen on daphnid reproduction, we measured the number of offspring and the proportion of male offspring produced by Daphnia magna during 21-day under different exposure treatments, constant, single-pulse, and multi-pulse exposure, at an equivalent TWA concentration. Constant exposure of 50 ng/L pyriproxyfen did not affect either the fecundity or the proportion of male offspring, while a single-pulse exposure of 525 ng/L pyriproxyfen over 2 day at four different age did not reduce fecundity, but the proportion of male offspring increased age dependently. Multi-pulses exposure of 131 ng/L pyriproxyfen over two days four times (total eight days) resulted in a decrease in fecundity and the highest proportion of male offspring. Daily observation demonstrated that male offspring was only produced several days after the exposure to a certain concentration of pyriproxyfen. Therefore, neither TWA nor peak concentration accurately evaluated the effects of pulsed exposure of pyriproxyfen on the reproduction of D. magna, particularly its effect on the proportion of male offspring.

This study examines the spatial difference in genetic variation for tolerance to a pesticide, fenitrothion, in Daphnia galeata at field sites in Lake Kasumigaura, Japan. We estimated genetic values of isofemale lines established from dormant eggs of D. galeata collected from field sampling sites with the toxicant threshold model applied using acute toxicity. We compared genetic values and variances and broad-sense heritability across different sites in the lake. Results showed that the mean tolerance values to fenitrothion did not differ spatially. The variance in genetic value and heritability of fenitrothion tolerance significantly differed between sampling sites, revealing that long-term ecological risk of fenitrothion may differ between local populations in the lake. These results have implications for aquatic toxicology research, suggesting that differences in genetic variation of tolerance to a chemical among local populations must be considered for understanding the long-term ecological risks of the chemical over a large geographic area.

Decisions in ecological risk management for chemical substances must be made based on incomplete information due to uncertainties. To protect the ecosystems from the adverse effect of chemicals, a precautionary approach is often taken. The precautionary approach, which is based on conservative assumptions about the risks of chemical substances, can be applied selecting management models and data. This approach can lead to an adequate margin of safety for ecosystems by reducing exposure to harmful substances, either by reducing the use of target chemicals or putting in place strict water quality criteria. However, the reduction of chemical use or effluent concentrations typically entails a financial burden. The cost effectiveness of the precautionary approach may be small. Hence, we need to develop a formulaic methodology in chemical risk management that can sufficiently protect ecosystems in a cost-effective way, even when we do not have sufficient information for chemical management. Information-gap decision theory can provide the formulaic methodology. Information-gap decision theory determines which action is the most robust to uncertainty by guaranteeing an acceptable outcome under the largest degree of uncertainty without requiring information about the extent of parameter uncertainty at the outset. In this paper, we illustrate the application of information-gap decision theory to derive a framework for setting effluent limits of pollutants for point sources under uncertainty. Our application incorporates a cost for reduction in pollutant emission and a cost to wildlife species affected by the pollutant. Our framework enables us to settle upon actions to deal with severe uncertainty in ecological risk management of chemicals. (C) 2013 Elsevier Ltd. All rights reserved.

We present a novel framework for estimating site-specific effects of pollutants on natural populations. Our method is based on fitness optimization and uses observed differences in tolerance (sensitivity) to a particular pollutant between populations at contaminated and uncontaminated sites (i.e., target and reference populations). In addition, the method uses laboratory estimates of the fitness cost of tolerance, that is, the reduction of population growth rate (fitness) of a target population compared to that of a reference population when both are maintained in uncontaminated conditions. As a case study, we applied this framework to analyze observed genetic differentiation in tolerance to the pyrethroid insecticide fenvalerate between Daphnia galeata populations in Lake Kasumigaura and an adjacent agricultural pond. The estimated exposure level at the contaminated site was about 0.015 mu g/L, and the population-level risk corresponded to about a 24 % reduction of the intrinsic rate of natural increase.

We compared predation by medaka, Oryzias latipes, on four age-classes of Daphnia pulex to examine the relationship between predation rate and prey body size. The number of individuals eaten by a medaka fish differed significantly among four size classes of D. pulex showing a humped relationship with increasing age classes. We found that the predation by medaka depended on prey body size and we discuss how size-specific predation by medaka can influence cladoceran populations.

