Mathematical models of short-range dispersal in defoliating lepidopterans

The gypsy moth (Lymantria dispar) is among the most destructive invasive species in North America, responsible for defoliating millions of hectares of oak forest. The spatial dynamics of defoliating lepidopteran populations, such as those of the gypsy moth, are thus of great interest to forestry and conservation efforts. Despite numerous studies on the long-range dispersal patterns of defoliators, there is comparatively little theoretical understanding or field research concerning short-range dispersal via ballooning. Previous studies of ballooning have assumed random diffusion, but these models cannot account for non-random biases, such as the effect of wind on the angle of dispersal.Here, I develop models of short-range dispersal in larvae via ballooning, informed by methods from the seed dispersal kernel literature. I then fit models to field data of gypsy moth larvae dispersal using MCMC to perform Bayesian inference, and PSIS-LOO to perform model selection. I found that dispersal kernel models are able to reliably detect biases in angle of dispersal due to wind direction, and allow for testing of correlations between experimental variables and measures of dispersal. These modeling methods can help inform future studies into short-range larval dispersal and provide a novel framework with which to analyze dispersal data.

Measuring splash-dispersal of a major wheat pathogen in the field

Capacity for dispersal is a fundamental fitness component of plant pathogens. Empirical characterization of plant pathogen dispersal is of prime importance for understanding how plant pathogen populations change in time and space. We measured dispersal of Zymoseptoria tritici in natural environment. Primary disease gradients were produced by rain-splash driven dispersal and subsequent transmission via asexual pycnidiospores from infected source. To achieve this, we inoculated field plots of wheat (Triticum aestivum) with two distinct Z. tritici strains and a 50/50 mixture of the two strains. We measured effective dispersal of the Z. tritici population based on pycnidia counts using automated image analysis. The data were analyzed using a spatially-explicit mathematical model that takes into account the spatial extent of the source. We employed robust bootstrapping methods for statistical testing and adopted a two-dimensional hypotheses test based on the kernel density estimation of the bootstrap distribution of parameter values. Genotyping of re-isolated pathogen strains with strain-specific PCR-reaction further confirmed the conclusions drawn from the phenotypic data. The methodology presented here can be applied to other plant pathosystems.We achieved the first estimates of the dispersal kernel of the pathogen in field conditions. The characteristic spatial scale of dispersal is tens of centimeters – consistent with previous studies in controlled conditions. Our estimation of the dispersal kernel can be used to parameterize epidemiological models that describe spatial-temporal disease dynamics within individual wheat fields. The results have the potential to inform spatially targeted control of crop diseases in the context of precision agriculture.

Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between ‘spatial' and ‘non-spatial' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.

Using spatial genetics to quantify mosquito dispersal for control programs

BackgroundHundreds of millions of people get a mosquito-borne disease every year, of which nearly one million die. Mosquito-borne diseases are primarily controlled and mitigated through the control of mosquito vectors. Accurately quantified mosquito dispersal in a given landscape is critical for the design and optimization of the control programs, yet the field experiments that measure dispersal of mosquitoes recaptured at certain distances from the release point (mark-release-recapture MRR studies) are challenging for such small insects and often unrepresentative of the insect’s true field behavior. Using Singapore as a study site, we show how mosquito dispersal patterns can be characterized from the spatial analyses of genetic relatedness among individuals sampled over a short time span without interruption of their natural behaviors.Methods and FindingsWe captured ovipositing females of Aedes aegypti, a major arboviral disease vector, across floors of high-rise apartment blocks and genotyped them using thousands of genome-wide SNP markers. We developed a methodology that produces a dispersal kernel for distance that results from one generation of successful breeding (effective dispersal), using the distances separating full siblings, 2nd and 3rd degree relatives (close kin). In Singapore, the estimated dispersal distance kernel was exponential (Laplacian), giving the mean effective dispersal distance (and dispersal kernel spread σ) of 45.2 m (95%CI: 39.7-51.3 m), and 10% probability of dispersal >100 m (95%CI: 92-117 m). Our genetic-based estimates matched the parametrized dispersal kernels from the previously reported MRR experiments. If few close-kin are captured, a conventional genetic isolation-by-distance analysis can be used, and we show that it can produce σ estimates congruent with the close-kin method, conditioned on the accurate estimation of effective population density. We also show that genetic patch size, estimated with the spatial autocorrelation analysis, reflects the spatial extent of the dispersal kernel ‘tail’ that influences e.g. predictions of critical radii of release zones and Wolbachia wave speed in mosquito replacement programs.ConclusionsWe demonstrate that spatial genetics (the newly developed close-kin analysis, and conventional IBD and spatial autocorrelation analyses) can provide a detailed and robust characterization of mosquito dispersal that can guide operational vector control decisions. With the decreasing cost of next generation sequencing, acquisition of spatial genetic data will become increasingly accessible, and given the complexities and criticisms of conventional MRR methods, but the central role of dispersal measures in vector control programs, we recommend genetic-based dispersal characterization as the more desirable means of parameterization.

