Check out this thread from @sebastianschreiber.bsky.social on his course on #MathematicalMethodsinPopulationBiology. I am looking forward to seeing the topics covered in the class and the great illustrations of concepts from population bio. 🧪

RE: https://bsky.app/profile/did:plc:2puakrcswobz3vkbzsoyw4rr/post/3lgf3wdyamc2c

In Lecture 20 (final lecture!) in #MathematicalMethodsInPopulationBiology discussed analysis of nonlinear, stochastic difference equations using invasion growth rates (Lyapunov exponents) with applications to population viability and the storage effect

Of course had to discuss the zehn deutsche mark after presenting the CLT in #MathematicalMethodsInPopulationBiology

On Lecture 19 of #MathematicalMethodsInPopulationBiology continued discussed geometric random walks, the central limit theorem, and applications to population growth, population genetics, and bet-hedging

In Lecture 18 of #MathematicalMethodsInPopulationBiology discussed random walks S(n)=S(0)+X(1)+…+X(n) where X(1),X(2),… are i.i.d, the law of large numbers, and applications to vulture movement, population growth (D(n)=f(n)D(n-1)) and haploid genetics (Y(n)=fA(n)Y(n-1)/(fA(n)Y(n-1)+fB(n)(1-Y(n-1)). Breakout groups on an example where E[f(n)]>1 but E[log(f(n))]<0. Was lots of fun hearing the students trying to work out what these apparently contradictory statements mean for population growth.

Lecture 17’s quote of the day for #MathematicalMethodsInPopulationBiology was from @tao

In Lecture 17 of #MathematicalMethodsInPopulationBiology discussed absorption times and probabilities for discrete-time Markov chains and briefly discussed continuous-time Markov chains. Did a break out on computing stage-dependent life expectancies

As suggested by @petrelharp for my last #MathematicalMethodsInPopulationBiology toot, I redrew the rhino to be bucking probabilistic conventions

In Lecture 16 on #MathematicalMethodsInPopulationBiology discussed irreducibility, periodicity of states, primitive = aperiodic + irreducible, convergence in probability to the stationary distribution for aperiodic+irreducible, finite-state Markov chains, and strong law for irreducible, finite-state Markov chains

In Lecture 15 of #MathematicalMethodsInPopulationBiology began discussion on finite-state Markov chains, transition matrices with a non-traditional convention for ease of relaing to earlier matrix model results, the Chapman-Kolmogorov equations, and applications to SIS dynamics, Wright-Fisher, gambler's ruin, and rain in Davis. The students did break out work on a simplified model of human emotions.