A statistical genetics method is presented for estimating the genetic variance (heritability) of tolerance to pollutants on the basis of a standard acute toxicity test conducted on several isofemale lines of cladoceran species. To analyze the genetic variance of tolerance in the case when the response is measured as a few discrete states (quantal endpoints), the authors attempted to apply the threshold character model in quantitative genetics to the threshold model separately developed in ecotoxicology. The integrated threshold model (toxicant threshold model) assumes that the response of a particular individual occurs at a threshold toxicant concentration and that the individual tolerance characterized by the individual's threshold value is determined by genetic and environmental factors. As a case study, the heritability of tolerance to p-nonylphenol in the cladoceran species Daphnia galeata was estimated by using the maximum likelihood method and nested analysis of variance (ANOVA). Broad-sense heritability was estimated to be 0.199?+/-?0.112 by the maximum likelihood method and 0.184?+/-?0.089 by ANOVA; both results implied that the species examined had the potential to acquire tolerance to this substance by evolutionary change. Environ. Toxicol. Chem. 2012;31:813818. (c) 2012 SETAC

The response of ecological communities to environmental disturbances depends not just on the number of species they contain but also on the functional diversity of the constituent species; greater variation in the tolerance of species to different environmental disturbances is generally thought to confer greater resistance to the community. Here, I investigate how the functional diversity of communities changes with environmental disturbances. Specifically, I assume that there is variation in traits among species that confer tolerance or sensitivity to environmental disturbances. When a disturbance occurs, variation in species tolerances causes changes in the relative abundances of species, which in turn changes the average tolerance of the community. For example, if tolerance to an environmental disturbance is conferred by large body size, then the environmental disturbance should be expected to increase the average body size of individuals in the community. Despite this expectation, ecological interactions among species can affect the average community response. For example, if larger species are also strong competitors with each other, then this might reduce the increase in average body size in the community, because interspecific competition limits the grow in population density of large bodied species. Similarly, when disturbances affect multiple traits, the covariance in the distribution of trait values among species may restrict the response of any one trait; if two traits provide tolerance to the same disturbance but negatively covary among species, then the response of one trait will limit the response of the other trait at the community level. Using a Lotka-Volterra model for competitive communities, I derive general formulae that generate explicit predictions about the changes in average trait values in a community subject to environmental disturbances. These formulae demonstrate that competition can impede the change in average community trait values. However, the impediment is not considerable in comparison to the predominant factors of trait variances and species selection effects when species with the most similar trait values also experience the greatest interspecific competition. Similarly, negative covariances among different traits that confer resistance to the same environmental disturbance will impede their responses. I illustrate these results using phytoplankton data from a whole-lake experiment in which manipulation to the zooplankton community created a disturbance to the phytoplankton that changed the selective consumption of large vs. small phytoplankton.

Diaphanosoma brachyurum (Cladocera: Sididae) is a common limnetic species in summer-temperate and tropical water bodies. Few studies have investigated the sensitivity of D. brachyurum to toxic chemicals despite this species often being dominant in natural lakes and ponds. We performed acute toxicity tests of three heavy metals, copper (Cu), zinc (Zn), and cadmium (Cd), to D. brachyurum. For D. brachyurum, the lethal concentration (LC)(50) values of Cu (24-h LC50 = 16.4 mu g/L, 48-h LC50 = 10.4 mu g/L) and Zn (24-h LC50 = 253.4 mu g/L, 48-h LC50 = 174.1 mu g/L) were lower than those for D. magna, one of the most used test organisms for toxic chemicals. On the other hand, for D. brachyurum the 24-h LC50 of Cd (166.4 mu g/L) was much greater than that for D. magna, and the 48-h LC50 of Cd (69.8 mu g/L) was comparable. Our results indicate that D. brachyurum may be more strongly influenced by Zn and Cu than is D. magna. It is likely that the summer plankton community in which Diaphanosoma species is dominant is more sensitive to heavy metals than a community in which Daphnia species are dominant.

