# What is the population limit that makes consanguinity an issue?

A recent incident brought in the news one of the last uncontacted people - the Sentinelese:

the Sentinelese appear to have consistently refused any interaction with the outside world.

There is significant uncertainty as to the group's size, with estimates ranging between 40 and 500 individual

If I understood correctly, the Sentinelese have a rather small population for dozens if not hundreds of generations and I am wondering if consanguinity is not issue (e.g. serious childhood effects) for them.

Question: What is the population limit (lower bound) that makes consanguinity an issue?

• Yes, inbreeding depression can be a big problem for very small populations (It's also a big problem for conservation efforts of critically endangered species, such as the Kakapo). Unfortunately, I can't really answer your specific question regarding lower bound. – Eff Dec 6 '18 at 8:14

I don't have a great knowledge in population genetics but I think your question can be answered by the relationship between loss of heterozygosity and the effective population size.

For an ideal asexually reproducing genetically diploid population, the heterozygosity is lost with increasing generations according to this equation:

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

where $$H_t$$ is the heterozygosity at the generation $$t$$, $$H_0$$ is the heterozygosity of initial population and $$N$$ is the population size.

If you analyse this equation then you'll note that heterozygosity exponentially reduces at rate inversely proportional to the population size.

For real populations you have to replace the population size with effective population size. Effective population size for a sexually reproducing population would be:

$$\frac{1}{N_e} = \frac{1}{4N_m} + \frac{1}{4N_f}$$

Where $$N_e$$ is effective population size, $$N_m$$ is number of males and $$N_f$$ is number of females.

You can find the derivation of these formulas in Principles of Population Genetics by Hartl and Clark.

Other than that, the probability of extinction is also higher, the smaller the population is.

When would consanguinity be an issue depends on other factors too such as initial heterozygosity, presence of deleterious alleles in the gene pool and other environmental factors. I don't think there is some kind of mathematical/practical lower bound. The minimum viable population is approximated using simulations.