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Introduced populations in a stochastic world
Nicolas Bajeux, Frédéric Grognard, Ludovic Mailleret, Vincent Calcagno
To cite this version:
Nicolas Bajeux, Frédéric Grognard, Ludovic Mailleret, Vincent Calcagno. Introduced populations in a stochastic world. 10. Models in Population Dynamics and Ecology (CMPDE 16), Aix Marseille Université (AMU). FRA., Sep 2016, Marseille, France. �hal-02738988�
Introduced populations in a stochastic world
Nicolas Bajeux, Fr´ed´eric grognard, Ludovic Mailleret & Vincent Calcagno
INRIA Sophia-Antipolis, BIOCORE Team. INRA Sophia-Antipolis, M2P2 Team
Modelling the dynamics of introduced populations is a challenge of main importance in conservation and restoration biology. By assuming that in-troductions may occur repeatedly, we provide a model in which the popula-tion growth is represented by an Ordinary Differential Equapopula-tion. Populapopula-tion growth is disrupted by discrete time introduction events that are stochasti-cally distributed in propagule size and over time.
Because the considered introduction schemes involve essentially small population sizes, the model can include strong demographic Allee effects, which implies that a population is doomed to extinction when its size is below some threshold. Moreover, invasion success can be hampered by en-vironmental stochasticity, such as the occurence of catastrophes caused by external factors, that can drastically reduce the number of individuals in the population. This is also included in the model.
Assuming constant propagule pressure, i.e. the mean number of individu-als introduced by unit time is constant, we investigated introduction schemes over a trade-off ranging from frequent and small sizes introductions to rarer and larger ones. The computation of the probability to reach a target size leads to an integral equation of the Mean First Passage Time (MFPT) to reach the target. A fixed point study proved that there exists a unique so-lution to this equation, which can be numerically computed to identify the introduction strategy leading to the population target size in least time.
To comfort our investigation, we proceed in a numerical computation of the MFPT using Monte Carlo numerical solutions of a purely stochastic model representing the population growth with a birth-death process.
Literature reports that, in case of strong demographic Allee effects, it is preferable to favor rare and large introductions. Here we show how envi-ronmental stochasticity arising as catastrophes, coupled to stochastic fluctua-tions in propagule size and introduction timing, make intermediate strategies able to minimize the time to population establishment.