The sensitivities of seven cladoceran species (Ceriodaphnia reticulata, Chydorus sphaericus, Daphnia galeata, Diaphanosoma brachyurum, Moina macrocopa, Scapholeberis kingi, and Simocephalus vetulus) to carbamate insecticides (carbaryl and methomyl) were investigated by acute toxicity tests. The sensitivities to carbaryl and methomyl were highly correlated among the tested organisms, but the co-tolerance level varied markedly among species. C. reticulata showed the highest sensitivity, whereas M. macrocopa and S. kingi showed the lowest sensitivities to the two insecticides. These results indicate that the degree of chemical impacts on natural communities can vary depending on cladoceran species composition. The highly positive correlation between the EC(50) values for both insecticides indicates that the two chemicals have a shared mode of action on cladoceran species. Unlike previous reports, acute toxicity was not correlated with body size. The results are discussed in relation to community-level experiments, the functions of freshwater ecosystems, and ecological risk assessment.

Leptodora kindtii is a major predator of small zooplankton in eutrophic and fish-abundant lakes. However, as it is very difficult to culture in the laboratory, information about its sensitivity to pollutants is lacking. We have successfully established a laboratory clonal culture of Leptodora. In this study, acute toxicities of an insecticide and three heavy metals to Leptodora were estimated by using laboratory-cultured individuals. Our results suggest that Leptodora is more susceptible to contamination with those chemicals than the standard test organism, Daphnia.

Pleiotropic effects of deleterious mutations are considered to be among the factors responsible for genetic constraints on evolution by long-term directional selection acting on a quantitative trait. If pleiotropic phenotypic effects are biased in a particular direction, mutations generate apparent directional selection, which refers to the covariance between fitness and the trait owing to a linear association between the number of mutations possessed by individuals and the genotypic values of the trait. The present analysis has shown how the equilibrium mean value of the trait is determined by a balance between directional selection and biased pleiotropic mutations. Assuming that genes act additively both on the trait and on fitness, the total variance-standardized directional selection gradient was decomposed into apparent and true components. Experimental data on mutation bias from the bristle traits of Drosophila and life history traits of Daphnia suggest that apparent selection explains a small but significant fraction of directional selection pressure that is observed in nature; the data suggest that changes induced in a trait by biased pleiotropic mutation (i.e., by apparent directional selection) are easily compensated for by (true) directional selection.

Questions: Why can invasive species sometimes genetically contaminate closely related indigenous species by introgressive hybridization, resisting the post-zygotic isolating mechanism? Flow do recombination rates and epistasis among incompatibility genes, and the number of bet affect the introgression? Features of models: The individual-based model and gamete-based model. which tracks changes in the number of invasive genes per gamete due to selection and recombination by assuming random arrangement of genes within gamete Range of key variables: The recombination rate between adjacent loci ranges from 0 to 0.4 The epistatic effect between loci is measured by the exponent of the geometric function of heterozygosities representing individual fitness It ranges from 1 (additive) to 4 (strong epistasis) The number of loci is set to 2-10 for the gamete-based model Conclusions: Provided that the number of loci is not very small and the fitness of the F1 hybrid is not extremely low, complete genetic replacement by introgressive hybridization is accelerated by an increase in rates of total recombination across all loci and by the epistatic fitness effect among incompatibility loci

The spawning season of mantis shrimp Oratosquilla oratoria (Stomatopoda) in Tokyo Bay has changed from being unimodal (spring only) to bimodal (spring and summer). This shift in the pattern of spawning arose because reproductive maturation began to occur in smaller females, which presumably spawn in summer, and because the proportion of smaller mature females increased. Currently, recruitment appears to depend entirely on the summer cohort because of significantly lower juvenile survival in the spring cohort. In this study, we propose that the new summer spawning period and spawning by smaller-bodied individuals have supported the population. Our size- and age-structured mathematical model of O. oratoria population dynamics indicated that the number of eggs spawned in spring is lower than that in summer, and 98% of the annual recruitment is currently derived from summer spawning. The model also suggested that smaller-bodied spawners provided 84% of total recruitment and that if the proportion of smaller-bodied mature females had not increased, the population would have shown a larger decline than was observed. In reality, the stock size of O. oratoria has become extremely low, damaging the local fishery. Based on our model predictions, an efficient solution for population recovery is to reduce the mortality of small, unsalable individuals, which are currently fished and discarded.

