Sebastian Schreiber
@sebastianschreiber
Population biologist and mathematician wrestling with the complexities of nature armed with the theories of stochastic processes and dynamical systems. Dynamics of Ecological and Evolutionary Processes Lab
If the environment is ever "inhospitable", then asymptotic extinction occurs with probability one. One can use this classification to analytically identify the different demographic outcomes for mechanistic models of mate limiation and predator saturation 9/9
In addition to depending on the initial density, the asymptotic extinction probability depends on the initial environmental state and the rate at which the environment switches relative to the demographic rates. 8/n
If the initial density lies between the minimal and maximal Allee threshold, then there are complementary, positive probabilities of going asymptotically extinct or persisting. 7/n
Alternatively, if there is no environmental mismatch, the population fate depends on the initial density. If this density is below the minimal Allee threshold, asymptotic extinction occurs with probability one. If it is above the maximal Allee threshold, persistence occurs with probability one. 6/n
If the minimal carrying capacity in one environmental state is below the maximal Allee threshold in a different environmental state, then asumptotic extinction occurs with probability one. I call this "environmental (or demographic) mismatch". 5/n
One can use, PDMPs (piecewise deterministic Markov processes), to model the impacts of bounded, autocorrelated noise. In these models, the environment fluctuates between a finite number of states. If there is a strong Allee effect for all environmental states, one can prove a dichotomy. 4/n
Classical deterministic models show that Allee effects can generate alterantive stable states (extinction & persistence). However, when adding environmental stochasticity in a white noise form asymptotic extinction is inevitable. But these SDEs assume uncorrelated, unbounded environmental noise 3/n
For context, Allee effects occurs when per-capita growth rates increase with density (at least at low densities). This can occur due to mate limitation, predator saturation, or cooperative behavior. 2/n
Had a great time at the #SIAM2026 in #Cleveland . Met colleagues, heard great talks, & gave a talk about "bounded environmental stochasticity drives secondary allee thresholds" based on recent JTB paper (see bsky.app/profile/seba...) Main conclusions shown below. More details in this thread. 1/n
After a lovely hike in Stebbins Cold Canyon, did a few drawings including #trapinch from #pokédex, a scene from my #moomin cup (filled with darjeeling tea), and a #spider #penandink #crosshatching
Another moment of Baymax madness. Riding a hammerhead shark today. #penandink #shark #baymax #hammerhead
Some @tamu.bsky.social College Station memories: the math building, the amazing drinks at the Carport, and Buc-ees #penandink #cappuccino
Finished my 825 minutes of lectures at the Texas A&M workshop and finally had time to draw !!! ✍️ Snivy :) I will get a good scan when I am back home #pokédex #penandink #snivy
Pepe approves of the cork oaks dropping their winter leaves
After doing a bunch of editorial work and evaluating applications for a research award, took a break and did an #penandink drawing of #seedot from the #pokémon #pokédex Next, writing some #Rcode and #notes for the upcoming Stochastic Dynamics in Biology workshop at @tamu.bsky.social
My favorite quote about #chaos which was discovered without the help of computers by Henri Poincaré. Quote from his fantastic book, Science and Method (1908)
A #penandink #drawing of #wailmer from #pokédex for my niece's birthday 😆
Morning #sketch of #mudkip from #Pokédex. Trying to do a few of these type sketches each week, with regular inspiration from the amazing work of @pearlstardust.bsky.social
So nice having finals over. Indulging in drawing more. #penandink #endofquarter #drawing
This is what happens when you proctor exams for four hours for 1000+ students in a very large lecture hall
Baymax stole one of these inked sardines and is looking forward to a salty feast :D #baymax #penandink #sardines