Population dynamics under environmental and demographic stochasticity

Abstract: This work looks at the long term dynamics of diffusion processes modelling a single species that experiences both demographic and environmental stochasticity. In this setting, the long term dynamics of the population in the absence of demographic stochasticity is determined by the sign of $\Lambda_0$ , the external Lyapunov exponent: $\Lambda_0<$ implies (asymptotic) extinction and $\Lambda_0>$ implies convergence to a unique positive stationary distribution $\mu_0$. If the system is of size $\frac{1}{\epsilon^2}$ for small $\epsilon>0$, the extinction time is finite almost surely. One must therefore analyze the quasi-stationary distribution (QSD) $\mu_\epsilon$ of the system.

We look at what happens when the population size is sent to infinity, i.e., when $\epsilon\to 0$. In contrast to models that only take into account demographic stochasticity, our results demonstrate the significant effect of environmental stochasticity – it turns an exponentially long mean extinction time to a sub-exponential one.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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