Fig 1.
Schematic diagrams of the two-locus engineered underdominance (top left) and the killer-rescue (top right) gene drive systems.
Each system comprises of two independently inherited transgenic constructs carrying different configurations of lethal (killer), suppressor (rescue) and cargo (refractory) genes. In the case of engineered underdominance each construct carries a lethal gene, the cargo (refractory) gene and a suppressor of the lethal at the other locus. This differs from the killer-rescue system in which one construct carries a killer gene while the other carries the suppressor and a cargo (refractory) gene. The engineered underdominance system considered here can be thought of as two orthogonal killer-rescue systems split across two transgenic constructs. The engineered underdominance system has been shown to be threshold dependent (bottom left) and persist in time (i.e. it is self-sustaining) whereas the killer-rescue (bottom right) system initially increases in frequency before being eliminated from the population (i.e. it is self-limiting, even in absence of genetic changes such as resistant alleles or mutation of system components).
Table 1.
A table summarising the fitness and lethality parameters used throughout this study.
Within the mathematical model numbers of each transgenic construct carried by a particular genotype (i) are denoted and
for transgenic constructs A and B, respectively. Also shown within this table are the lethality parameters (γi) used to define each of the gene drive elements with γ = 1 representing 100% effective lethality whilst γ = 0 denotes a viable genotype. Here the different gene drives considered are denoted UD (engineered underdominance) and KR (killer-rescue) with SS and WS representing strong and weak suppression of lethals, respectively. Here strong suppression of lethals refers to the scenario whereby one copy of a suppressor transgene is sufficient to rescue against two copies of the associated lethal transgene, whereas for weak suppression two suppressor copies are required to save against two lethal copies. For killer-rescue constructs, parameter values were selected such that construct A represents the killer and B the rescue.
Table 2.
A table of definitions and typical values for each parameter and variable used within the model.
Fig 2.
After [36], a schematic representation of the two-deme model.
Here a separate population dynamics model is considered for each of the target population and non-target population. These are then linked by two-way migration. This is modelled as a continuous transfer of individuals between the two demes at a rate ψ which is expressed per day. Simply, each of the two demes continuously swap a fraction of their population with the other, thus the total amount of migration will depend on the size of each population. Whilst the rates of migration per day considered within this study may appear very low, they actually add up to quite high fractions of the overall populations being exchanged in each generation (comparable to values used in other studies [16, 36, 37]).
Fig 3.
Ecological parameters influence the size of a mosquito population in absence of any control measures.
Individual panels here show the effect on the mosquito population size of varying (a) α, representing the carrying capacity of the environment (eg. availability of larval habitats); (c) strength of density-dependent larval competition; (d) the intrinsic per capita population growth rate; and (e) adult mortality rate whilst the other three are held constant at a base value (see Table 2). Panel (b) shows the combined effect on the population size from varying both the availability of larval habitats and the strength of density dependence. Note that panels (a), (b) and (c) use logarithmic axes to aid in visualisation of results.
Fig 4.
Initial adult mosquito population sizes have no impact on a number of key performance indicators for two-locus engineered underdominance gene drive.
Panels (a) and (b) show the impacts of early- and late-acting fitness/lethal effects whilst the different lines represent the general pattern for a given indicator. The top row shows both the maximal and equilibrium amount of population suppression for a two-locus engineered underdominance gene drive system whereas the bottom row shows the time taken for a system to reach maximal population suppression. We find no difference between examples for different values of α. As such, lines are results from a set of numerical simulations spanning the full range of relative fitness parameters (i.e. 0 ≤ ϵA,B ≤ 1) for a randomly selected α.
Fig 5.
Initial adult mosquito population sizes have no impact on two performance indicators for the killer-rescue gene drive system.
Panels (a) and (b) show the impacts of early- and late-acting fitness/lethal effects, respectively. The lines represent a general pattern for a given indicator. The top row of plots show the maximum degree of population suppression given by a killer-rescue system whilst the bottom row of plots show the time-taken for the system to reach this level. We find no difference between examples for different values of α. As such, lines are results from a set of numerical simulations spanning the full range of relative fitness parameters (i.e. 0 ≤ ϵA,B ≤ 1) for a randomly selected value of α.
