Geoffrey R. Hosack

A statistical method for the elicitation of priors in Bayesian generalised linear models (GLMs) and extensions is proposed. Probabilistic predictions are elicited from the expert to parametrise a multivariate normal or multivariate t prior distribution for the unknown linear coefficients of the GLM, and an inverse gamma prior for the dispersion parameter if unknown. The elicited predictions condition on defined elicitation scenarios. Dependencies among scenarios are then elicited from the expert by conditioning on hypothetical outcomes. Elicited conditional medians parametrise a canonical vine copula model of dependence that may be truncated for efficiency. The statistical elicitation method permits prior parametrisation of GLMs with alternative choices of design matrices or observation models from the same elicitation session. Extensions of the method apply to multicategorical data, data with bounded support, semi-continuous data with point mass at zero, lognormal and log t models, and count data with overdispersion or zero-inflation. A case study elicits a prior for an extended GLM embedded in a statistical model of overdispersed counts described by a binomial-simplex mixture distribution. The elicited canonical vine model of dependence is found to incorporate substantial information into the prior. The procedures of the statistical elicitation method are implemented in the R package eglm.

Background: The dynamics of vector-borne disease transmission depend on the abundances of vectors. The dominant malaria vector species complex of Anopheles gambiae sensu lato is a target of vector control strategies designed to reduce and eliminate malaria transmission. The three most widely distributed dominant malaria vectors within the species complex are An. arabiensis , An. coluzzii and An. gambiae sensu stricto. Methods: Previous studies across the extent of the species complex range have been restricted to annual predictions of species occurrence or relative abundance. This study incorporated relative abundance data at the species level and abundance data at the species complex level to estimate and predict daily equilibrium vector abundances of each species. Statistical models with interpretable parameters were used to gain insight into how factors such as meteorological conditions, insecticide-treated net use and human density affect the spatial and temporal predictions. The statistical models were used to predict daily equilibrium vector abundance, which is an important factor in indices of malaria transmission such as the basic reproduction number and vectorial capacity. Results: Meteorological factors, such as precipitation and relative humidity, and human factors, such as population density and insecticide-treated nets, were important predictors of these three malaria vector species in Africa. Insecticide-treated net use was negatively associated with per capita vector abundance of the An. gambiae species complex and interacted with year to suggest a negative effect on the ratio of An. gambiae s.s. to An. arabiensis at the end of the prediction period that extended from 2002 to 2020. A predicted increasing interannual trend for An. coluzzii was potentially caused by changing species identification methods. Conclusions: The predicted equilibrium abundances of the three species showed potentially high levels of geographical overlap, niche overlap and evidence for stable coexistence despite substantial interspecific competition. Improving collection of longitudinal species abundance data across the spatial range of the An. gambiae species complex will facilitate future explorations of causal hypotheses that relate vector abundance to control measures, malaria interventions and meteorological conditions.

The multivariate sequential ordinal model is investigated for use in the Bayesian analysis of spatio-temporal ordinal data. The sequential ordinal model likelihood is equivalent to a binary model conditional on unknown regression coefficients and spatio-temporal random effects. Therefore, estimation and prediction in the space-time context can proceed using the well-established dynamic generalised linear model framework. Moreover, the sequential ordinal model avoids the ordering constraints on the threshold parameters that determine the category break points required by cumulative ordinal models, and so simplifies the estimation procedure for high-dimensional space-time applications using Bayesian inference. The dynamic spatio-temporal sequential ordinal model is applied to estimate foliage cover abundance of four actively managed invasive alien species. These invasive weed species are observed by means of a modified Braun-Blanquet score that is commonly used in vegetation studies and constitutes ordinal data. The multivariate ordinal data for the managed weeds species are sparsely distributed in space and time with few observations recorded in high foliage cover categories. A separable model for space-time dependence that maintains parameter interpretability in the presence of aggregated ordinal categories is therefore developed. Estimation and prediction is demonstrated using integrated nested Laplace approximation (INLA) methods developed for univariate spatio-temporal models. Bayesian estimation and prediction shows that the four invasive weed species differentially respond to habitat type, control effort and accessibility, and share similar magnitudes of dependence with short effective spatial ranges and strong temporal autocorrelations.

