The study of sexual selection is being revolutionised by the realisation that most populations exhibit some degree of polyandry, i. Polyandry can drastically change the operation of sexual selection on males as it reduces the reproductive success Mating pt2 males derive by mating with different females, by forcing their ejaculates to compete for fertilisation after copulation sperm competition.
Variation Mating pt2 polyandry within a population means that the impact of polyandry can differ drastically across males, depending on the polyandry of their own mating partners. Because the patterns through which males share mates within a population may have strong repercussions for variation in male reproductive success, measuring such patterns is critical to study the operation of sexual selection.
Several methods have been proposed to measure the pattern of mate sharing at the population level. We conclude that SCIC may be the most promising approach, as it is both internally consistent and robust across the parameter range. We discuss Mating pt2 important caveats and provide advice regarding the choice of method for future studies of sexual selection. The online version of this article doi: Sexual selection is the selective process arising from variation in reproductive success due to intrasexual competition over access to mates and their gametes Darwin ; Andersson Traditionally, competition over mates was viewed as the main source of intrasexual variation in reproductive success, and the strength of sexual selection on mating success was measured by the Bateman gradient, i.
The Darwin-Bateman paradigm predicts that the male Bateman gradient Mating pt2. Less appreciated, however, are the profound implications that female mating success M females can have on the strength of sexual selection on males. This is because, for males, mating is no longer a zero sum game as females become a shared resource, and males continue to compete after mating for the fertilisation of sets of ova, via sperm competition Parker and under cryptic female choice Childress and Hartl ; Thornhill Mating pt2, in polyandrous populations i.
Mating pt2 polyandrous populations, sperm competition intensity is therefore a key determinant of male reproductive success Parker and Mating pt2 ; Collet et al. The way in which sperm competition intensity is distributed across males dictates population-level patterns in sexual selection, determining both the total variation in male reproductive success and the strength of precopulatory sexual selection on mating success i.
For example, consider a population where males with relatively high mating success tend to mate with the most polyandrous females and as a consequence face intense sperm competition. Despite the relatively high mating success of these males, their reproductive success is limited by the high polyandry of their partners, which reduces their paternity share.
At the population level, such non-random mating patterns may weaken sexual selection on male mating success i. Understanding the operation of sexual selection therefore requires a measure of the relationship between Mating pt2 mating success of a male and the sperm competitive environment faced by his ejaculates, i.
Borrowing techniques developed in both social science and ecological research focusing on food webs and mutualistic interactions, two such measures have recently been proposed: Both methods utilise a network perspective of sexual interactions, where mating populations are described as a collection of nodes males Mating pt2 females that are connected by edges representing copulations Fig.
Such sexual networks have been extensively explored in studies investigating the spread of sexually transmitted infections Gupta et al.
Mating patterns show a tremendous variety both between and within populations Emlen and Oring ; Thornhill and Alcock ; Clutton-Brock ; Andersson ; Shuster and Wade ; Shuster The Mating pt2 surge in the availability of fine-grained behavioural data sets in combination with molecular parentage assignment e.
Yet, despite this potential, we are aware of no analytical or quantitative evaluations of these Mating pt2 tools. Each panel shows two visualisations of mating populations as sexual networks.
Network visualisations show nodes representing individual males red or females blue and links edges represent copulations.
Matrix representations show the same populations where males are rowsfemales are columns and filled squares represent copulations.
Inset pictures Mating pt2 of Wikimedia commons https: Secondly, we compare the performance of these three metrics in quantifying the assortativity of mating patterns based on mating success. Thirdly, we Mating pt2 randomly organised simulated populations to explore the sensitivity of these three metrics to each of three key axes of sexual selection variation: Furthermore, we examine how these three metrics i.
Finally, in light of these results, we consider the application of these metrics to the study of sexual selection. Conceptually, edges in these networks can either be directed or undirected.
In a directed network, if one male and one female are connected, one individual e. When females are polyandrous, their degree is greater than 1 and measures the intensity of sperm competition faced by their male partners Parker ; Parker and Birkhead The trait of interest in this context is node degree, which measures individual mating success see above. Developed for unipartite networks i.
Mating pt2 a network of one monogamous mating pair, E equals 2 if we treat edges as undirected or 1 if we treat edges as directed. This is because in undirected networks, the edge is Mating pt2 mutual and the correlation between trait values in this case node degree between linked nodes is therefore viewed from both directions Newman To highlight this difference, consider the following example network with two males as rows and two females as columns, 1 1 1 0where 1 means that the pair copulated.
This means that r Newman U can yield both positive and negative values of assortativity and behaves in a way similar to r Newman D when populations approach an even sex ratio, but the metrics can generate drastically divergent estimates of assortativity when sex ratios deviate from unity. Nestedness is a concept originally borne from ecological research, designed to quantify patterns of species co-occurrences in metacommunities, where sites with lower species richness contain reduced subsets of those sites with higher species richness Ulrich and Almeida-Neto This concept was later applied to ecological Mating pt2 such as mutualistic plant-pollinator networks Ulrich Mating pt2 al.
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Mutualistic plant-pollinator networks are nested when specialist plants those with few connections tend to connect to the most generalist pollinators those with many connections and specialist pollinators tend to connect to the most generalist plants Bascompte et al. In the context of sexual Mating pt2, a population is nested when males with Mating pt2 mating partners i.
Nestedness is therefore specific to patterns of disassortativity and bipartite networks, i. To calculate nestedness as outlined by Almeida-Neto et al. Then, for every pair of i and j rows maleswe calculate two values, DF decreasing fill and PO percentage overlap.
To calculate DF, we ask whether the upper row in the pair row i has a higher mating success M than the lower row row j.
The same process is calculated for all pairs of columns femaleswhere the i th female is the leftmost and the j th female is the female to its right. For all pairs of rows and columns, we then calculate thier individual nestedness Mating pt2 ij as:.
For Mating pt2, consider the top male rows in Fig. We can then measure the nestedness of the whole network as:. The aim of quantifying population-level patterns in assortative mating by mating success Mating pt2 to understand its influence on Mating pt2 strength of sexual selection on male mating success i. When females are polyandrous, males will be forced to sperm compete and, all else being equal, the reproductive success of a focal male Mating pt2 inversely proportional to the number of sperm competitors with which he competes i.
For example, consider a male that mates with two females; one of which does not remate, whilst the other copulates with two other males.
The sperm of this male does not face sperm competition within the first female. For the second female however, the sperm of the focal male must compete with the sperm of two other males. Assuming the simplest null model of sperm competition i.
This can be calculated for the i th male simply as:. This parameter can then be added to our regression model in Eq.
Typically, Bateman gradients are standardised by dividing reproductive success and mating success by their respective means Jones In this fashion, we can also standardise SCI by its population mean and provide a standardised slope for SCIC that facilitates comparisons across populations.
Mating pt2 instead, M males was standardised by subtracting the population mean and dividing by its standard deviation, as for selection gradients Mating pt2 phenotypic traits Lande and Arnold ; Wolf et al. We develop model populations displaying a range of mating systems to test the performance of all the metrics i.