### Abstract

We analyse patterns of the means and variances of genotypic fitnesses across different niches in a randomly mating haploid population. The population inhabits a spatially heterogeneous environment where it is subject to mutation and weak multilocus additive selection, with different selection coefficients in different niches. Approximate analytical expressions are derived for the stationary mean and variance of genotypic fitnesses among the niches in terms of environmental and genetic parameters. As a special case, we analyse an environment described by a variable t, distributed among the niches with mean t(*) and variance D(*), and quadratic decrease in correlation between environments as a function of the difference in values of t. If the niches have the same qualities, the mean and variance of genotypic fitnesses evolve to be quadratic functions of t that achieve their maximum and minimum, respectively, at t(*). With unequal niche qualities, these are non-polynomial functions that attain their extrema at different, usually intermediate values of t, although the coefficient of variation of the genotypic fitnesses still attains its minimum near t(*). The functions involve the total. mutation rate, the contribution of the loci to genotypic fitnesses, and the frequency and quality distributions of the niches. Thus, for this relatively simple model the norms of reaction may be calculated in terms of the detailed properties of the environmental heterogeneity, and the genetic system.

Original language | English (US) |
---|---|

Pages (from-to) | 241-248 |

Number of pages | 8 |

Journal | Genetical Research |

Volume | 68 |

Issue number | 3 |

State | Published - Dec 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Genetics

### Cite this

*Genetical Research*,

*68*(3), 241-248.

**Fitness patterns and phenotypic plasticity in a spatially heterogeneous environment.** / Zhivotovsky, Lev A.; Feldman, Marcus W.; Bergman, Aviv.

Research output: Contribution to journal › Article

*Genetical Research*, vol. 68, no. 3, pp. 241-248.

}

TY - JOUR

T1 - Fitness patterns and phenotypic plasticity in a spatially heterogeneous environment

AU - Zhivotovsky, Lev A.

AU - Feldman, Marcus W.

AU - Bergman, Aviv

PY - 1996/12

Y1 - 1996/12

N2 - We analyse patterns of the means and variances of genotypic fitnesses across different niches in a randomly mating haploid population. The population inhabits a spatially heterogeneous environment where it is subject to mutation and weak multilocus additive selection, with different selection coefficients in different niches. Approximate analytical expressions are derived for the stationary mean and variance of genotypic fitnesses among the niches in terms of environmental and genetic parameters. As a special case, we analyse an environment described by a variable t, distributed among the niches with mean t(*) and variance D(*), and quadratic decrease in correlation between environments as a function of the difference in values of t. If the niches have the same qualities, the mean and variance of genotypic fitnesses evolve to be quadratic functions of t that achieve their maximum and minimum, respectively, at t(*). With unequal niche qualities, these are non-polynomial functions that attain their extrema at different, usually intermediate values of t, although the coefficient of variation of the genotypic fitnesses still attains its minimum near t(*). The functions involve the total. mutation rate, the contribution of the loci to genotypic fitnesses, and the frequency and quality distributions of the niches. Thus, for this relatively simple model the norms of reaction may be calculated in terms of the detailed properties of the environmental heterogeneity, and the genetic system.

AB - We analyse patterns of the means and variances of genotypic fitnesses across different niches in a randomly mating haploid population. The population inhabits a spatially heterogeneous environment where it is subject to mutation and weak multilocus additive selection, with different selection coefficients in different niches. Approximate analytical expressions are derived for the stationary mean and variance of genotypic fitnesses among the niches in terms of environmental and genetic parameters. As a special case, we analyse an environment described by a variable t, distributed among the niches with mean t(*) and variance D(*), and quadratic decrease in correlation between environments as a function of the difference in values of t. If the niches have the same qualities, the mean and variance of genotypic fitnesses evolve to be quadratic functions of t that achieve their maximum and minimum, respectively, at t(*). With unequal niche qualities, these are non-polynomial functions that attain their extrema at different, usually intermediate values of t, although the coefficient of variation of the genotypic fitnesses still attains its minimum near t(*). The functions involve the total. mutation rate, the contribution of the loci to genotypic fitnesses, and the frequency and quality distributions of the niches. Thus, for this relatively simple model the norms of reaction may be calculated in terms of the detailed properties of the environmental heterogeneity, and the genetic system.

UR - http://www.scopus.com/inward/record.url?scp=0030484002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030484002&partnerID=8YFLogxK

M3 - Article

C2 - 9062081

AN - SCOPUS:0030484002

VL - 68

SP - 241

EP - 248

JO - Genetics Research

JF - Genetics Research

SN - 0016-6723

IS - 3

ER -