Random temporal variation in selection intensities acting on infinite diploid populations: Diffusion method analysis

Levikson, Benny; Karlin, Samuel

doi:10.1016/0040-5809(75)90046-5

Cited by 27 publications

(18 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Whether or not much of the genetical variation in nature is due to balanced polymorphism is another question. Indeed, fitnesses may be stochastic in their magnitudes due to local variations in the environment; such a system will tend to preserve genetical variability within populations (Karlin and Liebermann, 1974;Levikson and Karlin, 1975). It is concluded that the results of this experiment give no support for the neutral gene theory of protein evolution.…”

Section: Discussioncontrasting

confidence: 49%

The genetical response to natural selection by varied environments

Minawa

Birley

1978

Heredity

View full text Add to dashboard Cite

SUMMARYIn a large laboratory cage population of Drosophila melanogaster "Texas" 36 per cent of loei were found to be polymorphic and the average genie heterozygosity per individual was estimated at 82 per cent. Two large replicate subpopulations of "Texas" were established in each of three experimental environments which differed in their degree of environmental variability. The populations were sampled on two occasions, after 27 and after another 54 weeks. By the second sampling, statistical tests showed that the phenotypie distributions of all seven polymorphic loci studied had changed significantly.On the second occasion five loci had responded differently to the three environments and the remaining two loci showed significant changes of phenotype frequency between occasions. It was concluded from the rapidity of the changes that the observations were the result of intense natural selection. Hence the results did not agree with the neutral gene theory of protein evolution. The average genie heterozygosity of individuals was not directly related to the applied levels of environmental heterogeneity.

show abstract

Section: Discussioncontrasting

confidence: 49%

The genetical response to natural selection by varied environments

Minawa

Birley

1978

Heredity

View full text Add to dashboard Cite

show abstract

“…When a t ϵ 1, corresponding to no seed bank, the model reduces to the Haldane and Jayakar (1963) model analyzed by Levikson and Karlin (1975) and the moments simplify to…”

Section: Diffusion Approximation and Numerical Resultsmentioning

confidence: 99%

“…However, mathematical errors led both Wright (1948) and Kimura (1954) to conclude mistakenly that fluctuating selection could not maintain genetic variation. Their analyses were corrected by Gillespie (1973Gillespie ( , 1974 and extended to diploids by Levikson and Karlin (1975; for treatment of an ecological analog of eq. 1, see Hatfield and Chesson 1989).…”

Section: Diffusion Approximation and Numerical Resultsmentioning

confidence: 99%

Stable Two-Allele Polymorphisms Maintained by Fluctuating Fitnesses and Seed Banks: Protecting the Blues in Linanthus Parryae

Turelli¹,

Schemske²,

2001

View full text Add to dashboard Cite

Abstract. Motivated by data demonstrating fluctuating relative and absolute fitnesses for white-versus blue-flowered morphs of the desert annual Linanthus parryae, we present conditions under which temporally fluctuating selection and fluctuating contributions to a persistent seed bank will maintain a stable single-locus polymorphism. In L. parryae, blue flower color is determined by a single dominant allele. To disentangle the underlying diversity-maintaining mechanism from the mathematical complications associated with departures from Hardy-Weinberg genotype frequencies and dominance, we successively analyze a haploid model, a diploid model with three distinguishable genotypes, and a diploid model with complete dominance. For each model, we present conditions for the maintenance of a stable polymorphism, then use a diffusion approximation to describe the long-term fluctuations associated with these polymorphisms. Our protected polymorphism analyses show that a genotype whose arithmetic and geometric mean relative fitnesses are both less than one can persist if its relative fitness exceeds one in years that produce the most offspring. This condition is met by data from a population of L. parryae whose white morph has higher fitness (seed set) only in years of relatively heavy rain fall. The data suggest that the observed polymorphism may be explained by fluctuating selection. However, the yearly variation in flower color frequencies cannot be fully explained by our simple models, which ignore age structure and possible selection in the seed bank. We address two additional questions-one mathematical, the other biological-concerning the applicability of diffusion approximations to intense selection and the applicability of long-term predictions to datasets spanning decades for populations with long-lived seed banks. Through the seminal papers of Epling and Dobzhansky (1942) and Wright (1943a, b), the flower color polymorphism in the diminutive desert annual Linanthus parryae played a central role in shaping population genetic theory and opinions concerning the roles of natural selection, genetic drift, and migration in evolution. In their 1941 survey of 427 sampling locations in the Mojave Desert, California, Epling and Dobzhansky (1942) found a preponderance of monomorphic populations with most having white flowers. About 19% of their 1261 samples were polymorphic, and white flowers predominated in most of these. Wright (1943b; 1978, pp. 194-223) analyzed the spatial pattern of flower color frequencies and concluded that despite some evidence for directional selection favoring white, selection was generally negligible, and drift, migration and, possibly, mutation-selection balance determined allele frequencies in these populations. Wright argued that the effects of drift could explain the spatial pattern of polymorphic frequencies if effective local population sizes were on the order of 100 or less. However, after monitoring these same populations for another 15 years, Epling et al. (1960) found little change ...

