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Using optimal transport theory to estimate transition probabilities in metapopulation dynamics

Ecological Modelling

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https://doi.org/10.1016/j.ecolmodel.2017.06.003

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Abstract

This work considers the estimation of transition probabilities associated with populations moving among multiple spatial locations based on numbers of individuals at each location at two points in time. The problem is generally underdetermined as there exists an extremely large number of ways in which individuals can move from one set of locations to another. A unique solution therefore requires a constraint. The theory of optimal transport provides such a constraint in the form of a cost function, to be minimized in expectation over the space of possible transition matrices. We demonstrate the optimal transport approach on marked bird data and compare to the probabilities obtained via maximum likelihood estimation based on marked individuals. It is shown that by choosing the squared Euclidean distance as the cost, the estimated transition probabilities compare favorably to those obtained via maximum likelihood with marked individuals. Other implications of this cost are discussed, including the ability to accurately interpolate the population's spatial distribution at unobserved points in time and the more general relationship between the cost and minimum transport energy.

Additional publication details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Using optimal transport theory to estimate transition probabilities in metapopulation dynamics
Series title:
Ecological Modelling
DOI:
10.1016/j.ecolmodel.2017.06.003
Volume:
359
Year Published:
2017
Language:
English
Publisher:
Elsevier
Contributing office(s):
Patuxent Wildlife Research Center
Description:
9 p.
First page:
311
Last page:
319