Understanding Genetic Drift and Heterozygosity

Genetic drift refers to random fluctuations in allele frequencies within a population from one generation to the next. This process is driven by chance events, especially during reproduction.

A key consequence of genetic drift is the loss of genetic variation, specifically a reduction in heterozygosity over time. The strength of genetic drift is inversely proportional to population size; it is a much more potent force in smaller populations.

Comparing Population X and Population Y

We are given two populations:

• Population X: Size $N_X = 100$ individuals.
• Population Y: Size $N_Y = 10000$ individuals.

Both populations start with the same allele frequencies ($p=0.5$, $q=0.5$) and are observed after $t=1000$ generations.

Effect of Population Size on Drift and Heterozygosity

The rate at which genetic drift reduces heterozygosity is significantly influenced by population size ($N$). The expected heterozygosity after $t$ generations, $H_t$, can be approximated by the formula:

$H_t \approx H_0 \left(1 - \frac{1}{2N}\right)^t$

where $H_0$ is the initial heterozygosity.

• In smaller populations (like X, $N_X = 100$), the term $\frac{1}{2N_X}$ is larger ($\frac{1}{200}$). This means the factor $\left(1 - \frac{1}{2N_X}\right)$ is smaller, leading to a faster decline in heterozygosity.
• In larger populations (like Y, $N_Y = 10000$), the term $\frac{1}{2N_Y}$ is smaller ($\frac{1}{20000}$). This results in a larger factor $\left(1 - \frac{1}{2N_Y}\right)$, causing a slower decrease in heterozygosity.

Therefore, after 1000 generations, population X (smaller size) will experience a more pronounced effect of genetic drift, leading to a greater loss of heterozygosity compared to population Y (larger size).

Conclusion

Consequently, population Y, with its larger size, will retain a higher level of heterozygosity than population X after 1000 generations of genetic drift.