English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper is devoted to the analysis of a simple Lotka-Volterra food chainevolving in a stochastic environment. It can be seen as the companion paper ofHening and Nguyen (J. of Math. Biol. `18) where we have characterized thepersistence and extinction of such a food chain under the assumption that thereis no intraspecific competition among predators. In the current paper we focuson the case when all the species experience intracompetition. The food chain weanalyze consists of one prey and $n-1$ predators. The $j$th predator eats the$j-1$st species and is eaten by the $j+1$st predator; this way each speciesonly interacts with at most two other species - the ones that are immediatelyabove or below it in the trophic chain. We show that one can classify, based onthe invasion rates of the predators (which we can determine from theinteraction coefficients of the system via an algorithm), which species goextinct and which converge to their unique invariant probability measure. Weobtain stronger results than in the case with no intraspecific competitionbecause in this setting we can make use of the general results of Hening andNguyen (Ann. of Appl. Probab.). Unlike most of the results available in theliterature, we provide an in depth analysis for both non-degenerate anddegenerate noise.  We exhibit our general results by analysing trophic cascades in aplant--herbivore--predator system and providing persistence/extinction criteriafor food chains of length $n\leq 3$.

Persistence in Stochastic Lotka--Volterra food chains with intraspecific competition