We examined the relationship between individual-level and population-level effects of toxic chemicals, employing the equilibrium population size as an index of population-level effects. We first analyzed two-stage matrix models considering four life-history types and four density-dependent models, and then we analyzed ecotoxicological and life-history data of the fathead minnow (Pimephales promelas) and brook trout (Salvelinus fontinalis) as real examples. Our elasticity analysis showed that toxic impacts on density-dependent populations depended largely on the differences in density-dependence and in life histories of the organisms. In particular, the importance of adult survivability was considerably increased in iteroparous organisms with density-dependent juvenile survivability or fertility. Our results also suggested that population-level effects, as indicated by the percentage reduction in equilibrium population size, were often greater than the percentage reductions in vital rates of individuals. Our analysis indicates that assessing population-level risk and developing a risk-reduction strategy without considering density-dependence can be risky.

Pesticides often modify predatory interactions by enhancing (or inhibiting) the development of antipredator morphologies of freshwater cladocerans. In the present study, we assessed the impacts of an insecticide, carbaryl, on the life-history parameters of a polymorphic cladoceran, Bosmina longirostris, and on Bosmina-copepod interaction. In this Bosmina species, all juvenile individuals have the defensive morphology irrespective of presence of predators in juvenile stages, and they lose or maintain such morph compliance with the presence/absence of the predators in adult stages. In the present study, individual somatic growth and population growth rate decreased due to applied carbaryl. Moreover, the animals lost the defensive morphology when their body size was smaller than with no-carbaryl treatment even in the presence of predators, indicating that the insecticide inhibited persistence of the inherent antipredator morphology. Such a chemical disturbance will increase the predation risk to individuals and, in turn, influence the population dynamics of the bosminids through increased mortality.

We isolated eight polymorphic microsatellite loci from the zooplankton Moina macrocopa (Straus), which is sensitive to pollutants such as insecticides and heavy metals. The isolated loci were polymorphic, with three to seven alleles among 23 individuals. Expected heterozygosities ranged from 0.167 to 0.787. These loci can be used to examine cryptic genetic structure and to infer the connectivity among metapopulations.

We formulated responses in functional traits by competitive communities to continual environmental changes, and examined the association of the trait dynamics with species richness and interspecific competition. As an aggregate measure for community properties we employed the mean community trait value as the species traits averaged over an entire community with weighting by relative species abundances. For three particular types of community, in which there was competition for abiotic resources, competition for biotic resources, or species packing on an environmental gradient, we analytically proved that the responses of the mean community trait to environmental change were determined by the total trait range in the community but were weakly associated with the strength of competition and the number of species. These results were provided with simplifying assumptions that the species trait determining the resource utility equally spaced along an univariate resource axis and the competition between species was symmetrical between pairs of competing species and within the entire community. Some numerical simulations based on stochastically-generated communities and randomly-sampled natural communities indicated that relaxation of the simplifying assumptions did not considerably violate the above conclusion. The suggested determinacy of trait dynamics with variable species richness and competition regime implies that aggregated description of communities in terms of trait distributions among composite species is relevant in predicting community responses, in terms of functional traits and ecosystem function, to environmental changes. (C) 2008 Elsevier Ltd. All rights reserved.

The long-term response to directional selection and its selection limit are derived for a quantitative character that is controlled by pleiotropic mutations with direct deleterious effect on fitness. Directional selection is assumed to be weaker than the selection acting directly on mutations via deleterious effects (purging selection), which renders all mutations to eventual elimination. The analysis embedding this restrictive assumption indicates that the evolutionary response of the character starting from an equilibrium state, in which mutation and purging selection balance but no directional selection is operating, decreases monotonically with time at an exponential rate. And the fading rate of responses is mostly determined by the direct deleterious effect. Contrary to the expectation by the standard selection limit theory based on fixation of extant genetic variation, the present model predicts that the selection limit depends on the intensity of directional selection, the limit being proportional to the ratio of the directional selection intensity to the direct deleterious effect. A slightly larger genetic variance is maintained at the selection limit than would be without directional selection. (c) 2005 Elsevier Inc. All rights reserved.

The genetic variation of sex ratio and sex allocation were examined in a series of half-sib analyses on the sex ratio of braconid parasitoid wasp Heterospilus prosopidis populations collected in Hawaii and Arizona. The mean threshold value and the range of the threshold for change in the sex of offspring in response to resource quality (host size) were determined. Estimates of the narrow-sense heritability (h(2)) of sex ratio at a specific host size ranged from 0.185 to 0.315, and those of the sex changing point (threshold value) ranged from 0.220 to 0.342. The coefficient of variation (CVA) of sex ratio was significantly larger than CVA of body weight. We discuss factors that maintained the significant additive genetic variation of sex ratio.

