MALE GENETIC QUALITY AND THE INEQUALITY BETWEEN PATERNITY SUCCESS AND FERTILIZATION SUCCESS: CONSEQUENCES FOR STUDIES OF SPERM COMPETITION AND THE EVOLUTION OF POLYANDRY

Authors


Abstract

Studies of postcopulatory sexual selection typically estimate a male's fertilization success from his paternity success (P2) calculated at hatching or birth. However, P2 may be affected by differential embryo viability, thereby confounding estimations of true fertilization success (F2). This study examines the effects of variation in the ability of males to influence embryo viability upon the inequality between P2 and F2. It also investigates the consequences of this inequality for testing the hypothesis that polyandrous females accrue viability benefits for their offspring through facilitation of sperm competition (good-sperm model). Simulations of competitive mating trials show that although relative measures of male reproductive success tend to underestimate the strength of underlying good-sperm processes, good-sperm processes can be seriously overestimated using P2 values if males influence the viability of the embryos they sire. This study cautions the interpretation of P2 values as a proxy for fertilization success or sperm competitiveness in studies of postcopulatory sexual selection, and highlights that the good-sperm hypothesis needs empirical support from studies able to identify and separate unequivocally the males' ability to win fertilizations from their ability to influence the development of embryos.

Understanding why females mate with different partners within a single reproductive episode is not trivial. Polyandry enables intra- and intersexual selection to continue after mating in the form of sperm competition and/or cryptic female choice (reviewed in Parker 1970; Smith 1984; Eberhard 1996; Birkhead and Møller 1998; Simmons 2001). In addition, this behavior facilitates antagonistic interactions between the sexes if selection imposed by sperm competition drives the evolution of traits that increase the fitness of males at the expense of female fitness (Parker 1979; Johnstone and Keller 2000; Arnqvist and Rowe 2005). Traditional theory dictates that females should be reluctant to accept multiple partners due to asymmetries between the sexes in gamete size and provisioning of the zygote (Trivers 1972; Parker 1979), and evidence that mating can incur costs for females (Daly 1978; Rolff and Siva-Jothy 2002) supports the argument that polyandry should not be widespread. Nevertheless, females of many species mate polyandrously (Birkhead and Møller 1998; Jennions and Petrie 2000) and it has been proposed that this behavior can be explained if females accrue material or genetic benefits, or if males impose higher-than-optimal remating rates in females (Arnqvist and Nilsson 2000; Jennions and Petrie 2000; Arnqvist and Rowe 2005).

A series of genetic benefits has been suggested to increase fitness of polyandrous females (Yasui 1998; Jennions and Petrie 2000). Explanations based on intrinsic male quality propose that females can increase the probability that their eggs are fertilized by males of superior genetic quality, either through precopulatory or postcopulatory mechanisms (Kempenaers et al. 1992; Andersson 1994; Petrie 1994; Yasui 1997; Welch et al. 1998; Møller and Alatalo 1999; Jennions and Petrie 2000; Kokko et al. 2003; García-González and Simmons 2005a). Alternatively, multiple mated females can increase fitness by allowing male-by-female genetic incompatibilities to be resolved either before or after the fusion of the gametes (Zeh and Zeh 1997; Tregenza and Wedell 2000, 2002; Neff and Pitcher 2005). Experiments that manipulate the number of partners while controlling for mating frequency have supported genetic models based on the existence of postcopulatory phenomena: a meta-analysis of data arising from these studies shows that embryo viability, estimated as egg hatching success, is significantly enhanced in polyandrous matings (Simmons 2005). However, distinguishing whether these benefits are genetically based, and whether they arise because of fertilization biases due to intrinsic male genetic quality or due to interactions between parental genotypes is often not straightforward (Simmons 2005).

