Modeling the Evolution of Female Meiotic Drive in Maize

Abstract

Autosomal drivers violate Mendel's law of segregation in that they are overrepresented in gametes of heterozygous parents. For drivers to be polymorphic within populations rather than fixing, their transmission advantage must be offset by deleterious effects on other fitness components. In this paper, we develop an analytical model for the evolution of autosomal drivers that is motivated by the neocentromere drive system found in maize. In particular, we model both the transmission advantage and deleterious fitness effects on seed viability, pollen viability, seed to adult survival mediated by maternal genotype, and seed to adult survival mediated by offspring genotype. We derive general, biologically intuitive conditions for the four most likely evolutionary outcomes and discuss the expected evolution of autosomal drivers given these conditions. Finally, we determine the expected equilibrium allele frequencies predicted by the model given recent estimates of fitness components for all relevant genotypes and show that the predicted equilibrium is within the range observed in maize land races for levels of drive at the low end of what has been observed.

Keywords: abnormal chromosome 10; autosomal drive; neocentromere; segregation distortion; selfish genetic element.

Figure 1

The manner in which drive works in Ab10/N10 heterozygotes. One or more crossovers results in each MI product containing an Ab10 and N10 chromatid (a meiosis II segregation pattern). The Ab10 chromatids are then preferentially transmitted to the outermost positions of the meiotic spindles, and the bottom cell of the tetrad will become the egg nucleus. When there is an MI segregation pattern, Ab10 will end up in the egg 50% of the time, i.e., at random. Chromosomes are colored black, knobs are red, centromeres are blue, and spindle fibers are green. Ab10, abnormal chromosome 10; MI, meiosis I; N10, normal chromosome 10.

Figure 2

Global behavior of the model for randomly drawn values of parameters for different scenarios. Shown is the number of parameter combinations giving each of the four possible outcomes when global behavior is fully predicted by the sign of the eigenvalues in Equations (2) and (3). These outcomes represent 99.4–100% of parameter sets across the different scenarios. In the general scenario, all parameters can take any value in their range. For weak selection, each fitness component of the Ab10/Ab10 homozygote is within 90% of the N10/N10 homozygote. For constant dominance, the dominance parameters of the Ab10 chromosome across all fitness components are identical, such that h = h_f = h_s = h_m. The next three scenarios (recessive, additive, and dominant fitness) assume that the Ab10 chromosome has fitness effects that are either fully recessive (Ab10/N10 heterozygote fitness is the same as N10/N10 homozygote), additive (Ab10/N10 heterozygote fitness is exactly intermediate between the two homozygotes), or fully dominant (Ab10/N10 heterozygote fitness is the same as the Ab10 Ab10 homozygote). In each of these three, all fitness effects again have the same dominance parameter (h = h_f = h_s = h_m). The last column (actual drive) restricts the drive parameter to the range observed in maize land races (0.2 ≤ d ≤ 0.6). The four possible outcomes are: N10 goes to fixation regardless of the starting frequency (N10 fixation), Ab10 goes to fixation regardless of the starting frequency (Ab10 fixation), N10 or Ab10 goes to fixation depending on the starting frequency (unstable equilibrium), or Ab10 and N10 reach an internal equilibrium frequency regardless of the starting frequency (stable equilibrium). Not shown are the very few parameter combinations in which more than one internal equilibrium exists. These only occur in the general, constant dominance, and additive fitness scenarios for 37, 28, and 69 parameter combinations, respectively. The observed outcomes clearly show that weak selection favors Ab10 fixation and that recessive fitness effects strongly favor an internal equilibrium in which both the N10 and Ab10 chromosomes segregate. In all other cases, there are relatively few parameter combinations that allow invasion of an Ab10 driver. Ab10, abnormal chromosome 10; N10, normal chromosome 10.

Figure 3

The effect of the degree of dominance on behavior of the model. Lines represent values of drive, expressed as the frequency of Ab10 in ovules of heterozygotes, which is equal to one-half (1 + d), and seed set reduction in homozygotes, f, at which the eigenvalues associated with fixations are equal to one. The solid line is for ${\lambda }_1$: above this line ${\lambda }_1$ is > 1 (Ab10 fixation can be invaded by N10) and below it is < 1 (Ab10 fixation cannot be invaded by N10). The dashed line is for ${\lambda }_0$: above the line ${\lambda }_0$ is < 1 (N10 fixation cannot be invaded by Ab10) and below the line it is > 1 (N10 fixation can be invaded by Ab10). In most cases, these eigenvalues predict global behavior (see Figure 2). The expected global behavior is given for each of the delineated regions. The three panels are for different levels of dominance of fitness components, including partial dominance (A), additivity (B), or partial recessivity (C). The more dominant the fitness effects of the driver, the less likely that it will invade a population fixed for N10 (i.e., the smaller the region under the dashed line). Drivers with more recessive effects on fitness, on the other hand, and more likely to invade, and more likely to give a stable equilibrium [compare (C) to (A and B)]. In all three panels: h = h_f = h_s = h_m (dominance of fitness effects is the same for all fitness components), m = 0.05 (5% reduction in pollen viability in Ab10/Ab10 homozygotes), s = 0 (no reduction in seed viability due to maternal genotype), and v = 0.2 (10% reduction in viability from germination to adult in Ab10/Ab10 homozygotes). Ab10, abnormal chromosome 10; N10, normal chromosome 10.

Figure 4

Predicted frequency of Ab10 in ovules at the stable equilibrium using fitness parameters from a field experiment. The solid line is equilibrium for the average values of seed set, seed size (seed viability), and pollen viability measured in Higgins et al. (2017) (f = 0.650, s = 0.190, m = 0.063, h_f = 0.212, h_s = 0.327, and h_m = 0.176). The dashed line is the equilibrium after including hypothetical reductions in seed viability due to offspring genotype (v = 0.3 and h = 0.238) to illustrate how the predicted equilibrium changes. The gray box delineates the minimum and maximum values of drive and Ab10 frequencies observed in maize land races. Note that the maximum observed Ab10 frequency increases with the level of drive because frequencies were observed in adult plants, and the model censuses ovules (and pollen), which is postdrive. Ab10, abnormal chromosome 10; N10, normal chromosome 10.