The extinction probability is one of the most useful endpoints that are utilized in conservation biology. A parallel approach is advocated for the ecological risk assessment of chemical pollutants. The presented framework estimates extinction probability induced by pollutant chemicals in order to evaluate ecological hazards of pollution, and is applicable to any biological community (aquatic or terrestrial). The analytical framework, which is based on stochastic population dynamics theory, is briefly explained. The extinction risk estimation is feasible if ecotoxicological data concerning pollutant effects on population growth rate of organisms (the intrinsic rate of natural increase), and if environmental exposure concentration is provided. Tentative risk estimation was made for some agrochemicals and surfactants on zooplankton populations (Daphnia) as target organisms. (C) 2003 Elsevier Ltd. All rights reserved.

The chronic effect of p-nonylphenol on survival and reproduction for two generations of the freshwater cladoceran Daphnia galeata was examined by life table experiments. The effects on survival and reproduction were used as the intrinsic rate of natural increase, r, with the Euler-Lotka equation and were analyzed with a simple mathematical model (a power function). The population-level EC50, the concentration of a substance that reduces the intrinsic rate of natural increase by 50%, was estimated as 65.2 mug/L for the first generation and 81.5 mug/L for the second generation. No transgenerational effect that reinforces adverse responses in the offspring generation has been detected. From a 48-h immobility test an acute LC50 was estimated to be 60.8 mug/L. The acute LC50 is a good indicator of the chronic population-level effects of this chemical to this species. (C) 2002 Wiley Periodicals, Inc.

The chronic effect of linear alkylbenzene sulfonate (LAS(12)) on a daphnid species (Daphnia galeata) was examined by the life table experiment. The estimated responses in the intrinsic rate of population growth r were analyzed with two alternate concentration-response functions, i.e., the power function and the quadratic function. Based on the best-fit power function model with biases corrected by the jackknife procedure, the population-level EC50, which is defined as the concentration of chemicals that reduces the population growth rate (the intrinsic rate of natural increase) by 50%, was estimated as 2.5 mg/L. The 48-h acute immobility test yielded EC50 of 4.6 mg/L. The population-level effect of LAS(12) on this test species is considerably more sensitive than the acute lethal effects to neonates. (C) 2001 by John Wiley & Sons, Inc.

In order to evaluate population-level effects of p-nonylphenol on a cladoceran zooplankton (Daphnia galeata), the chronic effects on survival and reproduction were estimated with partial life table tests, which examined responses in life history characters until 3 weeks after birth. The observed responses in survival and reproduction were converted to reductions of the intrinsic rate of natural increase r. The population level EC50, which is defined as the exposure concentration that reduces r by 50%, was estimated as 16.1 mug l(-1) In order to examine the extent to which the population-level effect in terms of r is influenced by extra mortality in nature, which is induced by predation, starvation, etc., sensitivity (elasticity) measures of the intrinsic rate of natural increase to reductions in age-specific survival and reproduction were calculated under hypothetical predation schemes. The sensitivities of the intrinsic rate to changes in survival and reproduction invariably decline rapidly after the onset of reproduction irrespective of predation schemes. This implies that partial life cycle tests until 21 days after birth can provide reliable estimates of the population-level effects.

As concentration-response functions for chronic population-level effects of pollutant chemicals, three mathematical models were presented and examined for goodness of fit to published toxicological data that estimated the population-level effects of chemicals in terms of the intrinsic rate of population growth (r). Among the examined concentration-r functions, the power function model, that is, r(x) = r(O)[1 - (x/α)β], in which x is the exposure concentration and α and β are parameters, performed with the best fit to each data set. The power function model is characterized by two parameters representing the absolute value of toxicity, α, and the curvature of responses, β. The bootstrap simulation, conducted on the entire data set consisting of all published data that we collected, indicated that the observed variance of β among actual data sets could be mostly explained by the random error variation generated from the bootstrap resamplings. The generic β value, determined from the entire data set and expected to denote the best estimate of β if the variability of β was completely due to random sampling error, was estimated as 1.84. It was implied that the response of the intrinsic rate of natural increase (r) to chemical exposure was nearly quadratic in many cases.

