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.

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.

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.

Effects of ignoring survey design information for data reuse.

Data are currently being used, and reused, in ecological research at an unprecedented rate. To ensure appropriate reuse however, we need to ask the question: "Are aggregated databases currently providing the right information to enable effective and unbiased reuse?" We investigate this question, with a focus on designs that purposefully favor the selection of sampling locations (upweighting the probability of selection of some locations). These designs are common and examples are those designs that have uneven inclusion probabilities or are stratified. We perform a simulation experiment by creating data sets with progressively more uneven inclusion probabilities and examine the resulting estimates of the average number of individuals per unit area (density). The effect of ignoring the survey design can be profound, with biases of up to 250% in density estimates when naive analytical methods are used. This density estimation bias is not reduced by adding more data. Fortunately, the estimation bias can be mitigated by using an appropriate estimator or an appropriate model that incorporates the design information. These are only available however, when essential information about the survey design is available: the sample location selection process (e.g., inclusion probabilities), and/or covariates used in their specification. The results suggest that such information must be stored and served with the data to support meaningful inference and data reuse.

Monitoring the resilience of a no-take marine reserve to a range extending species using benthic imagery.

Global climate change is driving the redistribution of marine species and thereby potentially restructuring endemic communities. Understanding how localised conservation measures such as protection from additional human pressures can confer resilience to ecosystems is therefore an important area of research. Here, we examine the resilience of a no-take marine reserve (NTR) to the establishment of urchin barrens habitat. The barrens habitat is created through overgrazing of kelp by an invading urchin species that is expanding its range within a hotspot of rapid climate change. In our study region, a multi-year monitoring program provides a unique time-series of benthic imagery collected by an Autonomous Underwater Vehicle (AUV) within an NTR and nearby reference areas. We use a Bayesian hierarchical spatio-temporal modelling approach to estimate whether the NTR is associated with reduced formation of urchin barrens, and thereby enhances local resilience. Our approach controls for the important environmental covariates of depth and habitat complexity (quantified as rugosity derived from multibeam sonar mapping), as well as spatial and temporal dependence. We find evidence for the NTR conferring resilience with a strong reserve effect that suggests improved resistance to the establishment of barrens. However, we find a concerning and consistent trajectory of increasing barrens cover in both the reference areas and the NTR, with the odds of barrens increasing by approximately 32% per year. Thus, whereas the reserve is demonstrating resilience to the initial establishment of barrens, there is currently no evidence of recovery once barrens are established. We also find that depth and rugosity covariates derived from multibeam mapping provide useful predictors for barrens occurrence. These results have important management implications as they demonstrate: (i) the importance of monitoring programs to inform adaptive management; (ii) that NTRs provide a potential local conservation management tool under climate change impacts, and (iii) that technologies such as AUVs and multibeam mapping can be harnessed to inform regional decision-making. Continuation of the current monitoring program is required to assess whether the NTR can provide long term protection from a phase shift that replaces kelp with urchin barrens.

Modelling competition between hybridising subspecies.

The geographic niches of many species are dramatically changing as a result of environmental and anthropogenic impacts such as global climate change and the introduction of invasive species. In particular, genetically compatible subspecies that were once geographically separated are being reintroduced to one another. This is of concern for conservation, where rare or threatened subspecies could be bred out by hybridising with their more common relatives, and for commercial interests, where the stock or quality of desirable harvested species could be compromised. It is also relevant to disease ecology, where disease transmission is heterogeneous among subspecies and hybridisation may affect the rate and spatial spread of disease. We develop and investigate a mathematical model to combine competitive effects via the Lotka-Volterra model with hybridisation effects via mate choice. The species complex is structured into two classes: a subspecies of interest (named x), and other subspecies including any hybrids produced (named y). We show that in the absence of limit cycles the model has four possible equilibrium outcomes, representing every combination: total extinction, x-dominance (y extinct), y-dominance (x extinct), and at most a single coexistence equilibrium. We give conditions for which limit cycles cannot exist, then further show that the "total extinction" equilibrium is always unstable, that y-dominance is always stable, and that the other equilibria have stability depending on the model parameters. We demonstrate that both x-dominance and coexistence are achievable under a wide range of parameter values and initial conditions, which corresponds with empirical evidence of known competing-hybridising systems. We then briefly examine bifurcation behaviour. In particular, we note that a subcritical bifurcation is possible in which a "catastrophic" transition from x-dominance to y-dominance can occur, representing an invasion event. Finally, we briefly examine the common complication of time-varying carrying capacity, showing that such a case can make coexistence more likely.

