Modelling Population Dynamics in Realistic Landscapes with Linear Elements: A Mechanistic-Statistical Reaction-Diffusion Approach

Abstract

We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D) landscape crossed by linear one-dimensional (1D) corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid “2D/1D model”, i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape. Using the example of the range expansion of the tiger mosquito Aedes albopictus in France and its main highways as 1D corridors, we show that the model can be fitted to realistic observation data. We develop a mechanistic-statistical approach, based on the coupling between a model of population dynamics and a probabilistic model of the observation process. This allows us to bridge the gap between the data (3 levels of infestation, at the scale of a French department) and the output of the model (population densities at each point of the landscape), and to estimate the model parameter values using a maximum-likelihood approach. Using classical model comparison criteria, we obtain a better fit and a better predictive power with the 2D/1D model than with a standard homogeneous reaction-diffusion model. This shows the potential importance of taking into account the effect of the corridors (highways in the present case) on species dynamics. With regard to the particular case of A. albopictus, the conclusion that highways played an important role in species range expansion in mainland France is consistent with recent findings from the literature.

Using Early Data to Estimate the Actual Infection Fatality Ratio from COVID-19 in France

“…The mechanistic-statistical formalism, which is becoming standard in ecology [9][10][11] allows the analyst to couple a mechanistic model that describes a latent variable, here an ordinary differential equation model (ODE) of the SIR type, and uncertain, non-exhaustive data. To bridge the gap between the mechanistic model and the data, the approach uses a probabilistic model describing the data collection process.…”

Impact of Lockdown on the Epidemic Dynamics of COVID-19 in France

“…One of these approaches is based on the mechanistic-statistical formalism, which uses a probabilistic model to connect the data collection process and the latent variable described by the ODE model. Milestone articles and textbook have been written about this approach or related approaches (12), which is becoming standard in ecology (13,14). The application of this approach to human epidemiological data is still rare.…”

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“…Nevertheless, the advantage of the method presented here is that it can be easily generalized to general shaped domains and irregular distributions of detectors. Two immediate applications of our method can be the propagation of mosquitoes at country and city scale including corridor components [6] and modeling the evolution of environmental parameters in ecological systems due to the impact of climate change [11].…”

“…Also the propagation and proliferation of other types of viruses like the West Nile virus [3, 4] or the feline immunodeficiency virus [5], is studied using RD models. At metropolitan scale, the RD system is used to model the population dynamics of the tiger mosquito and has potential at the scale of a whole country [6]. Generalization to more than one population is constructed by coupling two or more RD equations, and is useful to explain the spread of seeds and animals.…”