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Notice what happens to the equation when it is certain that the male will be cannibalized (ENC=1 and C=1): the right side of the inequality becomes zero. Any value of A/P greater than zero (that is, any increase in number of offspring due to sexual cannibalism) thus conveys a selective advantage to sexual cannibalism (Buskirk et al. 1984). This relatively simple model organizes the costs and benefits of male complicity into comparable mathematical terms, describing the conditions by which sexual cannibalism favors male fitness.

The female perspective

Newman and Elgar supplement Buskirk’s hypothesis with an economic model from the female perspective, drawing on evidence from the orb-weaving spider. Specifically, these researchers address pre-copulatory cannibalism, in which the female consumes the male before sperm transfer is complete (post-copulatory cannibalism is assumed to never harm the female, unless the species raises young and requires future male aid). The mathematical description of Newman and Elgar involves complex dynamic programming, and will not be detailed here. However, it essentially illustrates that females are more likely to engage in pre-copulatory cannibalism if they can encounter several males during a season and have both a low and inconsistent food intake rate from non-mate sources (Newman and Elgar 1991). This model resonates well with the foraging strategy hypothesis, which also emphasizes the nutritional utility of sexual cannibalism for females.

The intersection of the two economic models illustrates the possibility for intersexual conflict in sexual cannibalism. There is a discrepancy between parameters of fitness benefit from the female and male perspectives (Newman and Elgar 1991). For example, consider a mating season in which males encounter many females, and females also frequently meet males. In these conditions, males will incur high costs from sexual cannibalism because they forgo ample mating opportunities. Simultaneously, females will be more inclined to consume mates before copulation because they have many chances to accept sperm later. The discord between male and female perspectives drives some level of conflict of interest in mating interactions. Depending on ecological conditions and species traits, members of the opposite sex experience different costs and benefits that determine the extent to which cannibalism is adaptively favorable.

Applications of economic models to mantises and spiders

The economic models of Buskirk; and Newman and Elgar help explain previous observations, including male mantises’ non-cooperation in sexual cannibalism. For most mantises males, the likelihood of finding a second mate is high, which increases the cost of self-sacrifice by Buskirk’s model. Even if the male’s biomass improves female fecundity, the resulting viability of the male’s offspring must not be great enough to overcome the cost to his future mating opportunity. (Gemeno and Claramunt 2006). Sexual cannibalism in mantises must be adaptive solely from the female perspective (conflict of interest).

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Source:  OpenStax, Mockingbird tales: readings in animal behavior. OpenStax CNX. Jan 12, 2011 Download for free at http://cnx.org/content/col11211/1.5
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