Evolution of branched regulatory genetic pathways: directional selection on pleiotropic loci accelerates developmental system drift

Abstract

Developmental systems are regulated by a web of interacting loci. One common and useful approach in studying the evolution of development is to focus on classes of interacting elements within these systems. Here, we use individual-based simulations to study the evolution of traits controlled by branched developmental pathways involving three loci, where one locus regulates two different traits. We examined the system under a variety of selective regimes. In the case where one branch was under stabilizing selection and the other under directional selection, we observed “developmental system drift”: the trait under stabilizing selection showed little phenotypic change even though the loci underlying that trait showed considerable evolutionary divergence. This occurs because the pleiotropic locus responds to directional selection and compensatory mutants are then favored in the pathway under stabilizing selection. Though developmental system drift may be caused by other mechanisms, it seems likely that it is accelerated by the same underlying genetic mechanism as that producing the Dobzhansky–Muller incompatibilities that lead to speciation in both linear and branched pathways. We also discuss predictions of our model for developmental system drift and how different selective regimes affect probabilities of speciation in the branched pathway system.

Appendix 1: Constraint and Speciation

When both branches are under directional selection, there is a possibility that the selection responses on the two branches may interfere with each other and thus constrain the ways by which the populations respond to selection. There are four ways by which a population can respond to selection for looser binding at both branches of the pathway. Where promoter _j and product _j represent the allelic values of promoter and product sites at locus j, looser binding evolves in both branches by any of the following routes:

• (1) product_A > promoter_B and product_A > promoter_C, with probability a;

• (2) product_A > promoter_B and product_A < promoter_C, with probability b;

• (3) product_A < promoter_B and product_A > promoter_C, with probability c;

• (4) product_A < promoter_B and product_A < promoter_C, with probability d.

These routes are mutually exclusive so a + b +  c + d = 1.

Reproductive isolation arises only if the two different populations take different, incompatible routes. The probability that strong reproductive isolation will not occur is thus the summation of the squared probabilities that a population will respond along a given route, Prob [high hybrid fitness] = a ² + b ² + c ² + d ². Routes 1 and 4 are symmetrical as are routes 2 and 3, so a = d and b = c.

With constraint, populations will be more likely to transverse routes 1 and 4 and less likely to transverse routes 2 and 3. Let T equal the constraint or equivalently, the correlation of the allelic values in the two pathways. Therefore,

$$ a = d = (1 + T)/4 $$

$$ b = c = (1 - T)/4 . $$

When T = 0, the interactions are independent and a = b = c = d. When T = 1, the pathways are completely constrained to evolve together, whereby a = d = 1/2 and b = c = 0. Thus Prob [high hybrid fitness] = 

$$ 2\left( {\frac{{1 + T}} {4}} \right)^2 + 2\left( {\frac{{1 - T}} {4}} \right)^2 = \frac{{1 + T^2 }} {4} $$

.

$$\eqalign{ 2\left( {\frac{{\left( 1 + T \right)^2 }} {{16}}} \right) + 2\left( {\frac{{\left( {1 - T} \right)^2 }} {{16}}} \right) = \frac{{\left( {1 + T} \right)^2 + \left( {1 - T} \right)^2 }} {8} \cr \qquad= \frac{{1 + 2T + T^2 + 1 - 2T + T^2 }} {8} = \frac{{2 + 2T^2 }} {8}} $$

$$ 1 - \frac{{1 + T^2 }} {4} = \frac{{4 - 1 - T^2 }} {4} = \frac{{3 - T^2 }} {4} $$

The probability that reproductive isolation will arise is Prob [low hybrid fitness] = 1−Prob [high hybrid fitness] = (3−T ²)/4, which ranges from 1/2 to 3/4 as T ranges from 1 to 0.

T can be estimated from this equation by substituting the observed frequency $\hat f$ of low hybrid fitness outcomes and rearranging, giving $\hat T = \sqrt {3 - 4\hat f}$. This estimates the extent to which evolution is correlated on the two branches of the pathway.

$$ \hat f = \frac{{3 - \hat T\,^2 }} {4}\quad 4\hat f - 3 = - \hat T\,^2 \quad \hat T\,^2 = 3 - 4\hat f $$