Population-level effects of chemical pollutants are evaluated in terms of decrements of mean extinction time of populations. Analytical solutions of the mean extinction time based on the diffusion approximation were applied to published chronic ecotoxicological data provided from life table experiments or population growth experiments. Assuming a fairly large population (a million) with environmental fluctuation of an observed magnitude, chemical exposure with a concentration of 10% of LC50 is expected to cause, on average, an extinction risk of 16% reduction in the mean extinction time, which is equivalent to that induced by a 1.2% reduction of the population size (or habitat area). Although the ecological risk assessment based on mean extinction time has many limitations, it may present a possibility for interpreting the ecological risk of chemical pollutants in the context of population vulnerability.

Artificial selection was conducted to reduce the behavioral responsiveness of female bruchid beetles, Callosobruchus chinensis, to the oviposition deterring pheromone excreted by conspecific females. Significant responses to selection were observed after two generations of selection. Realized heritability was estimated as 0.052 +/- 0.017 from cumulative responses regressed on cumulative selection differentials. These results indicate that this pheromone communication system has significant additive genetic variance needed for its evolution.

Inbreeding depression may induce rapid extinction due to positive feedbacks between inbreeding depression and reduction of population size, which is often referred to as extinction Vortex by inbreeding depression. The present analysis has demonstrated that the extinction Vortex is likely to happen with realistic parameter values of genomic mutation rate of lethals or semilethals, equilibrium population size, intrinsic rate of natural increase, and rate of population decline caused by nongenetic extrinsic factors. Simulation models incorporating stochastic fluctuations of population size further indicated that extinction by inbreeding depression is facilitated by environmental fluctuations in population size. The results suggest that there is a positive interaction between genetic stochasticity and environmental stochasticity for extinction of populations by inbreeding depression.

Populational extinction due to inbreeding depression is analyzed with simple population genetic and population ecological models. Two alternative genetic mechanisms of inbreeding depression, i.e. recessive deleterious genes and overdominant genes, are assumed in separate analyses in order to examine their relative importance. With both mechanisms the population size and the coefficient of inbreeding are maintained at stable equilibria if there is no non-genetic demographic disturbance or stress. With a certain amount of demographic disturbance the population declines rapidly due to interaction between the decrease of population size and the increase of inbreeding coefficient. Such rapid extinction occurs with both genetic mechanisms. However, in the case of overdominant genes extinction happens only if the equilibrium population size is small and the selection coefficient is large such that segregation load is large. In nature, extinction due to overdominant genes is considered to be much less likely than extinction due to recessive deleterious genes.

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.

A quantitative genetic model of density-dependent selection is presented and analysed with parameter values obtained from laboratory selection experiments conducted by Mueller and his coworkers. The ecological concept of r- and K-selection is formulated in terms of selection gradients on underlying phenotypic characters that influence the density-dependent measure of fitness. Hence the selection gradients on traits are decomposed into two components, one that changes in the direction to increase r, and one that changes in the direction to increase K. The relative importance of the two components is determined by temporal fluctuations in population density. The evolutionary rate of r and K (per-generation changes in r and K due to the genetic responses of the underlying traits) is also formulated. Numerical simulation has shown that with moderate genetic variances of the underlying characters, r and K can evolve rapidly and the evolutionary rate is influenced by synergistic interaction between characters that contribute to r and K. But strong r-selection can occur only with severe and continuous disturbances of populations so that the population density is kept low enough to prevent K-selection.

The dynamics of a finite number of phenotypic characters in a subdivided population, evolving by the combined effects of individual and group selection, is modeled using a quantitative genetic theory. This model of group selection allows prediction of per-generation evolutionary responses of metapopulation mean phenotypes. These predictions are based on measurements of the selection gradient in each group, the additive genetic variance-covariance matrix within groups, the group selection gradient, and the intergroup variance-covariance matrix. The equilibrium intergroup variance-covariance matrix is presented for a migrant pool model and individual selection within groups. Numerical calculations demonstrate that group selection can significantly influence the metapopulation mean phenotypes with a realistic amount of intergroup divergence of phenotypes through drift and migration.