  Sexually reproducing populations with small number of individuals may go
extinct by stochastic fluctuations in sex determination, causing all their
members to become male or female in a generation. In this work we calculate the
time to extinction of isolated populations with fixed number $N$ of individuals
that are updated according to the Moran birth and death process. At each time
step, one individual is randomly selected and replaced by its offspring
resulting from mating with another individual of opposite sex; the offspring
can be male or female with equal probability. A set of $N$ time steps is called
a generation, the average time it takes for the entire population to be
replaced. The number k of females fluctuates in time, similarly to a random
walk, and extinction, which is the only asymptotic possibility, occurs when k=0
or k=N. We show that it takes only one generation for an arbitrary initial
distribution of males and females to approach the binomial distribution. This
distribution, however, is unstable and the population eventually goes extinct
in 2^N/N generations. We also discuss the robustness of these results against
bias in the determination of the sex of the offspring, a characteristic
promoted by infection by the bacteria Wolbachia in some arthropod species or by
temperature in reptiles.

Populations and Evolution;Data Analysis, Statistics and Probability