GENETIC VARIATION IN A HETEROGENEOUS ENVIRONMENT. I. TEMPORAL HETEROGENEITY AND THE ABSOLUTE DOMINANCE MODEL

ABSTRACT The conditions for a stable polymorphism and the equilibrium gene frequency in an infinite population are compared when there is spatial or temporal environmental heterogeneity for the absolute dominance model. For temporal variation the conditions for stability are more restrictive and the equilibrium gene frequency is often at a low gene frequency. In a finite population, temporal environmental heterogeneity for the absolute dominance model was found to be quite ineffective in maintaining genetic variation and is often less effective than no selection at all. For comparison, the maximum maintenance for temporal variation is related to the overdominant model. In general, cyclic environmental variation was found to be more effective at maintaining genetic variation than where the environment varies stochastically. The importance of temporal environmental variation and the maintenance of genetic variation is discussed.

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GENETIC VARIATION IN A HETEROGENEOUS ENVIRONMENT. V. SPATIAL HETEROGENEITY IN FINITE POPULATIONS

Genetics ◽

10.1093/genetics/89.2.389 ◽

1978 ◽

Vol 89 (2) ◽

pp. 389-401

Author(s):

Philip W Hedrick

Keyword(s):

Genetic Variation ◽

Temporal Variation ◽

Spatial Model ◽

Finite Population ◽

Retardation Factor ◽

Spatial And Temporal Variation ◽

Dominance Model ◽

Temporal Model ◽

The Relationship ◽

Absolute Dominance

ABSTRACT The spatial model of Levene (1953) was examined in a finite population and compared to a temporal model. The spatial model was much more effective in retaining genetic variation in a finite population. Furthermore, the haploid spatial model was more effective in retaining genetic variation than the analogous diploid absolute dominance model. This is the opposite from that found for the temporal model, where the diploid model was more effective than the haploid. Here is an example where diploidy (sexual reproduction) may be disadvantageous. A model that permitted both spatial and temporal variation to act in concert gave retention of genetic variation in situations where either spatial or temporal variation, separately, did not. The relationship between the amount of heterozygosity and the retardation factor was discussed. An example of how spatial or temporal variation affects the proportion of populations fixed after a certain number of generations was given. It seems that these models have biological analogues, several examples of which are mentioned.

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PROBABILITY OF FIXATION AND MEAN FIXATION TIME OF AN OVERDOMINANT MUTATION

Genetics ◽

10.1093/genetics/74.2.371 ◽

1973 ◽

Vol 74 (2) ◽

pp. 371-380

Author(s):

Masatoshi Nei ◽

A K Roychoudhury

Keyword(s):

Population Size ◽

Gene Frequency ◽

Finite Population ◽

Retardation Factor ◽

Fixation Time ◽

Selection Intensity ◽

Infinite Population ◽

Probability Of Fixation

ABSTRACT The probability of fixation of an overdominant mutation in a finite population depends on the equilibrium gene frequency in an infinite population (m) and the product (A) of population size and selection intensity. If m < 0.5 (disadvantageous overdominant genes), the probability is generally much lower than that of neutral genes; but if m is close to 0.5 and A is relatively small, it becomes higher. If m > 0.5 (advantageous overdominant genes), the probability is largely determined by the fitness of heterozygotes rather than that of mutant homozygotes. Thus, overdominance enhances the probability of fixation of advantageous mutations. The average number of generations until fixation of an overdominant mutation also depends on m and A. This average time is long when m is close to 0.5 but short when m is close to 0 or 1. This dependence on m and A is similar to that of Robertson's retardation factor.

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Genetic variation in varying environments

Genetics Research ◽

10.1017/s0016672300020036 ◽

1981 ◽

Vol 37 (1) ◽

pp. 79-93 ◽

Cited By ~ 81

Author(s):

Trudy F. C. Mackay

Keyword(s):

Body Weight ◽

Genetic Variation ◽

Spatial Heterogeneity ◽

Temporal Variation ◽

Genetic Variance ◽

Environmental Variability ◽

Additive Genetic Variance ◽

Environmental Variation ◽

Heterogeneous Environments ◽

Varying Environments

SUMMARYIn order to assess the relationship between genetic and environmental variability, a large natural population of Drosophila melanogaster was replicated as eight subpopulations, which were subjected to four different patterns of environmental variation. The environmental variable imposed was presence of 15% ethanol in the culture medium. Experimental treatments of the populations were intended to simulate constant environmental conditions, spatial heterogeneity in the environment, and two patterns of temporal environmental variation with different periodicity (long- and short-term temporal variation). Additive genetic and phenotypic variation in sternopleural and abdominal chaeta number, and body weight, were estimated in two successive years, and measurements were taken of the genotype–environment correlation of body weight and sternopleural bristle score with medium type.Additive genetic variance of sternopleural chaeta number and of body weight was significantly greater in the three populations experiencing environmental heterogeneity than in the control population, but additive genetic variance of abdominal bristle score was not clearly affected by exposing populations to varying environments. Temporal environmental variation was equally, if not more, efficient in promoting the maintenance of genetic variation than spatial heterogeneity, but the cycle length of the temporal variation was of no consequence. Specific genotype–environment interactions were not present, therefore adaptation to heterogeneous environments is by selection of heterozygosity per se, rather than by differential survival of genotypes in the alternate niches.

