Presented by Lindsay Aschim and Brady Wilkerson

A mathematical model was created to see weather a harem or searching strategy resulted in a higher pregnancy probability from the female perspective in whale populations. The harem strategy is defined as an adult male remaining with a matrilineal pod for the entire breeding season. The searching strategy is defined as an adult male remaining with a matrilineal pod for a short fraction of the breeding season - a magnitude of about 2-3 hours. These matrilineal pods consist of aggregations of adult females with their immature male (up to 5 years old) and female offspring (Berta and Sumich 99). Although this paper looks mainly at Sperm and Pilot whales, this model can be applied to any species where there is a choice between the two strategies.

Previous studies have tried to answer this question. May & Beddington's 1980 model concluded that the searching strategy always gave a higher pregnancy probability, that females gained nothing by the harem strategy and other pods probability would actually be lowered with the harem strategy. Some assumptions that were made with this model are not true to actual conditions in nature and therefore negated these results. The main one being that the female is in oestrus for the entire season. Therefore, once a pod is found all mature females will become pregnant. The probability of a female becoming pregnant is the same as the probability that a pod will be found by a male. This only occurs in extreme cases; females are generally only receptive for a small fraction of the breeding season.

Whiteheads 1987 model accounted for this discrepancy by using the following parameters:

• Searching Strategy: (# Males/pod)(# Days in oestrus)/ avg. # days male encounters pod)
• Harem Strategy: # Males/pod

With these parameters a harem strategy is better if the time between encounters for a male is greater then the days a female is in oestrus. It was assumed that all males find a pod and that the time when a pod is found is irrelevant. This however is relevant since the male may find a pod after the last day a female is in oestrus.

Another study looked at Short Finned Pilot Whales, which also have a matrilineal breeding structure but employ a different reproductive strategy. This social structure is unusual as the males do not leave the group as they reach sexual maturity. There generally more then one adult male in each pod and they do not compete for sexual dominance (Amos et. al 1993). Both reproductive and non-reproductive females can copulate while not in oestrus. It was hypothesized that this enhances school stability by reducing inter male fighting and removing the need for mature males to move along schools in search for a mate. It was also thought it would increase the pregnancy probability for all female pod members since a male would constantly be there during the breeding season and during each females fraction of time in oestrus.

The objective of this paper was to compensate for the assumptions made in the May & Beddington and Whitehead models as well as to see if non-reproductive mating did increase pregnancy probability in pods.

The key parameters of the model were:

The results are as follows:

• If a and q are low then a harem strategy is better
• If a and q are high then a searching strategy is better

If there is a small chance that a male will find the female during the breeding season or if the fraction of time a female is in oestrus is small then it is more advantageous for the pod to "keep" a male for the entire breeding season. This follows basic reasoning - if the male is there for the entire season he will be able to mate with the female during the window of time that she is in oestrus, however, if this window is small and there is a searching strategy being employed, then there is a greater chance that the male will miss that fraction of time that the female is receptive. Thereby lowering the pregnancy probability.

As a increases, the searching strategy is better. In other words, if the number of pods increases per male and if each pod "keeps" a male there is less adult males available for other pods. Therefore other pods would experience a decrease in pregnancy rates. If the length of time the female is in oestrus is high then the females would not gain by keeping a male within the pod. The time a pod is found is less important. Because of this the chance a female has at becoming pregnant greatly correlates with the chance a pod is found by an adult male. This makes a searching strategy more advantageous for the general population - one male would be able to impregnate many pods.

Since the harem strategy may be advantageous at times it may be useful for the females to be able to induce the males into switching to a harem strategy if a searching strategy is the general rule. If the nonreproductive matings that the pilot whales practice cause the males to switch strategies then the female will always gain, as long as other females do not employ this practice. In other words, if for example, the male population is decreased in one particular season and this "trick" is employed then only a few pods will benefit and the overall pregnancy probability for the species will decrease, as the males will not be able to mate with as many pods. This is an example of natural selection that actually works against the overall benefit of the species. Elmen and Oring (1977) enforce the idea that natural selection only exists at a individual level - not on a species or population level. Therefore traits that are detrimental to the species can be passed on because it is advantageous on an individual level.

This model uses parameters that are nearly impossible to measure in the wild. Little is known about many whale populations and therefore much of the data must be inferred from other species. One study shows that harbor seals use a searching strategy because of the need for food (Van Parijs et.al 96). This a possible factor in the differing strategies of the two whales. Sperm whales were shown to have a higher pregnancy probability when the searching strategy was employed whereas Short finned Pilot whales were shown to benefit more from a harem strategy. However since these results were found using such highly speculative data they should not be held as conclusive.

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