Modelling competition between hybridising subspecies

Dispersal and interbreeding as survival strategies for species exposed to environment change

The success of individual species under a change to the environment is dependent on a number of factors, which include the changes to habitat, competition with other species and adaptability. Here we investigate the impact of differing dispersal characteristics of two competing species responding to the change using an idealized spatio-temporal model. The rate of dispersion is given by a combination of the growth term and the form of the diffusion term, which is set to give either normal diffusion or anomalous (super) diffusion. The later is brought about by employing fractional diffusion and we characterize the population as being more adventurous than the population undergoing normal diffusion. The more adventurous population is found, not surprisingly, to reach and occupy uninhabited ground before the population undergoing normal diffusion can get there. Interbreeding is found to be important in that it can aid the spread of the less adventurous population preventing its extinction. The response to an abrupt environment change, taken here to be a change in the distribution of the growth rate, is dependent on the initial conditions, the dispersion characteristics, and the level of interbreeding, leading to very different intermediate and final states. Our results highlight instances when a particular dispersal strategy gives a population an edge over another. In the cases considered here we find states where the more adventurous population can dominate across the domain, the two populations exist in separate parts of the domain separated by fronts, and both populations coexist across the domain in the medium term with one or other of the populations dominating across the domain in the long term. Given the long time to reach equilibrium where one or other of the populations dominate, consideration needs to be put to the time scale of change, as sufficiently frequent change can allow coexistence. We demonstrate the need to include dispersion characteristics when considering the factors affecting the response of species to a change in the environment.

Coexistence in two-species competition with delayed maturation

Inter- and intraspecific competition is most important during the immature life stage for many species of interest, such as multiple coexisting mosquito species that act as vectors of diseases. Mortality caused by competition that occurs during maturation is explicitly modelled in some alternative formulations of the Lotka-Volterra competition model. We generalise this approach by using a distributed delay for maturation time. The kernel of the distributed delay is represented by a truncated Erlang distribution. The shape and rate of the distribution, as well as the position of the truncation, are found to determine the solution at equilibrium. The resulting system of delay differential equations is transformed into a system of ordinary differential equations using the linear chain approximation. Numerical solutions are provided to demonstrate cases where competitive exclusion and coexistence occur. Stability conditions are determined using the nullclines method and local stability analysis. The introduction of a distributed delay promotes coexistence and survival of the species compared to the limiting case of a discrete delay, potentially affecting management of relevant pests and threatened species.

Spatial modelling for population replacement of mosquito vectors at continental scale

Malaria is one of the deadliest vector-borne diseases in the world. Researchers are developing new genetic and conventional vector control strategies to attempt to limit its burden. Novel control strategies require detailed safety assessment to ensure responsible and successful deployments. Anopheles gambiae sensu stricto (s.s.) and Anopheles coluzzii, two closely related subspecies within the species complex Anopheles gambiae sensu lato (s.l.), are among the dominant malaria vectors in sub-Saharan Africa. These two subspecies readily hybridise and compete in the wild and are also known to have distinct niches, each with spatially and temporally varying carrying capacities driven by precipitation and land use factors.

We model the spread and persistence of a population-modifying gene drive system in these subspecies across sub-Saharan Africa by simulating introductions of genetically modified mosquitoes across the African mainland and its offshore islands. We explore transmission of the gene drive between the two subspecies that arise from different hybridisation mechanisms, the effects of both local dispersal and potential wind-aided migration to the spread, and the development of resistance to the gene drive. Given the best current available knowledge on the subspecies’ life histories, we find that an introduced gene drive system with typical characteristics can plausibly spread from even distant offshore islands to the African mainland with the aid of wind-driven migration, with resistance beginning to take over within a decade. Our model accounts for regional to continental scale mechanisms, and demonstrates a range of realistic dynamics including the effect of prevailing wind on spread and spatio-temporally varying carrying capacities for subspecies. As a result, it is well-placed to answer future questions relating to mosquito gene drives as important life history parameters become better understood.