The postcopulatory analogy of the good genes model for female choice evolution, the good-sperm hypothesis (Yasui 1997), suggests that polyandrous females will accrue genetic quality for their offspring through facilitation of sperm competition if males achieving higher fertilization success are also more effective in producing viable offspring (Sivinski 1984; Parker 1992; Birkhead et al. 1993; Yasui 1997, 1998). The good-sperm model requires heritable variation among males in their general viability or condition (genetic quality), a premise for which there is little doubt (e.g., Houle 1992; Rowe and Houle 1996; Kokko 1998; Lynch and Walsh 1998; Welch et al. 1998; Wedekind et al. 2001; Sheldon et al. 2003; Hunt et al. 2004; Tomkins et al. 2004). In addition, the model assumes that the outcome of sperm competition is determined by the males' investment in sperm competition, and that males exhibit intrinsic differences in their ability to invest in sperm competitiveness. A large body of literature on sperm competition shows that even though females play an active role in the output of sperm competition (Wilson et al. 1997; Clark and Begun 1998; Clark et al. 1999; Clark 2002; Miller and Pitnick 2002; García-González and Simmons 2007b), fertilization success is often determined by ejaculate traits, sperm traits, or male genital morphology in a broad range of taxa including birds, mammals, fish and insects (Birkhead and Møller 1998; Hosken and Stockley 2004; Snook 2005; Evans and Simmons 2008; Simmons and Moore 2008). Importantly, although the inheritance of male traits that determine fertilization success may be constrained, for example by sex linkage or cytoplasmic genetic effects (Birkhead and Pizzari 2002; Pizzari and Birkhead 2002; Zeh 2004; Froman and Kirby 2005; Zeh and Zeh 2008), a wealth of research suggests that, at least in some species, traits contributing to fertilization success can be explained by intrinsic differences among males (e.g., Dziuk 1996; Radwan 1998; Konior et al. 2006). Furthermore, some recent studies implicate male condition dependence on investment in sperm competition traits in some taxa (e.g., Hosken et al. 2001; Simmons and Kotiaho 2002; Engqvist and Sauer 2003; Schulte-Hostedde et al. 2005; and see review by Simmons and Moore 2008). Thus, at least in some systems, the assumptions of the good-sperm model are supported. Furthermore, accumulating evidence from studies with increased power to detect intrinsic sire effects supports the notion that polyandry may increase the probability of fertilization by genetically superior males (García-González and Simmons 2005a; and see Evans and Simmons 2008). So far however, empirical support for the acquisition of offspring genetic quality through a good-sperm process is scant (Pai and Yan 2002; Hosken et al. 2003; Fisher et al. 2006; García-González and Simmons 2007b; Simmons and Kotiaho 2007), and only one study so far has found clear support for the fertilization success-offspring viability association predicted by the good-sperm model (Fisher et al. 2006).

In this article, I review an issue relating to sperm competition and male genetic quality that may affect the ability to detect and interpret underlying good-sperm processes. Recent verbal arguments point out that caution should be taken when estimating fertilization success because the assignment of paternity at late stages of offspring development can be confounded with mortality rates in embryos (e.g., Jennions and Petrie 2000; Birkhead et al. 2004; Simmons 2005; Evans et al. 2007; García-González and Simmons 2007a, and see below). It is useful to make the distinction between fertilization success sensu stricto, estimated at conception (referred to in this article as F2, or the proportion of eggs fertilized by the last male to mate a doubly mated female) from paternity success estimated at hatching or birth, typically P2, or the proportion of offspring sired by the second male to mate a doubly mated female (Boorman and Parker 1976). Because of methodological constraints, studies of postcopulatory sexual selection generally infer fertilization success (proxy for sperm competitive ability) from P2 values. However, paternity success measures are inescapably conditioned by the normal development of embryos from fertilization to hatching/birth. This begs the question of whether estimations of the ability of males to win fertilizations are confounded by differential embryo viability. Differential embryo viability across a female's mates can result from either intrinsic sire effects (García-González and Simmons 2005a; Ivy 2007), genetic incompatibilities between males and females (Olsson et al. 1999), differential allocation and maternal indirect genetic effects (Sheldon 2000; Tregenza et al. 2003), or paternal indirect genetic effects and interacting phenotypes (García-González and Simmons 2007a). Gilchrist and Partridge (1997) pioneering study showed that the apparent heritability of sperm competitiveness in Drosophila melanogaster was to a great degree explained by heritability of preadult viability. Later on, Olsson et al. (1999) highlighted that, in the context of cryptic female choice and genetic incompatibilities, parental relatedness may produce inbreeding-induced mortality that would introduce noise in paternity data. More recent studies indicate that the period between the onset of fertilization and hatching or birth is a critical stage in which differential embryo mortality across a female's mates occurs (Wedekind et al. 2001; García-González and Simmons 2007a; Evans and Simmons 2008). Studies examining good-sperm processes would typically look at the relationship between paternity success (P2) and post-hatching offspring viability (e.g., survival from juvenile to adult). This study examines the extent to which intrinsic sire effects on embryo viability can confound estimates of fertilization success when using paternity success data, and the consequences of these effects for the study of postcopulatory sexual selection, in particular for empirical tests of the good-sperm hypothesis.

Materials and Methods

THE INEQUALITY BETWEEN P2 AND F2

For the analyses, sperm competitiveness is assumed to be a male's investment in traits that determine his ability to fertilize a female's ova in sperm competition contexts, and to have, as in the good-sperm model (Yasui 1997), an additive genetic basis. Sperm competitiveness can be considered as the result of the action and interaction (including trade-offs) of all determinants of paternity integrated in a functional unit that is the ejaculate, to which behavioral, morphological, and physiological adaptations can be added. Sperm competitiveness is generally influenced by a number of traits that may include ejaculate volume (Gage and Morrow 2003), sperm quality (Gage et al. 2004; García-González and Simmons 2005b), sperm morphology (Radwan 1996; García-González and Simmons 2007b), seminal fluid products (Wolfner 1997; Poiani 2006; Fiumera et al. 2007) and genital morphology (Arnqvist and Danielsson 1999; House and Simmons 2003), among others (see also review by Snook 2005).

