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where the n is the number of loci that contribute equally to the quantitative trait. From this equation it is also apparent that a smoother distribution of phenotypic values would result from loci with more than two alleles because each locus would produce more than three genotypes under random mating. For the two locus phenotype shown in Fig. 9.2, the expected frequencies of the phenotypes are found by multiplying the frequencies of the Hardy-Weinberg genotype frequencies for each locus:

and then summing the frequencies of those genotypes that have identical phenotypes.

Problem box 9.1 Phenotypic distribution produced by Mendelian inheritance of three diallelic loci

Calculate the expected genotype frequencies for three locus genotypes in a population where mating is random, all loci have two alleles, and allele frequencies at all loci are V2. Then construct a histogram of phenotypic values using the minimum and maximum phenotypic values used in Fig. 9.2 by assuming that alleles have phenotypic values of V6 (lower-case letter alleles) and 1V2 (capital-letter alleles).

Another primary cause of variation among individuals in quantitative traits is the environment. Even if there is only a single genotype, the phenotype expressed by each individual in a population will vary somewhat depending on the environmental conditions each individual experiences. For example, the biomass and fruit production of plants is impacted by the amount of sunlight and nitrogen each individual receives. Another example of environmental variation in quantitative traits is the role n

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