Conventional control methods have dramatically reduced malaria, but it still kills over 300,000 children in Africa each year, and this number could increase as their effectiveness wanes. Novel control methods using gene drives rapidly reduce or modify malaria vector populations in laboratory settings, and hence are now being considered for field applications. We use modelling to assess how a gene drive might spread and persist in the malaria-carrying subspecies Anopheles gambiae sensu stricto (s.s.) and Anopheles coluzzii. These two subspecies interbreed and compete, so we model how these interactions affect the spread of the drive at a continental scale. In scenarios that allow mosquitoes to travel on prevailing wind currents, we find that a gene drive can potentially spread across national borders—and jump from offshore islands to the African mainland—but spread is eventually arrested when the drive allele is ousted by a resistant allele. As we learn more about the population dynamics of both genetically modified and wild mosquitoes, and as gene drive systems are further developed to allow local containment and evade resistance, our model will be able to answer more detailed questions about how they can be applied in the field effectively and safely.

Predicting the spread and persistence of genetically modified dominant sterile male mosquitoes

Background

Reproductive containment provides an opportunity to implement a staged-release strategy for genetic control of malaria vectors, in particular allowing predictions about the spread and persistence of (self-limiting) sterile and male-biased strains to be compared to outcomes before moving to (self-sustaining) gene-drive strains.

Methods

In this study, we: (i) describe a diffusion–advection–reaction model of the spread and persistence of a single cohort of male mosquitoes; (ii) elicit informative prior distributions for model parameters, for wild-type (WT) and genetically modified dominant sterile strains (DSM); (iii) estimate posterior distributions for WT strains using data from published mark-recapture-release (MRR) experiments, with inference performed through the Delayed-Rejection Adaptive Metropolis algorithm; and (iv) weight prior distributions, in order to make predictions about genetically modified strains using Bayes factors calculated for the WT strains.

Results

If a single cohort of 5000 genetically modified dominant sterile male mosquitoes are released at the same location as previous MRR experiments with their WT counterparts, there is a 90% probability that the expected number of released mosquitoes will fall to < 1 in 10 days, and that by 12 days there will be a 99% probability that no mosquitoes will be found more than 150 m from the release location.

Conclusions

Spread and persistence models should form a key component of risk assessments of novel genetic control strategies for malaria vectors. Our predictions, used in an independent risk assessment, suggest that genetically modified sterile male mosquitoes will remain within the locality of the release site, and that they will persist for a very limited amount of time. Data gathered following the release of these mosquitoes will enable us to test the accuracy of these predictions and also provide a means to update parameter distributions for genetic strains in a coherent (Bayesian) framework. We anticipate this will provide additional insights about how to conduct probabilistic risk assessments of stage-released genetically modified mosquitoes.

Graphical abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s13071-021-04982-1.

Quantifying the risk of vector-borne disease transmission attributable to genetically modified vectors

The relative risk of disease transmission caused by the potential release of transgenic vectors, such as through sterile insect technique or gene drive systems, is assessed with comparison with wild-type vectors. The probabilistic risk framework is demonstrated with an assessment of the relative risk of lymphatic filariasis, malaria and o'nyong'nyong arbovirus transmission by mosquito vectors to human hosts given a released transgenic strain of Anopheles coluzzii carrying a dominant sterile male gene construct. Harm is quantified by a logarithmic loss function that depends on the causal risk ratio, which is a quotient of basic reproduction numbers derived from mathematical models of disease transmission. The basic reproduction numbers are predicted to depend on the number of generations in an insectary colony and the number of backcrosses between the transgenic and wild-type lineages. Analogous causal risk ratios for short-term exposure to a single cohort release are also derived. These causal risk ratios were parametrized by probabilistic elicitations, and updated with experimental data for adult vector mortality. For the wild-type, high numbers of insectary generations were predicted to reduce the number of infectious human cases compared with uncolonized wild-type. Transgenic strains were predicted to produce fewer infectious cases compared with the uncolonized wild-type.