Spatially-explicit modeling improves empirical characterization of dispersal: theory and a case study

Dispersal is a key ecological process. An individual dispersal event has a source and a destination, both are well localized in space and can be seen as points. A probability to move from a source point to a destination point can be described by a dispersal kernel. However, when we measure dispersal, the source of dispersing individuals is usually an area, which distorts the shape of the dispersal gradient compared to the dispersal kernel. Here, we show theoretically how different source geometries affect the gradient shape depending on the type of the kernel. We present an approach for estimating dispersal kernels from measurements of dispersal gradients independently of the source geometry. Further, we use the approach to achieve the first field measurement of dispersal kernel of an important fungal pathogen of wheat, Zymoseptoria tritici. Rain-splash dispersed asexual spores of the pathogen spread on a scale of one meter. Our results demonstrate how analysis of dispersal data can be improved to achieve more rigorous measures of dispersal. Our findings enable a direct comparison between outcomes of different experiments, which will allow to acquire more knowledge from a large number of previous empirical studies of dispersal.

The total dispersal kernel: a review and future directions

The distribution and abundance of plants across the world depends in part on their ability to move, which is commonly characterized by a dispersal kernel. For seeds, the total dispersal kernel (TDK) describes the combined influence of all primary, secondary and higher-order dispersal vectors on the overall dispersal kernel for a plant individual, population, species or community. Understanding the role of each vector within the TDK, and their combined influence on the TDK, is critically important for being able to predict plant responses to a changing biotic or abiotic environment. In addition, fully characterizing the TDK by including all vectors may affect predictions of population spread. Here, we review existing research on the TDK and discuss advances in empirical, conceptual modelling and statistical approaches that will facilitate broader application. The concept is simple, but few examples of well-characterized TDKs exist. We find that significant empirical challenges exist, as many studies do not account for all dispersal vectors (e.g. gravity, higher-order dispersal vectors), inadequately measure or estimate long-distance dispersal resulting from multiple vectors and/or neglect spatial heterogeneity and context dependence. Existing mathematical and conceptual modelling approaches and statistical methods allow fitting individual dispersal kernels and combining them to form a TDK; these will perform best if robust prior information is available. We recommend a modelling cycle to parameterize TDKs, where empirical data inform models, which in turn inform additional data collection. Finally, we recommend that the TDK concept be extended to account for not only where seeds land, but also how that location affects the likelihood of establishing and producing a reproductive adult, i.e. the total effective dispersal kernel.

Replicated point processes with application to population dynamics models

In this paper we study spatially clustered distribution of individuals using point process theory. In particular we discuss the spatially explicit model of population dynamics of Shimatani (2010) which extend previous works on Malécot theory of isolation by distance. We reformulate Shimatani model of replicated Neyman-Scott process to allow for a general dispersal kernel function and we show that the random immigration hypothesis can be substituted by the long dispersal distance property of the kernel. Moreover, the extended framework presented here is fit to handle spatially explicit statistical estimators of genetic variability like Moran autocorrelation index, Sørensen similarity index, average kinship coefficient. We discuss the pivotal role of the choice of dispersal kernel for the above estimators in a toy model of dynamic population genetics theory.

Dynamics of a Nonlocal Dispersal Model with a Nonlocal Reaction Term

In this paper, we study a class of nonlocal dispersal problem with a nonlocal term arising in population dynamics: [Formula: see text] where [Formula: see text] is a bounded domain, [Formula: see text], [Formula: see text] represents the nonlocal dispersal operator with continuous and non-negative dispersal kernel. The kernel [Formula: see text] is assumed to be non-negative and is allowed to have a degeneracy in a smooth subdomain [Formula: see text] of [Formula: see text]. When [Formula: see text] is either positive or vanishes in a subdomain, we respectively investigate the existence, multiplicity and asymptotical stability of positive steady states under the local/global variation of parameter by means of sub-supersolution method, Lyapunov–Schmidt reduction, and bifurcation theory.