I have used a hypothetical distribution of sperm competitiveness (henceforth this distribution is referred to as S) consisting of 60,000 values (Mean = 0.495, SD = 0.19, range 0.192–0.999; Fig. 1). This distribution has been used elsewhere as an example distribution to look at the consequences of the relative nature of fertilization success on the study of postcopulatory sexual selection (F. García-González, unpubl. data). Briefly, the distribution S has been generated from the distribution of numbers of sperm stored in the spermatheca after single matings in the fly Bactrocera (Dacus) cucurbitae (data for copulations in which sperm transfer was complete; fig. 1 in Yamagishi and Tsubaki 1990). In this species, ejaculate size determines paternity success when females mate with multiple males in a rapid succession, according to a mechanism of sperm mixing (Yamagishi et al. 1992). I adjusted variation of the real sperm number values (sperm competitiveness) to a scale from 0 to 1, and then grouped the real sperm number values in the categories 0–0.1, 0.1–0.2,…,0.9–1.0, to subsequently calculate the frequency of each category. I have created continuity in sperm competitiveness by generating random numbers that adjust to the frequency of each category. This protocol generated a distribution of values for sperm competitive ability identical to the real distribution of sperm numbers (equal shape, mean, range, and coefficient of variation) but containing a large number of values. The distribution of sperm inseminated in B. cucurbitae is merely used as a biologically realistic example of the distribution of sperm competitive ability in a population of males. The simplification that sperm competitiveness is exclusively determined by the investment in ejaculate size imposes no limitation to the interpretation of the results. The distribution S can be any distribution of a given determinant of paternity or overall sperm competitiveness being under stabilizing selection. The bell-shaped S distribution, however, deviates from normality (K-S d = 0.08, P < 0.01; Lilliefors P < 0.01), and a normal distribution has also been examined.

Figure 1.

S, the frequency distribution of sperm competitive ability used as an example (see text for details). The line indicates the normal curve.

The analysis assumes that embryo viability is also determined by female genetic quality. However, it assumes that a female's contribution to embryo viability is constant for all her mates (i.e., the female contribution is based on pure genetic transmission and there is no differential allocation). More complex situations involving maternal and paternal effects can be added to this simple scenario. In addition, for simplicity, it is assumed that there is genetic covariance for the males' ability to induce prehatching and posthatching offspring viability.

I have conducted simulations of sperm competition trials involving random pairing of males extracted from the hypothetical distribution S. A random sperm mixing mechanism of sperm competition following the principle of the fair raffle (Parker 1990), in which fertilization success of a male is a function of his investment in sperm competition relative to the investment of the competitor male, is simulated. Fertilization success for the second male to mate a female is therefore F2=s2/(s1+s2), where s1 and s2 are sperm competitiveness for the first and second male, respectively, on a scale from 0 to 1 (without including 0; minimum value of sperm competitive ability for a male from the distribution S is 0.192). Importantly, paternity success is a measure that is influenced by the successful development of embryos, such that paternity success for the second male to mate a female is P2=s2.v2/(s1.v1+s2. v2), where v1 and v2 are the viability of the embryos sired by the first and second male, respectively. Given that variation in the ability of females to contribute to embryo viability is assumed to be constant across their mates, this study explores the variation in embryo viability due to male genetic effects. Values for v1 and v2, the proportion of embryos that successfully develop until hatching or birth for each male, have been extracted from a distribution of embryo viability (henceforth V). Distributions of male ability to induce offspring viability are largely unknown. For this reason, the analysis assumes a distribution of embryo viability with the same structure as that for sperm competitive ability. The distribution V is therefore characterized by the same parameters as S. However, different relationships between the distributions S and V have been examined. I have first examined one scenario in which good-sperm processes are absent. In this scenario sperm competitive ability and offspring viability are not genetically correlated (correlation coefficient between S and V, rS,V= 0.00, P= 0.89, n= 60,000). In a second scenario good-sperm processes do take place. For this scenario different degrees for the correlation between sperm competitive ability and embryo viability have been investigated, which represent different “strengths” for the underlying good-sperm processes: weak (correlation coefficient between S and V, rS,V= 0.07, P << 0.001), moderate (rS,V= 0.25, P << 0.001), and strong (rS,V= 0.45, P << 0.001) good-sperm processes (all n= 60,000).

The protocol used to look at the effects of variation in male genetic quality over the inequality between paternity success and fertilization success involves two steps. The first step consists of the simulation of double matings (n= 10,000) using values of sperm competitive ability extracted at random and their associated embryo viability values, to subsequently calculate F2 values and P2 values as stated above. The second step works toward assessing the likelihood of mistakenly inferring erroneous fertilization values from paternity values influenced by differential embryo viability. This step involves the calculation of probabilities for obtaining differences of various magnitudes between P2 values and the F2 values that generate them. For this purpose, the array of F2 values generated in the simulations is grouped in the categories 0–0.1, 0.2–0.3,…,0.9–1.0. Then, for every double mating the absolute difference between P2 and F2 is calculated, and the probability that the absolute difference between P2 and F2 (Prob. abs. diff. P2F2) is higher than 0.1, 0.2, 0.3 is calculated from the array of F2 values in each category. These probabilities are calculated on the basis of differences between individual pairs of P2F2 values. For example, the Prob. abs. diff. P2F2 > 0.3 for an F2 value of 0.43 is the probability that the P2 value arising from that F2 value is higher than 0.73 or lower than 0.13.

