Small population size
From Academic Kids

Species with a small population size are subject to a higher chance of extinction because their small population size makes them more vulnerable to genetic drift, resulting in stochastic variation in their gene pool, their demography and their environment.
Contents 
Demographic effects
The influence of stochastic (random) variation in demographic (reproductive and mortality) rates is much higher for small populations than large ones. Stochastic variation in demographic rates causes small populations to fluctuate randomly in size. The smaller the population the greater the probability that fluctuations will lead to extinction.
One demographic consequence of a small population size, the probability that all offspring in a generation are of the same sex, is easy to calculate: it is given by <math>1/2^{n1}<math> (The chance of all animals being females is <math>1/2^n<math>, the same holds for all males, thus the equation). This can be a problem in very small populations. In 1977, the last 18 Kakapo on a Fiordland island in New Zealand were all male, though the probability of this was only 0.0000076. With a population of just 3 individuals the probability of them all being the same sex is 0.25. Put another way, for every 4 species reduced to 3 individuals (or more precisely 3 individuals in the effective population), one will go extinct just because they are all the same sex.
Environmental effects
Stochastic variation in the environment (year to year variation in rainfall, temperature) can produce temporally correlated birth and death rates (i.e. 'good' years when birth rates are high and death rates are low and 'bad' years when birth rates are low and death rates are high) that lead to fluctuations in the population size. Again, smaller populations are more likely to go extinct due to these environmentally generated population fluctuations than are large populations.
Genetic consequences
Conservationists are often worried about a loss of genetic variation in small populations. There are 2 types of genetic variation that are important when dealing with small populations.
 The degree of homozygosity within individuals in a population; i.e. the proportion of an individuals loci that contain homozygous rather than heterozygous alleles. Many deleterious alleles are only harmful in the homozygous form.
 The degree of monomorphism/polymorphism within a population; i.e. how many different forms of the same allele exist in the gene pool of a population. Polymorphism may be particularly important at loci involved in the immune response.
There are 2 mechanisms operating in small populations that influence these 2 types of genetic variation.
 Genetic drift  Genetic variation is determined by the joint action of natural selection and genetic drift (chance). In small populations the relative importance of genetic drift (chance) is higher; deleterious alleles can become more frequent and 'fixed' in a population due to chance. Any allele, deleterious, beneficial or neutral is more likely to be lost from a small population (gene pool) than a large one. This results in a reduction in the number of forms of alleles in a small population and in extreme cases to monomorphism where there is only one form of the allele. Continued fixation of deleterious alleles in small populations is called Muller's ratchet, and can lead to mutational meltdown.
 Inbreeding  In a small population, related individuals are more likely to breed together. The offspring of related parents have a far higher number of homozygous loci than the offspring of unrelated parents.
There are two types of consequence of loss of genetic variation in small populations:
 Inbreeding depression  Inbreeding depression is usually taken to mean any immediate harmful effect, on individuals or the population, of a decrease in either type of genetic variation. Despite the strong theoretical support for inbreeding depression it has been very difficult to prove in real populations and there is debate over its significance.
 Inability of the population to adapt/evolve to changing conditions, “without variability evolution is impossible”
The effective population size is commonly lower than the actual population size.
See also
Topics in population genetics 

Key concepts: HardyWeinberg law  Fisher's fundamental theorem  neutral theory 
Selection: natural  sexual  artificial  ecological 
Genetic drift: small population size  population bottleneck  founder effect 
Founders: Ronald Fisher  J.B.S. Haldane  Sewall Wright 
Related topics: evolution  microevolution  evolutionary game theory  fitness landscape 
List of evolutionary biology topics 