The polygyny threshold model is an explanation of polygyny

Polygyny

Polygyny is a form of marriage in which a man has two or more wives at the same time. In countries where the practice is illegal, the man is referred to as a bigamist or a polygamist...

, the mating of one male of a species with multiple females. The model shows how females may gain a higher level of biological fitness

Fitness (biology)

Fitness is a central idea in evolutionary theory. It can be defined either with respect to a genotype or to a phenotype in a given environment...

 by mating with a male who already has a mate. The female makes this choice despite other surrounding males because the choice male's territory, food supply, or other important characteristics are better than those of his competitors, even with two females on the territory.

Graphical depiction

The graphical depiction of the model presented in Gordon H. Orians' 1969 paper is often used to explain the concept. The graph shows two curves on a graph of biological fitness versus environmental quality. Environmental quality refers to the quality of the male's territory. The left curve, labeled monogamous, is the perceived biological fitness for a female entering into a monogamous relationship with a given male. The right curve, labeled bigamous, shows the fitness of the same female entering into a relationship with a different male who already has one female mate but who has defended more resources. The second curve is roughly the first curve shifted to the right some amount. The given shapes of the curve will change with other intrinsic factors like genetic quality and male paternal investment. It is important to note that the designation "female" and "male" here are oft accurate; however, in some mating systems the operational sex ratio

Operational sex ratio

In the evolutionary biology of sexual reproduction, the operational sex ratio is the ratio of sexually competing males that are ready to mate to sexually competing females that are ready to mate...

leans towards females, who then have motivation to engage in resource defence polyandry (provided the requirements of economic defendability are met).

The intersection of the vertical dotted line on the left with the monogamous curve indicates the biological fitness of a female who chooses a monogamous male with a lower environmental quality. The intersection of the vertical dotted line on the right with the bigamous curve indicates the biological fitness of a female who enters into a bigamous relationship with the male of a higher environmental quality. The difference between these two intersection points, labeled PT, is the polygyny threshold. It is the gain of environmental quality for the female when she chooses the bigynous relationship and thus the minimum environmental quality difference necessary to make bigyny beneficial for the female. Also important is the vertical line drawn from the intersection of the line with the bigyny curve to the monogyny curve above. This represents the fitness gain of a female who chooses bigyny over monogyny due to, here, resource holding differences.

Orians predicted that animals exhibiting resource defence polygyny would fit to this model when living in successive habitats, where territory quality is very variable. Using the territory quality to decide whether to pursue a monogamous or polygynous mating relationship. This is shown in the red-winged blackbird by Pribil and Searcy (2001). Female red-winged blackbirds prefer to mate with males with territories over water and also unmated males. The females were given a choice between unmated males or previously mated males with the superior territories over water. In 12 out of 14 trials (86%) females choice the already mated male with the superior territory.