In addition, I have used the same protocols described above to calculate the probabilities for the deviations between P2 and F2 in the following cases: (A) sperm competitive ability follows the S distribution and embryo viability follows a uniform distribution (mean = 0.5, SD = 0.29, Min. 0.0, Max. 1, n= 60,000), (B) sperm competitive ability follows the S distribution and embryo viability follows a normal distribution (mean = 0.5, SD = 0.12, Min. = 0.013, Max. = 0.994, n= 60,000), (C) sperm competitive ability follows a normal distribution and embryo viability follows a uniform distribution, and (D) both sperm competitive ability and embryo viability follow a normal distribution. In these cases, only a scenario in which good-sperm processes are absent has been simulated. It should be noted that a uniform distribution for embryo viability most likely represents an unrealistic case for extreme variance in this trait; this distribution is used solely to illustrate how variance in embryo viability affects the inequality between P2 and F2.

The inequality between P2 and F2 would be influenced by the mechanism of sperm competition operating in the species. Apart from a mechanism of sperm mixing based on the fair raffle principle, I have simulated a loaded raffle in which the sperm of the males in role 2 (second mates) are either favored or disfavored (Parker 1998). This situation may represent, for instance, the result of the females' sperm storage organ morphology on the probability of fertilization. Mating roles have been drawn randomly (i.e., roles are not associated to male general viability or sperm competitiveness). Thus, it is worth noting that being in the favored or disfavored role has no effect on a male's sperm competitive ability as such (i.e., his investment in sperm competition traits) but it will affect his fertilization success and, consequently, his paternity success. I have simulated a situation in which a last-in first-out mechanism results in every second male sperm doubling its probability of fertilizing a female's ova with respect to every sperm of the first male. The competitive loading of sperm in the second male role relative to sperm in the first male role, rL, equals in this case 2, and thus F2= 2 s2/(s1+ 2 s2) (Parker 1998). Also, I have simulated the reverse case (rL= 0.5; sperm of second male disfavored). Finally, I have simulated a sperm loading factor of 10, which leads to second males obtaining nearly complete sperm precedence (see Results), and represents a mechanism of sperm competition that can be considered equivalent to sperm displacement by sperm flushing. All these cases have been examined under scenarios in which good-sperm processes are absent or moderate.

IMPLICATIONS OF THE INEQUALITY BETWEEN F2 AND P2 FOR EMPIRICAL TESTING OF THE GOOD-SPERM MODEL

A typical study examining good-sperm processes would look at the correlation between P2, as a proxy for F2, and offspring viability. I have examined the relationship between paternity success for the second male (i.e., P2) and the viability of the second male's offspring (i.e., v2) that typical sperm competition experiments would obtain, and I have compared this with the underlying fertilization success-offspring viability relationship (F2, v2), and with the sperm competitive ability-offspring viability relationship (s2, v2). To do so, for each strength of good-sperm process described above, I have simulated three sets (a), (b), and (c), of 10,000 sperm competition experiments each, in which each sperm competition experiment consists of 50 random double matings. These simulations have been conducted by random resampling of sperm competitive ability values (s1 and s2) from the 60,000 values from the distribution S. From the set of simulations (a) I have calculated the correlation coefficient between F2 and v2 for each array of values within each simulated sperm competition experiment (number of correlation coefficients = 10,000, sample size for each correlation coefficient = 50). The association between F2 and v2 represents the best possible indicator of good-sperm processes (the relationship between sperm competitiveness and offspring viability) in an empirical study, assuming that fertilization success could be measured just after or soon after fertilization (i.e., before influences due to differential embryo mortality). From the set of simulations (b) I have calculated the correlation coefficients for the relationship between P2 and v2 in the same way. This association represents the indicator of good-sperm processes that would be calculated in experimental studies in which fertilization success is estimated from paternity success. From the set of simulations (c) I have calculated the 10,000 correlation coefficients for the relationship between s2 and v2, representing the real indication for the existence of good-sperm processes (relationship between sperm competitive ability-embryo viability), with the power given by the sample size (number of matings) used in each simulated test (n= 50). For each set of correlation coefficients, the mean correlation coefficient and the 95% confidence limits were calculated to assess the ability of s2, F2 and P2 values to detect real underlying good-sperm processes at the population level.

In addition to these simulations, the same process has been repeated three times, using the distributions S and V, but simulating a loaded raffle sperm mixing mechanism with sperm loadings for the second male (rL) equal to 0.5, 2, or 10 (see above).

Simulations and data analyses have been carried out using PopTools 2.7.5 (Hood 2006), Microsoft Office Excel 2003 and Statistica 6.0 (Statsoft 1996).

