Buongiorno vi giro l'annuncio del OWPS di domani (notate che nella mail scrivono June 25 ma poi hanno mandato una seconda mail di rettifica). Buona giornata Alessandra

---------- Forwarded message --------- Da: One World Probability ow.probability@gmail.com Date: mer 23 giu 2021 alle ore 08:14 Subject: [owps] OWPS Talks June 25 To: owps@lists.bath.ac.uk

Dear All,

Thursday June 25 we have a session on Probability Theory and Population Genetics, Speakers: Cornelia Pokalyuk and Anton Wakolbinger.

This is the last session before the summer break!

(Note: the time is in UTC. Due to time changes, you should check what that translates to in your location) ------------------------------------------------

(14:00-16:00 UTC) Speakers: Cornelia Pokalyuk and Anton Wakolbinger

Fixation of slightly beneficial alleles from a backward and a forward perspective Cornelia Pokalyuk and Anton Wakolbinger (Goethe Universität Frankfurt)

For a slightly beneficial mutant whose mean offspring number is by a factor 1+s larger than that of the wild types, the probability of being established in a large population is \approx 2s/v^2, where v^2 is the offspring variance. This approximation has been derived (for v^2=1) by Haldane (1927). In our tandem talk we will present some mathematics behind and beyond Haldane's formula within the class of Cannings models (which in the neutral case generalize the prototypic Wright-Fisher model from multinomial to exchangeable offspring numbers). It turns out that for ``moderately strong'' selection the {\em forward perspective} of the Galton-Watson approximation helps to prove the Haldane asymptotics in the large population limit, whereas for ``moderately weak'' selection a {\em backward perspective} is appropriate, which relies on an ancestral selection graph in discrete time. These parts of the presentation are based on F. Boenkost, A. Gonz\’alez Casanova, C.P., A.W., Haldane's formula in Cannings models:

- The case of moderately weak selection, Electron. J. Probab. 26(4) (2021)

- The case of moderately strong selection, arXiv:2008.02225 [1] [math.PR], submitted.

In the last part of the talk we will give an outlook on work in progress on analoga of Haldane's formula for a class of Cannings models with asymptotically infinite offspring variance.

A. Introduction Anton Wakolbinger

B. Forwards perspective Cornelia Pokalyuk

C. Backwards perspective Anton Wakolbinger

D. Outlook Cornelia Pokalyuk

The Zoom link is on the OWPS webpage. It can also be accessed directly via

https://tum-conf.zoom.us/j/67179046628 https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Ftum-conf.zoom.us%2Fj%2F67179046628&data=04%7C01%7Cowps%40lists.bath.ac.uk%7Ca3166538925e4992f4ba08d9360e08ec%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637600256273938672%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=wKK8TcOiD0IQOkvX7BOWWnI%2BS24znmmpwM5eU0ktUNQ%3D&reserved=0

Meeting ID:671 7904 6628

Passcode: 160041

Best wishes, Julien and Nina