Functional group based marine ecosystem assessment for the Bay of Biscay via elasticity analysis.

The transitory and long-term elasticities of the Bay of Biscay ecosystem to density-independent and density-dependent influences were estimated within a state space model that accounted for both process and observation uncertainties. A functional group based model for the Bay of Biscay fish ecosystem was fit to time series obtained from scientific survey and commercial catch and effort data. The observation model parameters correspond to the unknown catchabilities and observation error variances that vary across the commercial fisheries and fishery-independent scientific surveys. The process model used a Gompertz form of density dependence, which is commonly used for the analysis of multivariate ecological time series, with unknown time-varying fishing mortalities. Elasticity analysis showed that the process model parameters are directly interpretable in terms of one-year look-ahead prediction elasticities, which measure the proportional response of a functional group in the next year given a proportional change to a variable or parameter in the current year. The density dependent parameters were also shown to define the elasticities of the long term means or quantiles of the functional groups to changes in fishing pressure. Evidence for the importance of indirect effects, mediated by density dependence, in determining the ecosystem response of the Bay of Biscay to changes in fishing pressure is presented. The state space model performed favourably in an assessment of model adequacy that compared observations of catch per unit effort against cross-validation predictive densities blocked by year.

Making inference from wildlife collision data: inferring predator absence from prey strikes.

Wildlife collision data are ubiquitous, though challenging for making ecological inference due to typically irreducible uncertainty relating to the sampling process. We illustrate a new approach that is useful for generating inference from predator data arising from wildlife collisions. By simply conditioning on a second prey species sampled via the same collision process, and by using a biologically realistic numerical response functions, we can produce a coherent numerical response relationship between predator and prey. This relationship can then be used to make inference on the population size of the predator species, including the probability of extinction. The statistical conditioning enables us to account for unmeasured variation in factors influencing the runway strike incidence for individual airports and to enable valid comparisons. A practical application of the approach for testing hypotheses about the distribution and abundance of a predator species is illustrated using the hypothesized red fox incursion into Tasmania, Australia. We estimate that conditional on the numerical response between fox and lagomorph runway strikes on mainland Australia, the predictive probability of observing no runway strikes of foxes in Tasmania after observing 15 lagomorph strikes is 0.001. We conclude there is enough evidence to safely reject the null hypothesis that there is a widespread red fox population in Tasmania at a population density consistent with prey availability. The method is novel and has potential wider application.

Assessing Habitat Use by Snapper (Chrysophrys auratus) from Baited Underwater Video Data in a Coastal Marine Park.

Baited Underwater Video (BUV) systems have become increasingly popular for assessing marine biodiversity. These systems provide video footage from which biologists can identify the individual fish species present. Here we explore the relevance of spatial dependence and marine park boundaries while estimating the distribution and habitat associations of the commercially and recreationally important snapper species Chrysophrys auratus in Moreton Bay Marine Park during a period when new Marine National Parks zoned as no-take or "green" areas (i.e., areas with no legal fishing) were introduced. BUV studies typically enforce a minimum distance among BUV sites, and then assume that observations from different sites are independent conditional on the measured covariates. In this study, we additionally incorporated the spatial dependence among BUV sites into the modelling framework. This modelling approach allowed us to test whether or not the incorporation of highly correlated environmental covariates or the geographic placement of BUV sites produced spatial dependence, which if unaccounted for could lead to model bias. We fitted Bayesian logistic models with and without spatial random effects to determine if the Marine National Park boundaries and available environmental covariates had an effect on snapper presence and habitat preference. Adding the spatial dependence component had little effect on the resulting model parameter estimates that emphasized positive association for particular coastal habitat types by snapper. Strong positive relationships between the presence of snapper and rock habitat, particularly rocky substrate composed of indurated freshwater sediments known as coffee rock, and kelp habitat reinforce the consideration of habitat availability in marine reserve design and the design of any associated monitoring programs.