Results

THE INEQUALITY BETWEEN P2 AND F2

Variation in the ability of males to induce embryo viability leads to deviations from the equality between paternity success (P2) and fertilization success (F2), as showed in Figure 2, in which the absolute difference between P2 and F2 is plotted against the F2 value from which P2 arises. Paternity values can greatly differ from the fertilization value from which they arise. For example, an F2 value of 0.5 can generate values of P2 ranging from 0.2 to 0.8 (Fig. 2). The way that variation in S and V across males affects the inequality between P2 and F2 follows from the way P2 and F2 is calculated; the higher the difference between (1) the difference in sperm competitive ability values between two males mating to a female and (2) the difference in embryo viability values between these two males, the higher the extent to which P2 does not reflect F2.

Figure 2.

The inequality between paternity success (P2) and fertilization success (F2) due to intrinsic sire effects on embryo viability. The absolute difference between P2 and F2 (Abs. diff. P2F2) is plotted against the F2 value from which P2 arises. Each panel represents 10,000 double matings for each of the different strengths of underlying good-sperm processes (G-S), that is, strengths for the simulated relationship between sperm competitive ability (S) and embryo viability (V) at the population level (n= 60,000). These strengths are: Absent good-sperm processess, correlation coefficient between S and V, rS,V= 0.00; Weak, rS,V= 0.07; Moderate, rS,V= 0.25; Strong, rS,V= 0.45 (all P's << 0.001).

The importance of a deviation between P2 and F2 depends on its magnitude and the probability of obtaining such deviation. The probabilities for the deviations between P2 and F2 can be seen in Figure 3. Although, in general, the weaker the strength of good-sperm processes the higher the probability that P2 does not reflect F2, the inequality between P2 and F2 due to variation in embryo viability across males can induce high probabilities of mistakenly inferring F2 in all scenarios. For instance, an F2 value of 0.5 can generate P2 values that would lie within 0.2–0.3 or within 0.7–0.8 with a probability of about 0.1 in all cases. The probabilities for differences of between 0.1 and 0.2 units are appreciable in all scenarios (Fig. 3). Probabilities are higher for intermediate F2 values because of the impossibility that low (or high) values of F2 can generate much lower (or higher) P2 values.

Figure 3.

Probabilities that the absolute difference between P2 and F2 is higher than 0.1 (solid circles), 0.2 (open squares), or 0.3 (open circles) across the range of F2 values, for the different strengths of underlying good-sperm processes (see text). Probabilities are calculated from the simulation of 10,000 double matings for each case. The horizontal line indicates a probability of 0.05.

Hypothetical distributions of sperm competitive ability and embryo viability have been used to assess the influence of intrinsic sire effects on the power of P2 to reflect F2. Thus, the reported deviations between P2 and F2 values and their associated probabilities are illustrative, as they depend on the particular distributions of sperm competitive ability and embryo viability used as examples. Results are, however, similar, in the sense that considerable deviations between P2 and F2 can be obtained, using different distributions of sperm competitive ability and embryo viability (Fig. 4). Results are also similar when a loaded sperm mixing mechanism is simulated (online Supplementary Fig. S1).

Figure 4.

Probabilities that the absolute difference between P2 and F2 is higher than 0.1 (solid circles), 0.2 (open squares), or 0.3 (open circles) across the range of F2 values, for different examples of distributions of sperm competitive ability and embryo viability. (A) sperm competitive ability follows the S distribution and embryo viability follows a uniform distribution. (B) Sperm competitive ability follows the S distribution and embryo viability follows a normal distribution. (C) Sperm competitive ability follows a normal distribution and embryo viability follows a uniform distribution. (D) Both sperm competitive ability and embryo viability follow a normal distribution (see text for details of these distributions). Probabilities are calculated from the simulation of 10,000 double matings for each case (see text). Coefficient of correlation for the relationship between sperm competitive ability and embryo viability is zero in all cases (all n's = 60,000, all P's << 0.001). The horizontal line indicates a probability of 0.05.

IMPLICATIONS OF THE INEQUALITY BETWEEN P2 AND F2 FOR TESTS OF THE GOOD-SPERM HYPOTHESIS

Results obtained so far indicate that variation across males in their ability to induce embryo viability introduces noise in the estimation of fertilization success data from paternity success data. In this section I have assessed the consequences of these effects for empirical tests of the good-sperm model. I have calculated, across the different scenarios simulated, the mean and 95% confidence limits for the distribution of 10,000 correlation coefficients for the relationship between F2 and v2 (the best possible indicator of good-sperm processes in an empirical study), between P2 and v2 (the proxy indicator for the existence of good-sperm processes obtained in studies using paternity success data), and between s2 and v2 (the real indication for the existence of good-sperm processes) (see Materials and Methods).

The analysis of the correlation coefficients has important implications for empirical tests of the good-sperm model (see Table 1). When good-sperm processes are absent, sire effects on embryo viability are likely to generate correlation coefficients between paternity success (P2) and offspring viability that would be interpreted as evidence for the good-sperm process, if paternity success is used as a proxy for fertilization success or sperm competitive ability (see mean and 95% CL values for the relationship between P2 and v2 when rS,V= 0.00 in Table 1).

