The students absolutely nailed it, and I was genuinely surprised by how financially literate they were in interpreting the simulation results. People often forget how mathematics can be a tremendous help in making better, more informed decisions in everyday life!

In our session today, we wrapped up the activity by simulating the Gambler’s Ruin in R, using a popular scratchcard game as the example. The game costs £5 per card and has a win probability of roughly 1 in 3.3. One of the photos shows one of these simulations.

8/8 This study emphasizes the importance of considering recurrent mutations in highly diverse species for accurate population genetics inference.

(Abstract also available in European Portuguese).

7/8 To illustrate how mutation models can influence the quantification of forces other than drift, we further present a case study showing that the BM model exaggerates the intensity of selective constraints acting on the three codon positions of the bacterium Pseudomonas fluorescens.

6/8 We address these biases by proposing a Bayesian estimator for population size that accounts for recurrent mutations. You can find them here: github.com/mrborges23/m...

5/8 Our analyses further reveal that the BM model tends to overestimate the effective population size, particularly in bacteria, where estimated population sizes can be more than five times larger than those expected by the recurrent mutation model.

4/8 By examining mutation rates and effective population sizes across the Tree of Life, we demonstrate that the BM model remains valid for most species but significantly deviates in bacteria.

3/8 However, one can alternatively assume a recurrent mutation model (RM), which additionally considers mutations contributing to shifts in allele frequency.
In this study, we compare these two models.

2/8 A common assumption is that mutations are infrequent, so when a new mutation arises, the previous one has either become fixed or lost. This assumption implies that mutations occur exclusively at fixed sites and is referred to as the boundary mutation model (BM).

1/8 Mutations are fundamental for evolution, and their mathematical modelling in population genetics heavily relies on our perception of their frequency and the timescale over which they occur.