Figure 1.
Fruitfly trait heritability as a function of network size.
The broad-sense heritability for twelve quantitative traits in Drosophila melanogaster as a function of the estimated size of the underlying gene regulatory network. When network topology (average connectivity) is considered in a regression model, R2≈0.68 (p = 0.023). Note that the data points are drawn from what must be considered an exploratory, hypothesis-generating method that requires extensive testing to confirm the networks. Data from [16]–[18].
Figure 2.
Epistasis in the Boolean gene networks used in these models.
Panel A shows the distribution of 24000 epistasis estimates across all network sizes and topologies. Directional epistasis is prevalent (94% of all single- versus double-mutants). Panel B shows mean weighted epistasis (±95% CI) as a function of network size and topology. The weighting, with weights calculated as the standard deviation of epistasis within network size, was required to achieve homoskedasticity for statistical analysis. Without weighting, a strong negative relationship between epistasis and network size is observed (data not shown).
Figure 3.
The rates of change of genotypic and phenotypic variance over 250 generations in a constant environment.
On the left, the mean (±95% CI) rate of change of additive genetic variance (dVA/dt; Panel A) and phenotypic variance (dVP/dt; Panel C), given a network genetic architecture, as a function of network size and recombination rate. On the right (Panels B and D), the same parameters given a linear genetic architecture. The results are generally consistent with the analytical solutions assuming additivity of Crow and Kimura [9] and Bürger [10].
Figure 4.
Quantitative trait heritability after 250 generations, given network (A) or linear (B) genetic architectures.
The mean heritability (±95% CI) of the ecologically-critical trait when the genetic architecture is defined as a network, as a function of network size and topology; smaller networks and scale-free topology increase heritability (Panel A). The mean heritability (±95% CI) of the trait when the genetic architecture is purely linear, as a function of number of genes and the width of the fitness function (see Methods). Contrary to the network architecture, when the architecture is purely linear heritability is (weakly) positively related to the number of underlying genes.
Table 1.
Factors influencing quantitative trait heritability in a stable environment.
Figure 5.
Population recovery times given network genetic architectures.
Mean time (±95% CI) required for a population to recover to pre-impact population size after a sudden environmental change when the genetic architecture is defined as a network, as a function of network size and the degree of environmental change (dE; arbitrary units). Population recovery takes long if either network size or the degree of environmental change is greater.
Table 2.
Primary factors influencing population recovery time following a sudden environmental impact.
Table 3.
Factors influencing quantitative trait heritability following a sudden environmental impact.
Figure 6.
Recovery time (A-C) and pre-change heritability (D) when experimentally controlling for additive genetic variation.
When the environmental change is smaller (20 units), the relationship between network size and recovery time is clear, but when the impact is larger (30 units), the relationship is lost (Panel A). Panel B partitions recovery time between the additive genetic variance trigger (VA trigger) for the environmental change and degree of environmental change, demonstrating the effect of the environment with respect to the role of VA. Averaging over degrees of environmental change and considering recovery time as a function of network size and VA, the positive relationship between network size and recovery time is more apparent that solely considering the VA (Panel C). Panel D shows that, although there is an equivalent amount of additive variation present in the population for each network size, smaller networks tend to have higher pre-change heritability (i.e., pre-heritability) than larger networks.
Table 4.
Factors influencing recovery time when the environment changes at a given (5, 10, or 20 units) level of additive genetic variance.
Figure 7.
An example network, functional map, and chromosome.
Part A shows an example 13-gene Boolean network. Black nodes are up-regulated (“on”; state = 1) genes and white nodes are down-regulated (“off”; state = 0). If an edge connecting two nodes is black, the “head” gene (upstream) activates the “tail” gene (downstream), and if an edge is gray, the head represses the tail gene. Part B provides the functional map; for example, if the head gene is “off” and the edge connecting the head and tail genes is an activator, then the tail gene is off (upper-right quadrant). Part C shows the chromosome corresponding to the network in Part A. Each block represents a gene (numbers along the left-hand side); within each block, the top number defines the “head” (i.e., immediately-upstream) gene while the bottom number defines the functional relationship (e.g., if 0, then the head gene is a repressor).