Table 1.  Mean correlation coefficients and 95% confidence limits (within brackets) for the distributions of correlation coefficients calculated for the relationships between s2 and v2 (s2, v2), between F2 and v2 (F2, v2), and between P2 and v2 (P2, v2), for each scenario simulated regarding the strength of the good-sperm processes. The number of correlation coefficients for the calculation of means and 95% CL is 10,000 for each relationship in each case (see text for details), whereas the sample size for each correlation coefficient is 50 (i.e., 10,000 sperm competition experiments of sample size 50 each have been simulated for each relationship in each scenario).
 Strength of good-sperm processes
Absent (rS,V=0.00)*Weak (rS,V=0.07)*Moderate (rS,V=0.25)*Strong (rS,V=0.45)*
  1. *Population wide correlation coefficients for the good-sperm association between S and V are based on a sample size of 60,000.

s2, v20.000.070.250.44
(−0.27 0.28)(−0.21 0.35)(−0.07 0.56)(0.15 0.66)
F2, v20.000.050.170.28
(−0.28 0.28)(−0.24 0.32)(−0.14 0.45)(0.00 0.52)
P2, v20.480.500.540.58
(0.25 0.68)(0.28 0.68)(0.31 0.72)(0.38 0.75)

Another important result emerges from the analysis of cases in which good-sperm processes are present in the population. The inequality between P2 and F2 due to variance in embryo viability across males would result in an overestimation of the correlation between sperm competitiveness and offspring viability, if fertilization success is estimated at birth or hatching. In other words, good-sperm processes would be overestimated using P2 data (compare mean correlation coefficients and 95% CL for the relationship between P2 and v2, when weak, moderate, and strong good-sperm processes take place, to the “real” underlying population-wide relationship between S and V, and to the coefficients for the relationship between s2 and v2). This result arises because P2 values are determined to a greater or lesser extent by embryo viability. Therefore, the correlation between sperm competitive ability (estimated from P2) and offspring survival (e.g., from juvenile to adult) would be confounded by covariance between two components of offspring viability (male-induced prebirth and postbirth offspring viability).

In addition, the analysis of the correlation coefficients indicates that when good-sperm processes are weak or moderate the chances that these processes are detected using true fertilization success data (F2) are low (Table 1). There are two reasons for this result. First, there are limitations of the sample size (n= 50 for each sperm competition experiment) on the power to detect underlying weak-to-moderate good-sperm processes, as indicated by the mean and 95% CL for the correlation coefficients between s2 and v2 when rS,V= 0.07 and when rS,V= 0.25 population-wide (Table 1). Thus, even in the hypothetical case that determining true sperm competitive ability were possible, a sample size of 50 matings trials in a sperm competition experiment would not be enough to detect weak to moderate good-sperm processes. The second reason explaining why the use of true fertilization success data may not properly account for underlying good-sperm processes is that fertilization success is a relative measure of sperm competitiveness. A male's fertilization success depends not only on his sperm competitive ability but also on the ability of competitor males to win fertilizations. Random effects due to the relative nature of fertilization success introduce noise in the estimations of sperm competitive ability, and consequently, in associations involving this trait (F. García-González, unpubl. data). A comparison of the mean correlation coefficients and 95% CL for the relationships between F2 and v2 and between s2 and v2 across all the different good-sperm scenarios (Table 1) supports the notion that the relative nature of fertilization success implies an underestimation of the real association between sperm competitive ability and offspring viability.

Results obtained under a loaded raffle are qualitatively and quantitatively similar to those obtained under a fair raffle sperm mixing mechanism (online Supplementary Table S1).

In summary, on the one hand our ability to detect good-sperm processes can be hindered if we work with true fertilization success values (F2), whereas on the other, when testing the good-sperm prediction with P2 data, good-sperm processes can be overestimated or simply appear because of covariation between two measures of male intrinsic quality that may be independent of sperm competitiveness.

Discussion

Studies on postcopulatory sexual selection generally estimate fertilization success (F2) from paternity assigned at hatching or birth (P2). However, P2 values are not only the result of sperm competitive ability but they are also influenced by embryo survival from conception to birth. I have analyzed the effects of heritable variation across males in their ability to induce normal embryo development on the power of paternity success values to reflect fertilization success. Results show that intrinsic sire effects on embryo viability can be responsible for deviations between P2 values and the F2 values from which the former arise, and that these deviations can lead to errors when interpreting sperm competition data. The inequality between P2 and F2 depends on the variance in sperm competitiveness, the variance in the ability of males to induce embryo viability, and on the relationship between both traits. An important consequence of the inequality between P2 and F2 is that it would hinder the examination of postcopulatory models of sexual selection. The findings in this manuscript suggest that two critical points need to be taken into account in the examination of good-sperm processes: the potential inequality between P2 and F2 due to sire influences on embryo viability, and the relative nature of fertilization or paternity success measures.

