BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexandru Hening (Texas A&M University) DTSTART:20230323T163000Z DTEND:20230323T170000Z DTSTAMP:20260421T124007Z UID:MoRN/71 DESCRIPTION:Title: Po pulation dynamics under environmental and demographic stochasticity\nb y Alexandru Hening (Texas A&M University) as part of Seminar on the Mathem atics of Reaction Networks\n\n\nAbstract\nThis work looks at the long term dynamics of diffusion processes modelling a single species that experienc es both demographic and environmental stochasticity. In this setting\, the long term dynamics of the population in the absence of demographic stocha sticity 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 analy ze the quasi-stationary distribution (QSD) $\\mu_\\epsilon$ of the system. \n\nWe 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 significan t effect of environmental stochasticity – it turns an exponentially long mean extinction time to a sub-exponential one.\n LOCATION:https://researchseminars.org/talk/MoRN/71/ END:VEVENT END:VCALENDAR