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Coevolution does not slow the rate of loss of heterozygosity in a stochastic host-parasite model with constant population size

10.1101/2020.04.07.024661 ◽

2020 ◽

Cited By ~ 2

Author(s):

Ailene MacPherson ◽

Matthew J. Keeling ◽

Sarah P. Otto

Keyword(s):

Genetic Variation ◽

Natural Selection ◽

Population Size ◽

Finite Population ◽

Extensive Literature ◽

Stochastic Perturbations ◽

Frequency Dependent Selection ◽

Infinite Population ◽

Negative Frequency Dependent Selection ◽

Host Parasite

AbstractCoevolutionary negative frequency dependent selection has been hypothesized to maintain genetic variation in host and parasites. Despite the extensive literature pertaining to host-parasite coevolution, the effect of matching-alleles (MAM) coevolution on the maintenance of genetic variation has not been explicitly modelled in a finite population. The dynamics of the MAM in an infinite population, in fact, suggests that genetic variation in these coevolving populations behaves neutrally. We find that while this is largely true in finite populations two additional phenomena arise. The first of these effects is that of coevolutionary natural selection on stochastic perturbations in host and pathogen allele frequencies. While this may increase or decrease genetic variation, depending on the parameter conditions, the net effect is small relative to that of the second phenomena. Following fixation in the pathogen, the MAM becomes one of directional selection, which in turn rapidly erodes genetic variation in the host. Hence, rather than maintain it, we find that, on average, matching-alleles coevolution depletes genetic variation.

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MAINTENANCE OF GENETIC VARIATION WITH A FREQUENCY-DEPENDENT SELECTION MODEL AS COMPARED TO THE OVERDOMINANT MODEL

Genetics ◽

10.1093/genetics/72.4.771 ◽

1972 ◽

Vol 72 (4) ◽

pp. 771-775 ◽

Cited By ~ 1

Author(s):

Philip W Hedrick

Keyword(s):

Genetic Variation ◽

Finite Population ◽

Selection Model ◽

Frequency Change ◽

Fourth Moment ◽

Frequency Dependent ◽

Frequency Dependent Selection ◽

Infinite Population ◽

Dependent Model ◽

Frequency Dependent Model

ABSTRACT A frequency-dependent selection model proposed by Huang, Singh and Kojima (1971) was found to be more effective at maintaining genetic variation in a finite population than the overdominant model. The fourth moment parameter of the distribution of unfixed states showed that there was a more platykurtic distribution for the frequency-dependent model. This agreed well with the expected gene frequency change found for an infinite population.

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A MARKOV PROCESS OF GENE FREQUENCY CHANGE IN A GEOGRAPHICALLY STRUCTURED POPULATION

Genetics ◽

10.1093/genetics/76.2.367 ◽

1974 ◽

Vol 76 (2) ◽

pp. 367-377

Author(s):

Takeo Maruyama

Keyword(s):

Genetic Variation ◽

Markov Process ◽

Diffusion Process ◽

Gene Frequency ◽

Transition Probabilities ◽

Large Population ◽

Sample Path ◽

Time Parameter ◽

Frequency Change ◽

Structured Population

ABSTRACT A Markov process (chain) of gene frequency change is derived for a geographically-structured model of a population. The population consists of colonies which are connected by migration. Selection operates in each colony independently. It is shown that there exists a stochastic clock that transforms the originally complicated process of gene frequency change to a random walk which is independent of the geographical structure of the population. The time parameter is a local random time that is dependent on the sample path. In fact, if the alleles are selectively neutral, the time parameter is exactly equal to the sum of the average local genetic variation appearing in the population, and otherwise they are approximately equal. The Kolmogorov forward and backward equations of the process are obtained. As a limit of large population size, a diffusion process is derived. The transition probabilities of the Markov chain and of the diffusion process are obtained explicitly. Certain quantities of biological interest are shown to be independent of the population structure. The quantities are the fixation probability of a mutant, the sum of the average local genetic variation and the variation summed over the generations in which the gene frequency in the whole population assumes a specified value.