Simulations of sperm competition trials reveal that, when paternity data are used, differential embryo viability caused by intrinsic sire effects may lead to an overestimation of underlying good-sperm processes, or to erroneous indications for their existence. The confounding effects generated from the inequality between P2 and F2 due to sire influences on embryo viability are especially important if good-sperm processes are absent, weak, or moderate. These findings indicate that caution needs to be taken when using P2 values as a proxy for fertilization success or sperm competitiveness. Results in this study provide quantitative evidence in support of previous arguments questioning the use of paternity success as a perfect predictor of fertilization success (Gilchrist and Partridge 1997; Olsson et al. 1999; Jennions and Petrie 2000; Simmons 2005; Evans et al. 2007; García-González and Simmons 2007a), and emphasize that the consequences of differential embryo mortality affecting paternity success values are not limited to situations of genetic incompatibilities between parental haplotypes (Olsson et al. 1999).

In addition, results in this study support the notion that another important aspect to consider in studies of postcopulatory sexual selection is the relative nature of fertilization success (F. García-González, unpubl. data). The good-sperm model predicts a relationship between absolute entities: investment in traits that determine the output of sperm competition (sperm competitive ability) and offspring viability (Yasui 1997). However, a male's overall sperm competitive ability can only be inferred from his fertilization success, a measure that is conditional to the sperm competitive abilities of rival males. Thus, random effects may introduce noise in the ability of fertilization success to predict sperm competitive ability (F. García-González, unpubl. data). Results from the simulations indicate that the real underlying association between sperm competitive ability and offspring viability predicted by the good-sperm model (Yasui 1997) can be underestimated or even go undetected when using fertilization success measures. Paternity success measures are also affected by problems inherent to their relative nature, and therefore, if P2 values are not affected by differential embryo viability, they would tend to underestimate good-sperm processes.

Obtaining unequivocal data for testing the good-sperm model is challenging. The detection of underlying good-sperm processes requires large sample sizes, and the empirical detection of good-sperm processes can be confounded by the effects shown in this study. Phenotypic investigations of the relationship between fertilization success and offspring viability are particularly susceptible to these effects, compared with studies focusing on the genetic architecture of traits contributing to sperm competitive ability. Quantitative genetic analyses have proved useful for investigating postcopulatory processes (Simmons and Kotiaho 2007), and studies on the genetic basis of sperm traits significantly advance our understanding of postcopulatory phenomena (Simmons and Moore 2008). However, as pointed out elsewhere (F. García-González, unpubl. data), our understanding of postcopulatory sexual selection greatly benefits from analyses looking at the sperm competitiveness phenotype as estimated from fertilization success. Quantitative genetic studies focusing on specific traits are generally limited to the investigation of one or a few traits. The relevance of these traits for sperm competition needs to be tested with selection experiments or fertilization success trials. In addition, rarely a considerable portion of variance in success at fertilizing ova is explained by just one or a few traits, probably because of the complexity of interactions that ultimately regulate fertilization success (Moore et al. 2004). Effort must be made to identify and control confounding effects in phenotypic studies, because it is in these studies that the outcome of this complexity is revealed.

The present study provides a framework that can be extended to situations in which embryo survival is not only determined by direct transmission of genes in sires coding for embryo viability, but also by environmental influences that are themselves genetically determined, that is, indirect genetic effects (Mousseau and Fox 1998; Wolf et al. 1998). García-González and Simmons (2007a) have recently showed the existence of paternal effects and interacting phenotypes (Moore et al. 1997) on embryo viability in an insect species. If these effects are widespread they would contribute to the inequality between P2 and F2. Future research addressing indirect genetic effects on embryo viability, and also investigating whether sperm competition traits need to be analyzed as interacting phenotypes (Moore and Pizzari 2005; Simmons and Moore 2008) is warranted.

Several methodological measures may be taken to alleviate confounding effects when testing the good-sperm model. The most obvious is that fertilization success should be estimated before mortality of embryos occur, or otherwise the closest to conception as possible. In addition, to minimize confounding effects due to the relative nature of fertilization or paternity success measures, it would be desirable to look at the relationship between sperm competitive ability and offspring viability using the difference in fertilization success between two males paired with a female (Hosken et al. 2003), and the difference in offspring viability between the two males. Independence of the measures of sperm competitiveness and offspring viability can be attained by obtaining viability measures from single matings (Hosken et al. 2003; Fisher et al. 2006). This procedure presents two other advantages. First, it reduces variation due to differences in sample size arising from paternity biases: if viability measures are taken from matings involving both types of males, less competitive males render lower numbers of offspring to be screened for viability than more competitive males. Second, it controls for indirect genetic effects in the form of interacting phenotypes on offspring survival (see above).

To date, the most convincing phenotypic study providing data in support of the good-sperm model has been carried out by Fisher et al. (2006) on the marsupial Anthechinus stuartii (see also Hosken et al. 2003; but see Tregenza et al. 2003). Fisher et al. (2006) found that the survival of offspring produced by females mated to males with superior sperm competitive ability was higher than that of offspring from females mated to males with lower ejaculate competitiveness. These authors used independent matings for estimating fertilization success and viability measures, and estimated ejaculate competitiveness for individual males across different polyandrous females. Sperm competitive ability was estimated from paternity assessed just at birth, minimizing the likelihood of obtaining a spurious correlation between offspring survival and paternity success, although potentially confounding effects stemming from differential mortality during gestation and embryo implantation could have still caused P2 measures to contain variance due to embryo viability. Ultimately, the good-sperm model needs support from studies that can unequivocally separate the males' ability to win fertilizations from their ability to influence the development of embryos.

