Technical Comments

Comment on “Bateman in Nature: Predation on Offspring Reduces the Potential for Sexual Selection”

Science  03 May 2013:
Vol. 340, Issue 6132, pp. 549
DOI: 10.1126/science.1233246

Abstract

Byers and Dunn (Reports, 9 November 2012, p. 802) claimed that predation on offspring reduced the potential for sexual selection in pronghorn. We argue that the potential for sexual selection is not affected by random offspring mortality when relative reproductive success is considered and increases when measured with the opportunity for selection, a metric that describes the potential for selection.

Byers and Dunn (1) conducted a 10-year study on pronghorn (Antilocapra americana), in which they investigated the effect of natural selection on sexual selection by measuring how the Bateman slope, defined as the slope of a linear regression of the number of offspring on the number of mates (24), changed according to fawn mortality. They concluded that predation on fawns reduced the potential for sexual selection. We argue that this conclusion is questionable for three reasons that we detail below.

First, in analyses of sexual selection, the number of offspring is traditionally measured during the period when the fertilization of ova occurs (35). By choosing the number of offspring at weaning as a proxy of male reproductive success, the authors incorporated a strong component of random natural selection, as most predation happens before weaning. It is inevitable that Bateman slopes will, on average, decrease proportionally to offspring mortality rate, compared with the Bateman slope measured at birth. To illustrate this point, we generated data for a population with a highly skewed distribution of paternity. We assumed that females can produce only one young and that each mating leads to fertilization. In this context, the Bateman slope is 1 before any mortality selection on offspring (Fig. 1). Then, we simulated 1000 episodes of random juvenile mortality for a given mortality rate and calculated the mean Bateman slope. A mortality rate of 70% (0.70) caused the Bateman slope to decrease proportionally to 0.30 (Fig. 1) [see figure 1, E and F, in (1)]. We repeated this procedure using several mortality rates and also found that Bateman slopes decrease as mortality rates increase (Figs. 1 and 2). The arithmetic relationship between Bateman slopes and mortality, however, explains all the variation in the data (r2 = 0.999) (Fig. 2). This relationship was also very high in the Byers and Dunn study, where most of the variation observed in their figure 1F was mirrored by variation in fawn mortality (Fig. 1E) [see also figure 3 in (1)] (r2 = 0.87). It is therefore not surprising that only fawn mortality is significant in their table 2, which also presents an overparameterized model of the effects of six highly collinear variables [see, for instance, figure 1, A and B, in (1)] on Bateman slopes based on a sample size of 10.

Fig. 1 Bateman slopes simulated over 1000 iterations at 0% (black) and 70% (gray) offspring mortality.

Based on the assumptions that all copulations are successful and that females produce only one offspring per mating, the Bateman slope at birth equals 1. The right axis presents the frequency distribution of the Bateman slope calculated for a simulated 70% random mortality over 1000 iterations.

Fig. 2 Bateman slopes (filled circles), Bateman slopes calculated on relative reproductive success (empty circles), and the opportunity for selection (triangles) calculated at different juvenile mortality rates.

Points show mean values ± SD for 1000 iterations at each mortality rate.

Second, we argue that Byers and Dunn should have used relative rather than absolute measures of reproductive and mating success to compare Bateman slopes. Assuming that predation is independent of male mating and reproductive success, the relative reproductive success of males measured on weaned offspring should remain the same as that measured at birth. In our simulation, Bateman slopes based on relative measures of reproductive success obtained before and after random fawn mortality were nearly identical (Fig. 2). This result contradicts Byers and Dunn’s assertion that natural selection decreases the potential for sexual selection.

Third, we do not agree with Byers and Dunn that the Bateman slope represents the potential for selection, because it quantifies how differences in mating success actually translate into reproductive success (3, 4). The upper limit of sexual selection is typically described by the opportunity for selection I, which increases with the variance in reproductive success (3, 4). Random predation on offspring could increase variance in male reproductive success. As such, I estimated in (1) increases when measured on fawn survival to weaning compared with when it is measured on mating success, suggesting that the potential for sexual selection in this population actually increases with fawn mortality. Our simulation also supports this contention (Fig. 2).

Contrary to Byers and Dunn, we conclude that the potential for sexual selection does not change with increasing random natural mortality when measured by a Bateman slope and increases when measured with the opportunity for selection. The usefulness of the opportunity for selection and the Bateman slope to quantify the potential for selection has been questioned recently [(6, 7), but see (8)]. Therefore, it remains unknown whether environmental variation can short-circuit or promote sexual selection in nature.

References and Notes

  1. Acknowledgments: We thank M. Festa-Bianchet for his constructive comments on the manuscript. P.B. was supported by a postdoctoral fellowship from the Fonds Québécois de la Recherche sur la Nature et les Technologies, F.P. was funded by the Canada Research Chair in Evolutionary Demography and Conservation, and D.G. was funded by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (327312-2011).
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