Parameter Estimation in a PDE Model for the Spatial Spread of Cocoa Black Pod Disease

Fomba, Christian Gaele Nembot; Hoopen, Gerben Martijn Ten; Soubeyrand, Samuel; Roques, Lionel; Ambang, Zachée; Soh, Patrice Takam

doi:10.1007/s11538-021-00934-z

Cited by 4 publications

(9 citation statements)

References 32 publications

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“…The third class of methods make use of specific mathematical modelling to infer dispersal from observations of ongoing dynamics (Soubeyrand et al, 2009a; Rieux et al, 2013; Bousset et al, 2015; Grosdidier et al, 2018). If phenomenological models can hardly disentangle the observed data from the dispersal process per se , mechanistic-statistical models do so and enable a proper inference of dispersal using spatio-temporal datasets (Wikle, 2003a; Soubeyrand et al, 2009a; Roques et al, 2011; Soubeyrand and Roques, 2014; Hefley et al, 2017; Nembot Fomba et al, 2021). These models allow for the parsimonious representation of both growth and dispersal processes in heterogenous environments (Papaïx et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

“…Whereas reaction-diffusion equations have been classically used to describe biological invasions, their incorporation into mechanistic-statistical approaches to estimate parameters of interest from spatio-temporal data essentially dates back to the early 2000s. Examples include the study of the invasion processes of the House Finch bird over the eastern United States (Wikle, 2003a), the pine processionary moth in France (Roques et al, 2011; Soubeyrand and Roques, 2014), the wolf in Eastern France (Louvrier et al, 2020) and the spread of the black pod disease in a cocoa plot (Nembot Fomba et al, 2021). By contrast to reaction-diffusion equations, integro-differential equations rely on dispersal kernels, individuals being redistributed according to the considered kernel (Fife, 1996; Hutson et al, 2003; Kolmogorov et al, 1937).…”

Section: Introductionmentioning

confidence: 99%

“…Despite being a major issue in biology, properly characterising the dispersal kernels is a challen-ging task for many species, especially when dispersing individuals are numerous, small (and thus difficult to track) and move far away (Nathan, 2001). In that quest, mechanistic-statistical models enable a proper inference of dispersal using spatio-temporal datasets (Wikle, 2003a; Soubeyrand et al, 2009a; Roques et al, 2011; Soubeyrand and Roques, 2014; Hefley et al, 2017; Nembot Fomba et al, 2021) while allowing for the parsimonious representation of both growth and dispersal processes in heterogenous environments (Papäıx et al, 2022). They require detailed knowledge of the biology of the species of interest to properly model the invasion process.…”

Section: Introductionmentioning

confidence: 99%

“…Des-pite their long standing history, the incorporation of reaction-diffusion equations into mechanistic-statistical approaches to estimate parameters of interest from spatio-temporal data essentially dates back to the early 2000s ( e.g. Wikle, 2003a; Soubeyrand and Roques, 2014; Louvrier et al, 2020; Nembot Fomba et al, 2021). By contrast to reaction-diffusion equations, integro-differential equa-tions encode trajectories modelled by jump diffusion processes and rely on dispersal kernels, in-dividuals being redistributed according to the considered kernel (Fife, 1996; Hutson et al, 2003; Kolmogorov et al, 1937).…”

Section: Introductionmentioning

confidence: 99%

“…g . Wikle, 2003a; Soubeyrand and Roques, 2014; Louvrier et al, 2020; Nembot Fomba et al, 2021). By contrast to reaction-diffusion equations, integro-differential equations encode trajectories modelled by jump diffusion processes and rely on dispersal kernels, individuals being redistributed according to the considered kernel (Fife, 1996; Hutson et al, 2003; Kolmogorov et al, 1937).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A mechanistic-statistical approach to infer dispersal and demography from invasion dynamics, applied to a plant pathogen