The present study emphasizes the value of obtaining data on the sources of variation in fertilization success and embryo viability. Several factors may contribute to the maintenance of genetic variance in sperm competitive ability, including sex-biased inheritance, antagonistic pleiotropy in determinants of paternity, and male × female or male × male genotypic interactions (Wilson et al. 1997; Clark 2002; Pizzari and Birkhead 2002; Birkhead et al. 2004; Bjork et al. 2007; Dowling et al. 2007; Zeh and Zeh 2008). I have recently shown that random effects arising from the relative nature of fertilization success represent an obstacle for the detection of additive genetic variance in sperm competitive ability (F. García-González, unpubl. data). Likewise, differential embryo survival across a female's offspring due to variation in sire genetic quality can represent another confounding factor if genetic variance in sperm competitiveness is examined using paternity success values. In those cases in which heritability or repeatability of sperm competitive ability is inferred from P2 values, the possibility that intrinsic sire effects on embryo viability play a role needs to be considered, because these effects alone may drive congruence in putative sperm competitiveness (Gilchrist and Partridge 1997). That P2 values may need to be corrected with measures of embryo survival is a measure that is either acknowledged or followed by a number of researchers (e.g., see comments in Lewis and Austad 1990; Wilson et al. 1997; Arnqvist and Danielsson 1999; Clark 2002; Evans et al. 2003) but still not widely applied in the majority of studies in the area.

External fertilizing species are proving to be ideal study systems to separate male effects on sperm competitive ability and on offspring viability. In these species, experimental designs to investigate the sources of variation on true fertilization success and/or components of offspring viability are amenable, and their use is providing unequivocal evidence for the implication of intrinsic male quality or genetic compatibility processes on fitness traits (e.g., Wedekind et al. 2001; Evans and Marshall 2005; Rudolfsen et al. 2005; Evans et al. 2007; Marshall and Evans 2007; Pitcher and Neff 2007). Fertilization success and embryo viability can also be studied in internal fertilizing species for which morphological markers that allow paternity assignment during embryo development are available (Weigensberg et al. 1998; García-González and Simmons 2007a). In internal fertilizers, half-sibling designs or diallel crosses are powerful tools to evaluate the implication of intrinsic sire effects on embryo development (García-González and Simmons 2005a; Ivy 2007; Jennions et al. 2007). If the biology of the species or the methodology available does not allow for the assignment of paternity soon after conception, effort should be made to assess embryo survival for the different males or male genotypes (see for instance Clark et al. 2000; Mack et al. 2002). For instance, embryo survival can be assessed for the offspring of males mated singly to virgin females to correct subsequent paternity estimates, provided that embryo survival is seen to be repeatable across a male's mates.

The results obtained in this article also highlight that the study of the evolution of polyandry would benefit from a better understanding of the interplay between different components of offspring viability. There are few studies providing unequivocal evidence for association between the prebirth and postbirth components of offspring fitness. For instance, Wedekind et al. (2001) found two different components of genetic quality during embryo development in the Alpine whitefish. Early embryo mortality was mainly affected by male × female interactions, whereas late embryo mortality was affected primarily by sire effects (see also Evans et al. 2007). Similarly, Ivy (2007) found significant additive genetic variance for offspring survival and strong paternal effects for hatching success but no sire effects for development time from oviposition to hatching in the cricket Gryllodes sigillatus. In the present study the male components to prehatching and posthatching offspring viability have been assumed to be genetically correlated. This simplifies the illustration of the effects of sire effects on embryo viability. Nevertheless, the central finding of the analysis remains if these two components of male quality are not genetically correlated. Variation across males in their influence on embryo viability generates, inevitably, inequality between P2 and F2 that will confound the analysis of associations involving P2 values as a surrogate for sperm competitive ability.

In conclusion, variation in the genetic quality of a female's mates that is expressed during the development of embryos may confound fertilization success measures estimated from paternity assigned at hatching or birth. The implications of sire effects on embryo viability are important for the study of postcopulatory sexual selection, in particular for the study of the genetic basis of sperm competitive ability, for analyses of the good-sperm model, and in general for studies in which individual measures of sperm competitive ability or fertilization success are relevant. To advance the understanding of the role that sperm competition plays in the evolution and maintenance of polyandrous behavior more research is needed in several areas. These include studying the sources of variation in fertilization success and embryo viability, the genetic basis of prebirth and postbirth components of offspring viability, and the influence of paternal effects and other indirect genetic effects on embryo viability.

Associate Editor: R. Snook

ACKNOWLEDGMENTS

I am grateful to L. Simmons and J. Evans for comments on earlier drafts of the manuscript, and to two anonymous referees for insightful comments that improved the final version. This work was supported by the Australian Research Council.

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