Comparing the estimation properties of different statistics for measuring sexual isolation from mating frequencies

Sexual isolation is a key component of reproductive isolation, involving mate choice among mature adults. While there are various statistics for estimating sexual isolation from mating frequencies, their ability to produce unbiased estimates varies considerably, depending on the particular situation. We investigated, under different biological scenarios, the estimation properties (statistical bias, efficiency, root mean square, statistical test) of 12 statistics commonly used in the literature for measuring sexual isolation. Yule's Q , V , YA (and related indices) and I _PSI are revealed to be the most efficient, with the smallest biases and root mean square deviations. Yule's Q , YA and I _PSI show better estimation properties when using infinite sample sizes, while I _PSI is preferable using smaller sample sizes. Other statistics investigated should be avoided, at least within the range of conditions considered. Regarding the parametric test of hypothesis, the best alternative is YA . We discuss the advantages and drawbacks of the various estimators, and propose I _PSI as the safest for biological sample sizes.  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 85 , 307–318.     

Sampling scale can cause bias in positive assortative mating estimates: evidence from two intertidal snails

Assortative mating in the wild is commonly estimated by correlating between traits in mating pairs (e.g. the size of males and females). Unfortunately, such an approach may suffer from considerable sampling bias when the distribution of different expressions of a trait in the wild is nonrandom (e.g. when segregation of different size classes of individuals occurs in different microhabitats or areas). Consequently, any observed trait correlation in the wild can be an artefact of pooling heterogeneous samples of mating pairs from different microhabitats or areas rather than true nonrandom matings. This bias in estimating trait correlations as a result of sampling scale is termed the scale‐of‐choice effect (SCE). In the present study, we use two intertidal littorinid species from Hong Kong to show how the SCE can bias size‐assortative mating estimates from mating pairs captured in the wild, empirically demonstrating the influence of this effect on measures of positive assortative mating. This finding cautions that studies overlooking the SCE may have misinterpreted the magnitude and the cause of assortative mating, and we provide a new analytical approach for protecting against this potential bias in future studies.     

A novel method for estimating the strength of positive mating preference by similarity in the wild

Mating preference can be a driver of sexual selection and assortative mating and is, therefore, a key element in evolutionary dynamics. Positive mating preference by similarity is the tendency for the choosy individual to select a mate which possesses a similar variant of a trait. Such preference can be modelled using Gaussian‐like mathematical functions that describe the strength of preference, but such functions cannot be applied to empirical data collected from the field. As a result, traditionally, mating preference is indirectly estimated by the degree of assortative mating (using Pearson's correlation coefficient, r) in wild captured mating pairs. Unfortunately, r and similar coefficients are often biased due to the fact that different variants of a given trait are nonrandomly distributed in the wild, and pooling of mating pairs from such heterogeneous samples may lead to “false–positive” results, termed “the scale‐of‐choice effect” (SCE). Here we provide two new estimators of mating preference (C_rough and C_scaled) derived from Gaussian‐like functions which can be applied to empirical data. Computer simulations demonstrated that r coefficient showed robust estimations properties of mating preference but it was severely affected by SCE, C_rough showed reasonable estimation properties and it was little affected by SCE, while C_scaled showed the best properties at infinite sample sizes and it was not affected by SCE but failed at biological sample sizes. We recommend using C_rough combined with the r coefficient to infer mating preference in future empirical studies.     

The scale‐of‐choice effect and how estimates of assortative mating in the wild can be biased due to heterogeneous samples

The mode in which sexual organisms choose mates is a key evolutionary process, as it can have a profound impact on fitness and speciation. One way to study mate choice in the wild is by measuring trait correlation between mates. Positive assortative mating is inferred when individuals of a mating pair display traits that are more similar than those expected under random mating while negative assortative mating is the opposite. A recent review of 1134 trait correlations found that positive estimates of assortative mating were more frequent and larger in magnitude than negative estimates. Here, we describe the scale‐of‐choice effect (SCE), which occurs when mate choice exists at a smaller scale than that of the investigator's sampling, while simultaneously the trait is heterogeneously distributed at the true scale‐of‐choice. We demonstrate the SCE by Monte Carlo simulations and estimate it in two organisms showing positive (Littorina saxatilis) and negative (L. fabalis) assortative mating. Our results show that both positive and negative estimates are biased by the SCE by different magnitudes, typically toward positive values. Therefore, the low frequency of negative assortative mating observed in the literature may be due to the SCE's impact on correlation estimates, which demands new experimental evaluation.     