show abstract

“…Much of this earlier work focuses on the dynamics of a mutation in an infinite population (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24). However, these infinite-population approaches are fundamentally unsuitable for analyzing the fixation probabilities of mutations that are neutral or deleterious on average (and even for mutations that are beneficial on average, population sizes must often be unrealistically large for Significance Evolution in variable environments depends crucially on the fates of new mutations in the face of fluctuating selection pressures.…”

mentioning

confidence: 99%

Fate of a mutation in a fluctuating environment

Cvijović

Good

Jerison

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

144

134

View full text Add to dashboard Cite

Natural environments are never truly constant, but the evolutionary implications of temporally varying selection pressures remain poorly understood. Here we investigate how the fate of a new mutation in a fluctuating environment depends on the dynamics of environmental variation and on the selective pressures in each condition. We find that even when a mutation experiences many environmental epochs before fixing or going extinct, its fate is not necessarily determined by its time-averaged selective effect. Instead, environmental variability reduces the efficiency of selection across a broad parameter regime, rendering selection unable to distinguish between mutations that are substantially beneficial and substantially deleterious on average. Temporal fluctuations can also dramatically increase fixation probabilities, often making the details of these fluctuations more important than the average selection pressures acting on each new mutation. For example, mutations that result in a trade-off between conditions but are strongly deleterious on average can nevertheless be more likely to fix than mutations that are always neutral or beneficial. These effects can have important implications for patterns of molecular evolution in variable environments, and they suggest that it may often be difficult for populations to maintain specialist traits, even when their loss leads to a decline in time-averaged fitness.population genetics | fixation probability | fluctuating environment | effective diffusion E volutionary trade-offs are widespread: Adaptation to one environment often leads to costs in other conditions. For example, drug resistance mutations often carry a cost when the dosage of the drug decays (1), and seasonal variations in climate can differentially select for certain alleles in the summer or winter (2). Similarly, laboratory adaptation to specific temperatures (3, 4) or particular nutrient sources (5, 6) often leads to declines in fitness in other conditions. Related trade-offs apply to any specialist phenotype or regulatory system that incurs a general cost to confer benefits in specific environmental conditions (7). Despite the ubiquity of these trade-offs, it is not always easy to predict when a specialist phenotype can evolve and persist. How useful must a trait be on average to be maintained? How regularly does it need to be useful? How much easier is it to maintain in a larger population compared with a smaller one?The answers to these questions depend on two major factors. First, how often do new mutations create or destroy a specialist phenotype, and what are their typical costs and benefits across environmental conditions? This is fundamentally an empirical question, which depends on the costs and benefits of the trait in question, as well as its genetic architecture (e.g., the target size for loss-of-function mutations that disable a regulatory system). In this paper, we focus instead on the second major factor: given that a particular mutation occurs, how does its long-term fate depend on its fitn...

show abstract

Random temporal variation in selection intensities acting on infinite diploid populations: Diffusion method analysis

Cited by 27 publications

References 7 publications

The genetical response to natural selection by varied environments

The genetical response to natural selection by varied environments

Stable Two-Allele Polymorphisms Maintained by Fluctuating Fitnesses and Seed Banks: Protecting the Blues in Linanthus Parryae

Fate of a mutation in a fluctuating environment

Contact Info

Product

Resources

About