Fig 6.
Plots showing examples of the range of behaviour attainable from population dynamics models of engineered underdominance and killer-rescue gene drive systems with early-acting lethals.
Here the top row of panels ((a)-(c)) show effects in the engineered underdominance system whereas the bottom row ((d)-(f)) demonstrate effects in the killer-rescue system. Columns display different degrees of density dependence. From left to right these are weak overcompensatory ((a) and (d), β = 1.1); intermediate overcompensatory ((b) and (e), β = 2.75); and strong overcompensatory ((c) and (f), β = 3.5) dynamics. Initial wild-type adult population sizes with these strengths of density dependence are ∼309 (for β = 1.1), ∼104 (for β = 2.75) and ∼89 (for β = 3.5). For β = 1.1 the system displays stable dynamics whereas for β = 2.75 and β = 3.5 we see oscillatory dynamics that are damped and neutral, respectively. Assuming the cargo (refractory) gene is fully effective in a single copy, it is important to consider here the number of wild-type mosquitoes (solid black lines) relative to all others since these are the only genotype in which females are capable of transmitting viruses. Note here the differences in scaling of both the x and y axes.
Fig 7.
Plot showing comparisons between population genetics models [18] and population dynamics models in two density dependence scenarios (β = 1.1 and β = 2.5).
The top two threshold lines are for lasting introgression of transgenes in the UD system with strongly and weakly suppressed lethals. The bottom two threshold lines are for increases in transgene frequency of the KR system with strongly and weakly suppressed lethals. The key shows the different scenarios plotted, however these are essentially super-imposed. Outcomes for weakly suppressed and strongly suppressed systems are different, but within those cases neither early versus late acting lethality nor varying beta (1.1 or 2.5) makes a significant difference on the thresholds plotted.
Fig 8.
A cartoon showing the general pattern of possible outcomes from numerical simulations of a two-locus engineered underdominance system with migration between a target and a non-target population.
Here the three panels represent examples of the outcome of a system for varying release ratios (increasing from left to right). In the white region (A) the system does not drive in either population and transgenes are eliminated. The grey region (B) produces an intermediate equilibrium state in which transgenes achieve some degree of partial introgression into both populations. In the black region (C) the system is efficient enough to drive in both populations. As different system configurations require different parameter values to achieve each possible outcome, axes here do not display actual values. Results from numerical simulations for a single example release ratio under each different genetic system and release scenario are given in S5–S8 Figs. Note that systems with weakly suppressed lethals (e.g S6 & S8 Figs) require larger release ratios in order to produce the same pattern of outcomes as a system with strongly suppressed lethals.
Fig 9.
Rates of migration can play a significant role in determining the effects of a killer-rescue system.
Results shown here are for a KR system with late-acting fitness/lethal effects introduced into a population of ∼309 individuals (half of which are females). Panels (a) and (b) show the effects of migration rate on the maximum and minimum population sizes (total of all genotypes) attained following the release of a KR system, respectively. Panels (c) and (d) show equivalent results for the maximum and minimum wild-type female population sizes, respectively. Finally, panel (e) shows the effects of migration rate on the maximum rescue transgene frequency that may be attained. In each panel the left-hand plot represents effects on the target population while right-hand plots are for a nearby non-target neighbouring population. In each case, solid lines show results for a KR system that confers zero fitness cost while dashed lines are for a system with 5% fitness cost per construct (i.e. ϵA = 1 = ϵB and ϵA = 0.95 = ϵB, respectively). Line colours represent a specific configuration of release strategy and genetic system and are detailed in the legend (with Bi. = bisex, Ma. = male-only, Fem. = female-specific, S. = strongly, W. = weakly, Rel. = release, Leth. = lethality and Sup. = suppression of lethals). Panels (b) and (d) appear to display just one line since all results precisely coincide with one another.