DISENTANGLING THE EFFECTS OF MATING PROPENSITY AND MATING CHOICE IN DROSOPHILA

Incipient sexual isolation between genotypes, lines, or populations of the same species is commonly measured in Drosophila by choice tests. Results of these tests are known to be influenced, in an undetermined manner, by the mating propensity of competitors and by discriminatory factors during courtship. We have approached the problem by measuring male and female propensities in separate, independent tests, and by examining whether these estimates could explain the results of the choice tests. First, male and female choice tests were used to measure sexual isolation between populations of Drosophila melanogaster and between populations of D. simulans. Significant deviations from random mating occurred in 31 out of 48 tests, in agreement with the propensity values of the tested genotypes. We conclude that mating propensity instead of discrimination is directly involved in the estimation of sexual isolation in our populations, and advise against the application of male and female choice tests to assess intraspecific isolation without a proper knowledge of the mating propensities of competing individuals. Second, multiple choice tests were used to assess isolation between D. melanogaster populations. In examining the dynamics of matings throughout the test, we show that if competing individuals differ in mating propensities and tests are long enough to allow most matings to happen, a spurious sexual isolation can appear. We recommend that multiple choice tests be terminated once 50 percent of matings had been observed.     

Influence of previous mating experience on future mating success in maleLucilia cuprina (Diptera: Calliphoridae)

Receptive and virginL. cuprina females were placed with a virgin male and an experienced male that had mated between one and five times previously. The experienced males secured significantly more matings than virgin males. Males with previous matings also gained experience in competing with males. Males directed mating attempts at each other, seemingly in the context of intrasexual competition. Experienced males directed more mating attempts at virgin males than vice versa. As their number of previous matings increased, experienced males made the first mating attempt at females more often and directed more mating attempts at females compared with virgin males. Females did not actively discriminate against experienced males, even though the proportion of matings secured on the first attempt by experienced males declined with increasing mating experience. Alternative behavioral explanations are discussed.     

Female mate choice and mating costs in the polyandrous butterflyPieris napi (Lepidoptera: Pieridae)

Males of the green-veined white butterfly (Pieris napi L.) transfer large ejaculates that represent on average 15% of their body mass when mating for a first time. Shortly after mating a male is able to transfer only a small ejaculate when mating a second time. Male ejaculate production plays a crucial role in the mating system ofP. napi because females use male-derived nutrients for egg production and somatic maintenance. Here we study how timing of female rematings and copulation duration are influenced by the mating history of their mates and, also, study if females exert mate choice to minimize their mating costs. Mating with a recently mated male increased female mating costs by increasing time in copula and mating frequency. Virgin females that mated with virgin males remated after an average of 6 days, whereas virgin females that mated with recently mated males remated after an average of 2 days. Moreover, copulations involving recently mated males lasted on average almost 7 h, whereas copulations involving virgin males lasted on average 2 h. Recently mated males were eager to remate, in spite of the fact that the size of the ejaculate they transfer is small and that they remain in copula for a long time. Hence it seems that males are more successful in the sexual conflict over mating decisions and that females do not minimize mating costs by choosing to mate preferentially with virgin males.     

Size-related mating and mate guarding in the orb-web spiderNephila clavata (Araneae,Araneidae)

The orb-web spiderNephila clavata satisfies three conditions for assortative mating proposed by Ridley (The Explanation of Organic Diversity. The Comparative Method and Adaptations for Mating, Clarendon, Oxford, 1983); (1) a large male advantage in male-male competition, (2) a correlation between female size and fecundity, and (3) a long pairing duration. To test Ridley's hypothesis, size assortative mating and guarding were examined in the field. When data were pooled over time, assortative mating was found but this was due to temporal covariation of body sizes of males and receptive females. After controlling for the effect of time, size assortative guarding was not detected, although females guarded by males were larger than those not guarded in the early breeding season. Possible reasons for the absence of size assortative guarding were discussed.     

Female Reproductive Status and Mate Choice in the Hide Beetle, Dermestes maculatus

Models of mutual mate choice predict that when the costs of mating indiscriminately increase, so may the choosiness of the conventionally non-choosy sex. In a series of behavioral trials, we tested both male and female chemo-reception and mate choice in the hide beetle, Dermestes maculatus. Using olfactometer bioassays we found that males detected and responded more rapidly to individual mated females but had a limited ability to detect virgin females or discriminate between virgin and mated females when presented simultaneously. Both mated and virgin females were unable to detect the presence of virgin males. Copulation behaviors were comparable when males were presented with a virgin or mated female either individually or simultaneously. However, when presented simultaneously, virgin females had a higher probability of receiving a copulation than their mated counterparts. Our data show that males respond to variation in female reproductive status, but that female propensity to mate does not change. We suggest that mutual mate choice may be an important force, even in systems in which there is apparently strong selection for female mate discrimination.     

