Fig. 2

Multigenic inheritance alters the role of linkage disequilibrium in the evolution of phenotypic traits. a The color table illustrates a simplified model of a population’s gene pool for a trait encoded by multiple genes. For simplicity, all the 7 genes are represented in a population by 8 alleles for each gene. Each allele differentially impacts the overall expression of a trait (shown in arbitrary units on the lower X-axis). b A population’s gene pool for a trait encoded by one gene with 8 alleles which impact the phenotypic trait expression as shown in (a). c A Matlab-generated (see code in Additional file 1 Section 6) distribution of phenotype expression in a population of 100,000 individuals with different number of genes encoding the trait and each represented by 8 alleles. The X-axis in all the three charts is the same from 1 to 8, the Y-axis is population frequency of the phenotype (no scale for simplicity). Arrows demonstrate the allelic composition of phenotype examples generated based on multigenic (panel a) and monogenic (panel b) trait inheritance. The probability that all alleles in a multigenic trait will change the trait in the same direction (for instance all A8 alleles in panel a) is inversely proportional to the number of genes and is the product of the probabilities of each particular allele occurring in the given phenotype. An increased number of genes affecting the trait, therefore, decreases the likelihood that a random sampling event, such as genetic recombination, will result in a significant deviation of the resulting trait expression. d Assuming the multigenic nature of mutation rates and body size (primary modeled traits), we modeled both as normally distributed (see panel c) and independently inherited. Selection was applied on body size (or other modeled trait) but not on mutation rate. The evolution of mutation rate in the model was completely independent of other traits. e The left and right charts demonstrate a typical distribution of phenotypic trait expression (DPhE) in a population. Directional selection (left chart, green arrows) will favor extreme phenotypes from the target phenotype tail (left chart, green box). Stabilizing selection (right chart, green arrows) will favor the population mean which is the target phenotype (right chart, green box). Under both scenarios, most germline mutations will be in the negative (disadvantageous) tail of the distribution of fitness effects, DFE (middle chart), imposing a fitness cost for germline mutations. The exact ratio of the tails of the resulting DFEs (and thus the cost/benefit ratio of germline mutations) are determined by the mode and strength of selection acting on a phenotype