A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are accommodated. A sufficient condition for the local asymptotic stability of a coexistence equilibrium in this system is then proven. Using this system, the generalisation of the Beverton-Holt and Leslie-Gower models of competition to multispecies systems with possible maturation delays is presented and shown to yield interesting stability properties. The stability of coexistence depends on the relative abundances of the species at the unique interior equilibrium. A sufficient condition for local stability is derived that only requires intraspecific competition to outweigh interspecific competition. The condition does not depend on maturation delays. The derived stability properties are used to develop a novel estimation approach for the coefficients of interspecific competition. This approach finds an optimal configuration given two conjectures. First, coexisting species strive to outcompete competitors. Second, persisting species are more likely in stable systems with strong dampening of perturbations and high ecological resilience. The optimal solution is compared to estimates of niche overlap using an empirical example of malaria mosquito vectors with delayed maturity in the Anopheles gambiae sensu lato species complex.

Mozzie enables simulation of the lifecycle and spatial spread of mosquitoes. Mozzie can be used to assess risks associated with disease-control strategies at local, regional or continental scales. Most particularly, strategies involving genetic alterations of mosquitoes to eliminate malaria, are of prime interest.

Background: The dynamics of vector borne disease transmission depend on the abundances of vectors. The dominant malaria vector species complex of Anopheles gambiae sensu lato is a target of vector control strategies designed to reduce and eliminate malaria transmission. The three most widely distributed dominant malaria vectors within the species complex are An. arabiensis, An. coluzzii and An. gambiae sensu stricto . Methods: Previous studies across the extent of the species complex range have been restricted to annual predictions of species occurrence or relative abundance. This study incorporated relative abundance data at the species level and abundance data at the species complex level to estimate and predict daily equilibrium vector abundances of each species. Statistical models with interpretable parameters were used to gain insight into how factors such as meteorological conditions, insecticide treated net use, and human density affect the spatial and temporal predictions. The statistical models were used to predict daily equilibrium vector abundance that is an important factor in indices of malaria transmission such as the basic reproduction number and vectorial capacity. Results: Meteorological factors, such as precipitation and relative humidity, and human factors, such as population density and insecticide treated nets, were important predictors of these three malaria vector species in Africa. Insecticide treated net use was negatively associated with per capita vector abundance of the An. gambiae species complex and interacted with year to suggest an a negative effect on the ratio of An. gambiae s.s . to An. arabiensis at the end of the prediction period that extended from 2002 to 2020. A predicted increasing interannual trend for An. coluzzii was potentially caused by changing species identification methods. Conclusion: The predicted equilibrium abundances of the three species showed potentially high levels of geographical overlap, niche overlap, and evidence for stable coexistence despite substantial interspecific competition. Improving collection of longitudinal species abundance data across the spatial range of the An. gambiae species complex will facilitate future explorations of causal hypotheses that relate vector abundance to control measures, malaria interventions and meteorological conditions.

A statistical method for the elicitation of priors in Bayesian generalised linear models (GLMs) and extensions is proposed. Probabilistic predictions are elicited from the expert to parametrise a multivariate t prior distribution for the unknown linear coefficients of the GLM and an inverse gamma prior for the dispersion parameter, if unknown. The elicited predictions condition on defined elicitation scenarios. Dependencies among scenarios are then elicited from the expert by additionally conditioning on hypothetical experiments. Elicited conditional medians efficiently parametrise a canonical vine copula model of dependence that may be truncated for efficiency. The statistical elicitation method permits prior parametrisation of GLMs with alternative choices of design matrices or observation models from the same elicitation session. Extensions of the method apply to multivariate data, data with bounded support, semi-continuous data with point mass at zero, and count data with overdispersion or zero-inflation. A case study elicits a prior for an extended GLM embedded in a statistical model of overdispersed counts described by a binomial-simplex mixture distribution. The elicited canonical vine model of dependence is found to incorporate substantial information into the prior. The procedures of the statistical elicitation method are implemented in the R package eglm.

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.

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 taking 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.