Question

Venom production in your rattlesnake population has a phenotypic mean of 400 mg, a phenotypic standard deviation of 36 mg, and a narrow-sense heritability of 0.25. The mean generation interval is 2 years. If you perform phenotypic selection by culling the bottom 10% of individuals each generation (i = 0.2), approximately how many years will it take for your population to reach a phenotypic mean of 450 mg?

Explain how 56 is the correct amount of years to reach a mean of 450mg

Answer 1

Answer 56 years

Calculating Phenotypic Variance

As previously mentioned, all instances of phenotypic variance (V_P) within a population are the result of genetic sources (V_G) and/or environmental sources (V_E). This relationship can be summarized as follows (Falconer & Mackay, 1996; Lynch & Walsh, 1998):

V_P= V_G + V_E

However, in order to determine the values for both V_G and V_E, researchers must consider a number of additional variables, as described in the following sections.

Genetic Sources of Variation

Genetic sources of variation can themselves be divided into several subcategories, including additive variance (V_A), dominance variance (V_D ), and epistatic variance (V_I). Together, the values for each of these subcategories yield the total amount of genetic variation (V_G) responsible for a particular phenotypic trait:

V_G = V_A + V_D + V_I

Defining the Subcategories of Genetic Variance

Of course, in order to fully understand this equation, one must also understand what each subcategory of genetic variance entails. The first subcategory, additive genetic variance, refers to the deviation from the mean phenotype due to inheritance of a particular allele and this allele's relative (to the mean phenotype of the population) effect on phenotype. In contrast, the second subcategory, dominance genetic variance, involves deviation due to interactions between alternative alleles at a specific locus. For example, say that a plant produces white flowers if its genotype is A₁A₁ and red flowers if its genotype is A₂A₂. If there is no dominance deviation or interaction between these alleles, then the A₁A₂ genotype would lead to pink flowers due to expression of both alleles. However, if there is an interaction between the alleles such that their expression is not equal, then the phenotype of the heterozygote (A₁A₂) would not be an approximate midpoint; rather, it would more closely resemble one of the homozygotes (either A₁A₁ or A₂A₂). For instance, if the A₂ allele was dominant to the A₁ allele, then the heterozygote would produce red flowers.

Finally, like dominance variance, the third category of genetic variance—epistatic variance—involves an interaction between alleles; however, in this case, the alleles are associated with different loci. This concept can be illustrated by returning to the flower color example, but this time assuming that a second locus (denoted B) determines whether flower pigment is produced. In this case, the B₁ allele is dominant, and it codes for the production of pigment; an absence of pigment means that a plant's flowers will be white. Thus, if the plant's genotype is either B₁B₁ or B₁B₂, its flower color will be determined by the genotype at the A locus. On the other hand, if the plant's genotype is B₂B₂, then no pigment is produced, so the flower color is always white and is not influenced by the genotype at the A locus.

Genetic Variance and Trait Heritability

Once researchers have determined the total amount of genetic variation responsible for a trait, they can use this information in calculations of the trait's heritability. Heritability is a measure of the proportion of phenotypic variance attributable to genetic variance, and it is an important predictor of the degree to which a population can respond to artificial or natural selection.

Consider, for example, a study involving the rare plant Scabiosa canescens that was conducted by researcher Patrik Waldmann in 2001. Like many rare species, this plant is often found in populations of very small size. Such populations are expected to have a low level of genetic diversity, which would limit their ability to adapt. In his study, Waldmann used genetic lines of S. canescens from both a small and a large natural population to estimate both additive and dominance genetic variation. However, contrary to expectations, Waldmann did not find a lower level of additive genetic variance in the offspring from the smaller population. This finding meant that the smaller population still had the ability to evolve, even though the population consisted of only 25 individuals.

Environmental Sources of Variation

Like their genetic counterparts, environmental sources of variation can also be placed into various subcategories; these include specific environmental variance (V_Es),general environmental variance (V_Eg), and genotype by environment interaction (V_GxE).Together, the values for each of these subcategories yield the total amount of environmental variation (V_E ) responsible for a particular phenotypic trait:

V_E = V_Eg + V_GxE + V_Es