Opportunities for mate choice in the fission‐performing ant Cataglyphis cursor

1. Sexual selection has been little studied in social insects. Nonetheless, because mating is generally for life, opportunities for selecting among mating partners should be exploited. 2. In some ants, males aggregate at nest entrances to mate with emerging gynes. Both males and females thus have access to multiple mates over a relatively protracted period, giving rise to opportunities for mate choice and multiple mating. 3. We provide data from field observations of the male mating biology of the ant, Cataglyphis cursor Fonscolombe. In this species, females mate with, on average, six males each at the nest entrance and found colonies with the help of workers. 4. Males were present at the field site for approximately 1 month in spring, with up to 40 males at a single nest entrance for, on average, 4.7 days. Individual males were observed to survive up to 3 days, and mate up to eight times. 5. Thus both males and females of this species have the ability to mate multiply and have a window permitting mate choice to occur. Workers actively attacked males and may take part in the mate choice process, making C. cursor an interesting model to study questions relating to sexual selection and male mating strategies.     

Mating games: the evolution of human mating transactions

We propose a new, evolutionary, game-theoretic model of conditionalhuman mating strategies that integrates currently disconnectedbodies of data into a single mathematically-explicit theoryof human mating transactions. The model focuses on the problemof how much resource a male must provide to a female to secureand retain her as a mate. By using bidding-game models, we showhow the male's minimally required resource incentive variesas a function of his own mate value, the value of the female,and the distribution of the mate values of their available alternativemates. The resulting theory parsimoniously accounts for strategicpluralism within the sexes, mate choice differences betweenthe sexes, and assortative mating, while generating a rich setof testable new predictions about human mating behavior.     

Estimating sexual selection and sexual isolation effects from mating frequencies

Abstract.— Sexual selection (defined as the change in genotypic or phenotypic frequencies of mated versus total population frequencies) and sexual isolation (defined as the deviation from random mating in mated individuals) show different evolutionary consequences and partially confounded causes. Traditionally, the cross-product estimator has been used to quantify sexual selection, whereas a variety of indexes, such as Yule V , Yule Q, YA , joint I , and others have been used to quantify sexual isolation. Because the two types of estimators use different scales, the effects of both processes cannot be monitored simultaneously. We describe three new related statistics that quantify both sexual selection ( PSS ) and sexual isolation ( PSI ) effects for every mating pair combination in polymorphic traits, as well as measure their combined effects ( PTI = PSI X PSS ). The new statistics have the advantage of providing information on every mating pair combination, quantifying the effects of sexual selection and isolation in the same units, and detecting asymmetry in sexual isolation. The ability of the new statistics to ascertain the biological causes of sexual selection and sexual isolation are investigated under different models involving distinct marginal frequencies, mate propensity, and mate choice coefficients. We also studied the use of classical isolation indexes applied on PSI coefficients, instead of on raw data. The use of the classical indexes applied to PSI coefficients considerably reduces the statistical bias of the estimates, revealing the good estimation properties of the new statistics.     

Size-dependent sex allocation and sexual selection in Aplysia kurodai, a hermaphrodite with nonreciprocal mating

Abstract. For simultaneous hermaphrodites, a male-to-female shift in sex allocation with growth, and weak sexual selection on the male function, is predicted by many theories, although empirical data for both predictions are insufficient for internally fertilizing hermaphrodites with nonreciprocal mating. To address these issues, I studied mating and egg-laying behavior of the sea hare, Aplysia kurodai (Gastropoda: Opisthobranchia) in the laboratory. Both frequency and duration of egg laying increased with body weight, indicating that fecundity increased with weight. On the other hand, frequency and duration of mating as males did not increase with body weight, suggesting that sperm usage was independent of weight. Therefore, sex allocation shifted from male to female functions with growth. The lack of a relationship between body weight and mating activities as males also suggests that there was no "female" choice for large partners. However, the frequency of mating as females increased with body weight, suggesting "male" choice for large partners. This "male" choice is further supported by the presence of size-assortative mating and a longer duration of mating when the female partner was large. In addition, the variance in mating frequency as females was larger than that as males. As a whole, the mating behavior in A. kurodai can be summarized as choosy as males and unchoosy as females, the opposite of the patterns known in most gonochoric and hermaphroditic animals.