Interplay of population genetics and dynamics in the genetic control of mosquitoes

Abstract

Some proposed genetics-based vector control methods aim to suppress or eliminate a mosquito population in a similar manner to the sterile insect technique. One approach under development in Anopheles mosquitoes uses homing endonuclease genes (HEGs)-selfish genetic elements (inherited at greater than Mendelian rate) that can spread rapidly through a population even if they reduce fitness. HEGs have potential to drive introduced traits through a population without large-scale sustained releases. The population genetics of HEG-based systems has been established using discrete-time mathematical models. However, several ecologically important aspects remain unexplored. We formulate a new continuous-time (overlapping generations) combined population dynamic and genetic model and apply it to a HEG that targets and knocks out a gene that is important for survival. We explore the effects of density dependence ranging from undercompensating to overcompensating larval competition, occurring before or after HEG fitness effects, and consider differences in competitive effect between genotypes (wild-type, heterozygotes and HEG homozygotes). We show that population outcomes-elimination, suppression or loss of the HEG-depend crucially on the interaction between these ecological aspects and genetics, and explain how the HEG fitness properties, the homing rate (drive) and the insect's life-history parameters influence those outcomes.

Keywords: genetic vector control; homing endonuclease gene; population dynamics; population genetics.

Figure 1.

Overview of outcomes. This summarizes the way in which mosquito population genetics and dynamics interact. The population genetic outcome depends on the fitness properties of the HEG (cost s, and its dominance h) and the homing rate (g). The population dynamic implications depend on the relationship between the life-history parameters (ρ = r/μ lifetime progeny net of density-independent juvenile mortality, and τ egg-to-adult generation time) and the HEG parameters, particularly the HEG load (0 for ww, s in HH population, or L (equation (3.3)) at mixed genotype equilibrium).

Figure 2.

Population genetic outcomes relationship with s and h. The population genetic outcome depends on the phenotypic fitness properties of the HEG (s, h) and the homing rate (g). The graph shows the regions of parameter space defined by s (the HEG fitness penalty) and h (the dominance of that fitness cost), plotted for g = 0.8.

Figure 3.

Dynamical behaviour. The HEG knockout is recessive lethal (s = 1, h = 0), homing rate g = 0.8. Heterozygous insects are released at time t = 0, 15 per host (i.e. + 25% of the natural population equilibrium 60 per host). The number of adults over time is shown for each genotype (ww: dashed line, Hw: dashed-dotted line, HH: dotted line, here always zero) and in total (solid line). Strength of density dependence b is 0.5 (weak, undercompensating, a,b), 2.5 (underdamped before release, c,d), or 3 (overcompensating, oscillating before release, e,f), the HEG is early-acting (a,c,e) or late-acting (b,d,f). See electronic supplementary material, figure S2 for further b = 1.097 and b = 5. In all figures and described results, the equilibrium size of the natural population remains comparable across different values of b (the density scale parameter a₁ is calculated from N* = 60 and b for each panel). In all population dynamics figures, life-history parameter values are estimated for Anopheles gambiae (table 1): time lag τ = 16 days, adult mortality rate μ = 0.123 per day, net population growth rate r = 1.096 per day.

Figure 4.

Effects of homing rate on population size. The population size is shown, the equilibrium N* where stable (filled symbols) or the average where oscillating (open symbols), for the spectrum of values of homing rate 0 ≤ g ≤ 1 (g = 0 results in wild-type population). The HEG is recessive lethal (s = 1, h = 0), early-acting (a) or late-acting (b). Strength of density dependence b is 0.5, 1.097, 2.5, 3 or 5 (key in a). Pre-release equilibrium N* = 60 per host for all values of b; in unstable natural populations, the pre-release average is higher than 60 (the same value as with g = 0).

Figure 5.

Effects of fitness properties due to gene disruption by the HEG on population size. Homing rate g = 0.8. All genotypes compete equally. These surface plots show the equilibrium N* (indicated by colour scales), for the spectrum of values 0 < s ≤ 1 and 0 ≤ h ≤ 1, following release of heterozygotes N₂(0) equal to 0.25 times the natural population equilibrium. Strength of density dependence b is 0.5 (weak, undercompensating; a,b) or 2.5 (strong, overcompensating; c,d), the HEG is early-acting (a,c) or late-acting (b,d).

Figure 6.

Effects of the HEG altering the scale at which density-dependent competition acts on population size. The post-release equilibrium N* is shown (indicated by colour scales), for a range of values of θ(−0.2 to +0.2), which alters the density scale parameter a₃, and the spectrum of dominance of that effects ϕ (from 0 recessive to 1 dominant), which alters a₂. The HEG has homing rate g = 0.8 and is early-acting (a,c,e) or late-acting (b,d,f). Strength of density dependence b is 0.5 (a,b), 2.5 (c,d) or 1.097 (e,f). The HEG knockout is recessive lethal (s = 1, h = 0), except in (e) and (f) where s = 0.8, h = 0.1 which results in the HEG going to fixation so then a₂ is irrelevant (similar pattern for any b).