Medea selfish genetic elements as tools for altering traits of wild populations: a theoretical analysis

Abstract

One strategy for controlling transmission of insect-borne disease involves replacing the native insect population with transgenic animals unable to transmit disease. Population replacement requires a drive mechanism to ensure the rapid spread of linked transgenes, the presence of which may result in a fitness cost to carriers. Medea selfish genetic elements have the feature that when present in a female, only offspring that inherit the element survive, a behavior that can lead to spread. Here, we derive equations that describe the conditions under which Medea elements with a fitness cost will spread, and the equilibrium allele frequencies are achieved. Of particular importance, we show that whenever Medea spreads, the non-Medea genotype is driven out of the population, and we estimate the number of generations required to achieve this goal for Medea elements with different fitness costs and male-only introduction frequencies. Finally, we characterize two contexts in which Medea elements with fitness costs drive the non-Medea allele from the population: an autosomal element in which not all Medea-bearing progeny of a Medea-bearing mother survive, and an X-linked element in species in which X/Y individuals are male. Our results suggest that Medea elements can drive population replacement under a wide range of conditions.

Figure 1

Characteristics of Medea allele and genotype spread as a function of introduction frequency, and of allele and population fitness as a function of Medea allele frequency. (A) The frequency of individuals lacking Medea (Non-Medea), heterozygotes (Heterozygous), and homozygotes for Medea (Homozygous Medea), are plotted with respect to Medea allele frequency. The fitness of the Medea allele, the non-Medea allele, and the population is also shown. (B) Medea allele frequency is plotted as a function of the number of generations for different introduction ratios of homozygous Medea/non-Medea males into a population of non-Medea females. (C) The population frequency of individuals with Medea (Medea Genotype Frequency) is plotted as a function of generations for different introduction ratios of homozygous Medea/non-Medea males into a population of non-Medea females. (D) Plot of allele and population fitness, and genotype frequency, as a function of Medea allele frequency, for a Medea that carries a 10% embryonic fitness cost. The UIEAF and SIEAF are indicated. Thin arrows indicate the directions in which the Medea allele frequency moves on either side of the UIEAF and SIEAF.

Figure 2

Equilibrium characteristics of autosomal Medea elements with fitness costs. (A) Diagram partitioning (V_Het, V_Homo) fitness parameter space into regions in which linear stability analysis indicate qualitatively similar behaviors are observed. This diagram is identical for a Medea with parental fitness cost. Qualitative behavior changes as each curve is crossed, with the occurrence of a bifurcation. Transcritical bifurcation occurs as Equilibrium 3 moves through Equilibrium 4 (i.e. the two collide), with the two equilibria exchanging stability. Curve c separates regions B and C. On this curve, Equilibrium 2 and 3 are coincident. Transcritical bifurcation occurs as the two equilibria collide, with the two equilibria exchanging stability. (B) Stable internal equilibrium values of the non-Medea allele are plotted as a function of fitness cost/fecundity loss for embryonic, sex-independent parental, or maternal costs.

Figure 3

When an autosomal Medea with a fitness cost and t₁=0 spreads, it drives the elimination of non-Medea individuals, but not non-Medea alleles, from the population. (A) Plot describing the number of generations required for Medea to be present in 99% of individuals, for a Medea element with a parental fertility/fecundity cost. Homozygous Medea male:non-Medea male introduction ratios are indicated on the Y-axis, and parental fertility/fecundity cost on the X axis. Area between lines indicates regions of parameter space within which a specific number of generations (indicated by numbers and arrows) are required for the frequency of Medea individuals to reach 99% or greater. Line color, shown in the heat map in the lower right, provides a measure of how many generations are required. Black lines (50+) indicate that fifty or more generations are required. The border between the black-lined region and the lower unlined region defines the critical male introduction ratio (CMIR). (B) Plot describing the number of generations required for Medea to be present in 99% of individuals, for a Medea element with an embryonic fitness cost. (C) Plot describing the number of generations required for Medea to be present in 99% of individuals, for a Medea element with a maternal fecundity cost.

Figure 4

When Medea is located on an autosome, and heterozygous Medea offspring of homozygous Medea mothers do not always survive, the non-Medea allele experiences a cost that can result in its elimination from the population. (A) Diagram partitioning (t₁, V_Het) parameter space into regions in which linear stability analysis indicates qualitatively similar behaviors are observed. Qualitative behavior changes as we cross each of these curves, with the occurrence of a bifurcation, as described in the legend to Figure 2. (B) Plot of allele and population fitness, and genotype frequency, as a function of Medea allele frequency, for a Medea that carries a 10% embryonic fitness cost and has t₁=0.5. Compare with the Medea shown in Fig. 1D, in which t₁=0. (C) Medea-bearing genotype frequency is plotted as a function of the number of generations for Medea elements with zero fitness cost and different levels of heterozygous offspring lethality (t₁), introduced into a population of non-Medea females using a fixed 1:1 ratio of Medea:non-Medea males. (D) Plot of Medea allele frequency as a function of the number of generations for the zero fitness cost Medea elements in (C). (E) Plot as in (C) for Medea elements with a 10% embryonic fitness cost. (F) Plot of Medea allele frequency as a function of the number of generations for Medea elements with a 10% embryonic fitness cost.

Figure 5

When Medea located on the X chromosome in a male heterogametic species spreads, the non-Medea allele is eliminated from the population. (A) Plot of allele and population fitness as a function of Medea allele frequency, for a Medea that carries a 10% embryonic fitness cost, located on the X chromosome. Lines and labels and other conditions are as in Fig. 1D. (B) Medea genotype frequency is plotted as a function of the number of generations for Medea elements on the X with different levels of an embryonic fitness cost, introduced into a population of non-Medea females using a fixed 1:1 ratio of Medea:non-Medea males. (C) Plot describing the number of generations required for Medea to be present in 99% of individuals, for a Medea element on the X with a 10% embryonic fitness cost. Compare with Fig. 3B. (D) Medea allele frequency is plotted as a function of the number of generations for the elements shown in (B).