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A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

Genetics Research ◽

10.1017/s0016672300002834 ◽

1969 ◽

Vol 13 (2) ◽

pp. 117-126 ◽

Cited By ~ 3

Author(s):

Derek J. Pike

Keyword(s):

Iterative Procedure ◽

Gene Frequency ◽

Finite Population ◽

Transition Matrices ◽

Single Cycle ◽

Gene Frequencies ◽

Mean And Variance ◽

The Mean ◽

The One ◽

Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

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Testing for local adaptation and evolutionary potential along 1 altitudinal gradients in rainforest Drosophila: beyond laboratory estimates

10.1101/068080 ◽

2016 ◽

Author(s):

Eleanor K. O’Brien ◽

Megan Higgie ◽

Alan Reynolds ◽

Ary A. Hoffmann ◽

Jon R. Bridle

Keyword(s):

Genetic Variation ◽

Environmental Change ◽

High Altitude ◽

Local Adaptation ◽

Biotic Interactions ◽

Environmental Variation ◽

Species Range ◽

Altitudinal Gradients ◽

Low Altitude ◽

The Relationship

ABSTRACTPredicting how species will respond to the rapid climatic changes predicted this century is an urgent task. Species Distribution Models (SDMs) use the current relationship between environmental variation and species’ abundances to predict the effect of future environmental change on their distributions. However, two common assumptions of SDMs are likely to be violated in many cases: (1) that the relationship of environment with abundance or fitness is constant throughout a species’ range and will remain so in future, and (2) that abiotic factors (e.g. temperature, humidity) determine species’ distributions. We test these assumptions by relating field abundance of the rainforest fruit fly Drosophila birchii to ecological change across gradients that include its low and high altitudinal limits. We then test how such ecological variation affects the fitness of 35 D. birchii families transplanted in 591 cages to sites along two altitudinal gradients, to determine whether genetic variation in fitness responses could facilitate future adaptation to environmental change. Overall, field abundance was highest at cooler, high altitude sites, and declined towards warmer, low altitude sites. By contrast, cage fitness (productivity) increased towards warmer, lower altitude sites, suggesting that biotic interactions (absent from cages) drive ecological limits at warmer margins. In addition, the relationship between environmental variation and abundance varied significantly among gradients, indicating divergence in ecological niche across the species’ range. However, there was no evidence for local adaptation within gradients, despite greater productivity of high altitude than low altitude populations when families were reared under laboratory conditions. Families also responded similarly to transplantation along gradients, providing no evidence for fitness trade-offs that would favour local adaptation. These findings highlight the importance of (1) measuring genetic variation of key traits under ecologically relevant conditions, and (2) considering the effect of biotic interactions when predicting species’ responses to environmental change.

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POPULATION GENETIC CONSEQUENCES OF FEEDING HABITS IN SOME FOREST LEPIDOPTERA

Genetics ◽

10.1093/genetics/92.3.1005 ◽

1979 ◽

Vol 92 (3) ◽

pp. 1005-1021

Author(s):

Charles Mitter ◽

Douglas J Futuyma

Keyword(s):

Genetic Variation ◽

Environmental Heterogeneity ◽

Feeding Habits ◽

Functional Relation ◽

Allozyme Variation ◽

Unexpected Result ◽

Polymorphic Loci ◽

Allozyme Loci ◽

Race Formation ◽

Relationship Of

ABSTRACT By surveying variation at allozyme loci in several phytophagous lepidopteran species (Geometridae), we have tested two hypotheses about the relationship of genetic variation to environmental heterogeneity: (1) that allozyme polymorphisms may exist because of associations between genotypes and "niches" (different host plants, in this instance), and (2) that the overall genetic variation of a species is correlated with environmental heterogeneity (or breadth of the species' overall ecological niche) .—Genetic differentiation among samples of oligophagous or polyphagous species taken from different host species was observed in one of three species, at only one of seven polymorphic loci. The data thus provide no evidence for pronounced genetic sub-structuring, or "host race" formation in these sexually reproducing species, although host plant-genotype associations in a parthenogenetic moth give evidence of the potential for diversifying selection.—In a comparison of allozyme variation in polyphagous ("generalized") and oligophagous ("specialized") species, heterozygosity appeared to be higher in specialized species, at all polymorphic loci but one. I t is possible that this unexpected result arises from a functional relation between breadth of diet and genetic variation.

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On sojourn times at particular gene frequencies

Genetics Research ◽

10.1017/s0016672300015494 ◽

1975 ◽

Vol 25 (2) ◽

pp. 89-94 ◽

Cited By ~ 8

Author(s):

Edward Pollak ◽

Barry C. Arnold

Keyword(s):

Markov Chains ◽

Gene Frequency ◽

Overlapping Generations ◽

Finite Population ◽

Diffusion Method ◽

Gene Frequencies ◽

Sojourn Times ◽

The Mean ◽

Number Of Visits ◽

Finite Markov Chains

SUMMARYThe distribution of visits to a particular gene frequency in a finite population of size N with non-overlapping generations is derived. It is shown, by using well-known results from the theory of finite Markov chains, that all such distributions are geometric, with parameters dependent only on the set of bij's, where bij is the mean number of visits to frequency j/2N, given initial frequency i/2N. The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.

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