Saubin

Coville

Xhaard

et al. 2023

Preprint

Self Cite

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1- Dispersal, and in particular the frequency of long-distance dispersal (LDD) events, has strong implications for population dynamics, with possibly the acceleration of the colonisation front, and evolution, with possibly the conservation of genetic diversity along the colonised domain. However, accurately inferring LDD is challenging as it requires both large-scale data and a methodology that encompasses the redistribution of individuals in time and space. 2- Here, we propose a mechanistic-statistical framework to estimate dispersal of one-dimensional invasions. The mechanistic model takes into account population growth and grasps the diversity in dispersal processes by using either diffusion, leading to a reaction-diffusion (R.D.) formalism, or kernels, leading to an integro-differential (I.D.) formalism. The ID formalism considers different dispersal kernels (e.g. Gaussian, Exponential, and Exponential-power) differing in their frequency of LDD events. The statistical model relies on dedicated observation laws that describe two types of samples possibly gathered in space and time during the invasion (an overall survey and/or a refined examination of clumped samples) while taking into account the variability in both habitat suitability and occupancy perception. 3- We first check the identifiability of the parameters and the confidence in the selection of the dispersal process. We observed good identifiability for nearly all parameters (Correlation Coefficient > 0.95 between true and fitted values), except for occupancy perception (Correlation Coefficient = 0.83-0.85). The Exponential-Power (i.e. fat-tailed) kernel is the dispersal process most confidently identified. We then applied our framework to data describing an annual invasion of the poplar rust disease along the Durance River valley over nearly 200 km. This spatio-temporal survey consisted of 12 study sites examined at seven time points. We confidently estimated that the dispersal of poplar rust is best described by an Exponential-power kernel with a mean dispersal distance of 2.01 km and an exponent parameter of 0.24 characterising a fat-tailed kernel with frequent LDD events. 4- By considering the whole range of possible dispersal processes our method forms a robust inference method. It can be employed for a variety of organisms provided they are monitored in time and space along a one-dimension invasion.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A mechanistic-statistical approach to infer dispersal and demography from invasion dynamics, applied to a plant pathogen

Saubin

Coville

Xhaard

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

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Global Dynamics of a Spore Producing Pathogens Epidemic System with Nonlocal Diffusion Process

Djidjou‐Demasse

Lemdjo

Seydi

2022

Trends in Mathematics

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In this paper, we analyze a nonlocal spatial epidemic model presenting the diffusion process of a spore producing plant pathogens responsible of one of the most destructive cocoa pods disease. The global existence, compactness and dissipativity of the semiflow generated by the system are established. By defining a threshold number (the basic reproduction number), we first express conditions for the existence of non-trivial stationary states. Next, we show that the qualitative dynamics of the model range from the extinction (i.e. the global stability of the disease-free stationary state), to the persistence (i.e. the global stability of the endemic stationary state) of the epidemics. Finally, we go through some simulations of our general analysis.

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A mechanistic-statistical approach for the field-based study of invasion dynamics

Kishino

2023

PCI Math Comp Biol

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Dispersal, and in particular the frequency of long-distance dispersal (LDD) events, has strong implications for population dynamics with possibly the acceleration of the colonisation front, and for evolution with possibly the conservation of genetic diversity along the colonised domain. However, accurately inferring LDD is challenging as it requires both large-scale data and a methodology that encompasses the redistribution of individuals in time and space. Here, we propose a mechanistic-statistical framework to estimate dispersal from one-dimensional invasions. The mechanistic model takes into account population growth and grasps the diversity in dispersal processes by using either diffusion, leading to a reaction-diffusion (R.D.) formalism, or kernels, leading to an integro-differential (I.D.) formalism. The latter considers different dispersal kernels (e.g. Gaussian, Exponential, and Exponential-power) differing in their frequency of LDD events.The statistical model relies on dedicated observation laws that describe two types of samples, clumped or not. As such, we take into account the variability in both habitat suitability and occupancy perception. We first check the identifiability of the parameters and the confidence in the selection of the dispersal process. We observed good identifiability for nearly all parameters

show abstract

Parameter Estimation in a PDE Model for the Spatial Spread of Cocoa Black Pod Disease

Cited by 4 publications

References 32 publications

A mechanistic-statistical approach to infer dispersal and demography from invasion dynamics, applied to a plant pathogen

A mechanistic-statistical approach to infer dispersal and demography from invasion dynamics, applied to a plant pathogen

Global Dynamics of a Spore Producing Pathogens Epidemic System with Nonlocal Diffusion Process

A mechanistic-statistical approach for the field-based study of invasion dynamics

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