Modeling extreme risks in ecology.

Extreme risks in ecology are typified by circumstances in which data are sporadic or unavailable, understanding is poor, and decisions are urgently needed. Expert judgments are pervasive and disagreements among experts are commonplace. We outline approaches to evaluating extreme risks in ecology that rely on stochastic simulation, with a particular focus on methods to evaluate the likelihood of extinction and quasi-extinction of threatened species, and the likelihood of establishment and spread of invasive pests. We evaluate the importance of assumptions in these assessments and the potential of some new approaches to account for these uncertainties, including hierarchical estimation procedures and generalized extreme value distributions. We conclude by examining the treatment of consequences in extreme risk analysis in ecology and how expert judgment may better be harnessed to evaluate extreme risks.

The control of vector-borne disease epidemics.

The theoretical underpinning of our struggle with vector-borne disease, and still our strongest tool, remains the basic reproduction number, R(0), the measure of long term endemicity. Despite its widespread application, R(0) does not address the dynamics of epidemics in a model that has an endemic equilibrium. We use the concept of reactivity to derive a threshold index for epidemicity, E(0), which gives the maximum number of new infections produced by an infective individual at a disease free equilibrium. This index describes the transitory behavior of disease following a temporary perturbation in prevalence. We demonstrate that if the threshold for epidemicity is surpassed, then an epidemic peak can occur, that is, prevalence can increase further, even when the disease is not endemic and so dies out. The relative influence of parameters on E(0) and R(0) may differ and lead to different strategies for control. We apply this new threshold index for epidemicity to models of vector-borne disease because these models have a long history of mathematical analysis and application. We find that both the transmission efficiency from hosts to vectors and the vector-host ratio may have a stronger effect on epidemicity than endemicity. The duration of the extrinsic incubation period required by the pathogen to transform an infected vector to an infectious vector, however, may have a stronger effect on endemicity than epidemicity. We use the index E(0) to examine how vector behavior affects epidemicity. We find that parasite modified behavior, feeding bias by vectors for infected hosts, and heterogeneous host attractiveness contribute significantly to transitory epidemics. We anticipate that the epidemicity index will lead to a reevaluation of control strategies for vector-borne disease and be applicable to other disease transmission models.

Assessing model structure uncertainty through an analysis of system feedback and Bayesian networks.

Ecological predictions and management strategies are sensitive to variability in model parameters as well as uncertainty in model structure. Systematic analysis of the effect of alternative model structures, however, is often beyond the resources typically available to ecologists, ecological risk practitioners, and natural resource managers. Many of these practitioners are also using Bayesian belief networks based on expert opinion to fill gaps in empirical information. The practical application of this approach can be limited by the need to populate large conditional probability tables and the complexity associated with ecological feedback cycles. In this paper, we describe a modeling approach that helps solve these problems by embedding a qualitative analysis of sign directed graphs into the probabilistic framework of a Bayesian belief network. Our approach incorporates the effects of feedback on the model's response to a sustained change in one or more of its parameters, provides an efficient means to explore the effect of alternative model structures, mitigates the cognitive bias in expert opinion, and is amenable to stakeholder input. We demonstrate our approach by examining two published case studies: a host-parasitoid community centered on a nonnative, agricultural pest of citrus cultivars and the response of an experimental lake mesocosm to nutrient input. Observations drawn from these case studies are used to diagnose alternative model structures and to predict the system's response following management intervention.