Comparing measures of breeding inequality and opportunity for selection with sexual selection on a quantitative character in bighorn rams

The reliability and consistency of the many measures proposed to quantify sexual selection have been questioned for decades. Realized selection on quantitative characters measured by the selection differential i was approximated by metrics based on variance in breeding success, using either the opportunity for sexual selection I-s or indices of inequality. There is no consensus about which metric best approximates realized selection on sexual characters. Recently, the opportunity for selection on character mean OSM was proposed to quantify the maximum potential selection on characters. Using 21years of data on bighorn sheep (Ovis canadensis), we investigated the correlations between seven indices of inequality, I-s, OSM and i on horn length of males. Bighorn sheep are ideal for this comparison because they are highly polygynous and sexually dimorphic, ram horn length is under strong sexual selection, and we have detailed knowledge of individual breeding success. Different metrics provided conflicting information, potentially leading to spurious conclusions about selection patterns. I, an index of breeding inequality, and, to a lesser extent, I-s showed the highest correlation with i on horn length, suggesting that these indices document breeding inequality in a selection context. OSM on horn length was strongly correlated with i, I-s and indices of inequality. By integrating information on both realized sexual selection and breeding inequality, OSM appeared to be the best proxy of sexual selection and may be best suited to explore its ecological bases.