Mechanical-Statistical Modeling in Ecology: From Outbreak Detections to Pest Dynamics

Emerging strains of watermelon mosaic virus in Southeastern France: model-based estimation of the dates and places of introduction

Where and when alien organisms are successfully introduced are central questions to elucidate biotic and abiotic conditions favorable to the introduction, establishment and spread of invasive species. We propose a modelling framework to analyze multiple introductions by several invasive genotypes or genetic variants, in competition with a resident population, when observations provide knowledge on the relative proportions of each variant at some dates and places. This framework is based on a mechanistic-statistical model coupling a reaction–diffusion model with a probabilistic observation model. We apply it to a spatio-temporal dataset reporting the relative proportions of five genetic variants of watermelon mosaic virus (WMV, genus Potyvirus, family Potyviridae) in infections of commercial cucurbit fields. Despite the parsimonious nature of the model, it succeeds in fitting the data well and provides an estimation of the dates and places of successful introduction of each emerging variant as well as a reconstruction of the dynamics of each variant since its introduction.

Dating and localizing an invasion from post-introduction data and a coupled reaction-diffusion-absorption model

Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in particular in the intents of reconstructing the past dynamics of the alien organisms and predicting their future spatial extents. Partial differential equations offer a rich and flexible modeling framework that has been applied to a large number of invasions. In this article, we are specifically interested in dating and localizing the introduction that led to an invasion using mathematical modeling, post-introduction data and an adequate statistical inference procedure. We adopt a mechanistic-statistical approach grounded on a coupled reaction-diffusion-absorption model representing the dynamics of an organism in an heterogeneous domain with respect to growth. Initial conditions (including the date and site of the introduction) and model parameters related to diffusion, reproduction and mortality are jointly estimated in the Bayesian framework by using an adaptive importance sampling algorithm. This framework is applied to the invasion of Xylella fastidiosa, a phytopathogenic bacterium detected in South Corsica in 2015, France.

Regulation of forest defoliating insects through small mammal predation: reconsidering the mechanisms

Population densities of forest defoliating insects may be regulated by small mammal predation on the pupae. When outbreaks do occur, they often coincide with warm, dry weather and at barren forest sites. A proposed reason for this is that weather and habitat affect small mammal population density (numerical response) and hence pupal predation. We propose an alternative explanation: weather and habitat affect small mammal feeding behaviour (functional response) and hence the outbreak risks of forest pest insects. We report results from laboratory and field-enclosure experiments estimating rates of pupal predation by bank voles (Myodes glareolus) on an outbreak insect, the European pine sawfly (Neodiprion sertifer), at different temperatures (15 and 20 °C), in different microhabitats (sheltered and non-sheltered), and with or without access to alternative food (sunflower seeds). We found that the probability of a single pupa being eaten at 20 °C was lower than at 15 °C (0.49 and 0.72, respectively). Pupal predation was higher in the sheltered microhabitat than in the open one, and the behaviour of the voles differed between microhabitats. More pupae were eaten in situ in the sheltered microhabitat whereas in the open area more pupae were removed and eaten elsewhere. Access to alternative food did not affect pupal predation. The results suggest that predation rates on pine sawfly pupae by voles are influenced by temperature- and habitat-induced variation in the physiology and behaviour of the predator, and not necessarily solely through effects on predator densities as previously proposed.

Estimating the delay between host infection and disease (incubation period) and assessing its significance to the epidemiology of plant diseases

Knowledge of the incubation period of infectious diseases (time between host infection and expression of disease symptoms) is crucial to our epidemiological understanding and the design of appropriate prevention and control policies. Plant diseases cause substantial damage to agricultural and arboricultural systems, but there is still very little information about how the incubation period varies within host populations. In this paper, we focus on the incubation period of soilborne plant pathogens, which are difficult to detect as they spread and infect the hosts underground and above-ground symptoms occur considerably later. We conducted experiments on Rhizoctonia solani in sugar beet, as an example patho-system, and used modelling approaches to estimate the incubation period distribution and demonstrate the impact of differing estimations on our epidemiological understanding of plant diseases. We present measurements of the incubation period obtained in field conditions, fit alternative probability models to the data, and show that the incubation period distribution changes with host age. By simulating spatially-explicit epidemiological models with different incubation-period distributions, we study the conditions for a significant time lag between epidemics of cryptic infection and the associated epidemics of symptomatic disease. We examine the sensitivity of this lag to differing distributional assumptions about the incubation period (i.e. exponential versus Gamma). We demonstrate that accurate information about the incubation period distribution of a pathosystem can be critical in assessing the true scale of pathogen invasion behind early disease symptoms in the field; likewise, it can be central to model-based prediction of epidemic risk and evaluation of disease management strategies. Our results highlight that reliance on observation of disease symptoms can cause significant delay in detection of soil-borne pathogen epidemics and mislead practitioners and epidemiologists about the timing, extent, and viability of disease control measures for limiting economic loss.

A statistical-reaction-diffusion approach for analyzing expansion processes

In this article, we propose a method for analyzing the spatial variations in the range expansion of the pine processionary moth (PPM), an invasive species in France. Based on binary measurements - the presence or absence of PPM nests - the proposed method allows us to infer the local effect of the environment on PPM population expansion. This effect is estimated at each position x using a parameter F(x) that corresponds to the local PPM fitness. The data type and the two stage PPM life cycle make estimating this parameter difficult. To overcome these difficulties we adopt a mechanistic-statistical approach that combines a statistical model for the observation process with a hierarchical,reaction-diffusion based mechanistic model for the expansion process. Bayesian inference of the parameter F(x) reveals that PPM fitness is spatially heterogeneous and highlights the existence of large regions associated with lower fitness. The factors underlying this lower fitness are yet to be determined.

Spatiotemporal structure of host-pathogen interactions in a metapopulation

The ecological and evolutionary dynamics of species are influenced by spatiotemporal variation in population size. Unfortunately, we are usually limited in our ability to investigate the numerical dynamics of natural populations across large spatial scales and over long periods of time. Here we combine mechanistic and statistical approaches to reconstruct continuous-time infection dynamics of an obligate fungal pathogen on the basis of discrete-time occurrence data. The pathogen, Podosphaera plantaginis, infects its host plant, Plantago lanceolata, in a metapopulation setting where the presence of the pathogen has been recorded annually for 6 years in approximately 4,000 host populations across an area of 50 km x 70 km in Finland. The dynamics are driven by strong seasonality, with a high extinction rate during winter and epidemic expansion in summer for local pathogen populations. We are able to identify with our model the regions in the study area where overwintering has been most successful. These overwintering sites represent foci that initiate local epidemics during the growing season. There is striking heterogeneity at the regional scale in both the overwintering success of the pathogen and the encounter intensity between the host and the pathogen. Such heterogeneity has profound implications for the coevolutionary dynamics of the interaction.