EXTRA-PAIR PATERNITY AND THE VARIANCE IN MALE FITNESS IN SONG SPARROWS (MELOSPIZA MELODIA)

STUDY SYSTEM

A resident, socially monogamous song sparrow population on Mandarte Island, BC, Canada, has been studied intensively since 1975 (Smith et al. 2006) and averaged 30 ± 12 (SD) breeding pairs during 1993–2008. Each year during March–August, all breeding attempts are monitored and all offspring surviving to about six days posthatch (81% of all eggs laid on average) are uniquely marked with metal and colored plastic rings (Smith et al. 2006). All offspring that survived to independence from parental care (about 24 days posthatch) are identified. All immigrants are caught and ringed soon after settling (1.1 immigrant/year on average) so that all resident song sparrows are individually identifiable throughout their lives. Mandarte's small size (about 6 ha) and simple habitat structure (Smith et al. 2006) mean that the probability of observing a living individual is effectively one (Wilson and Arcese 2008). There is therefore complete knowledge of the identities of all adults (≥1-year old) alive each year (Reid et al. 2005; Smith et al. 2006; Keller et al. 2008). The high average recruitment rate of independent offspring on Mandarte (about 30%), and the rarity of marked dispersers on surrounding islands, suggests that successful dispersal from Mandarte is infrequent (Arcese 1989; Keller 1998; Wilson and Arcese 2008). Local survival to recruitment can therefore be measured unusually precisely (Keller et al. 2001; Reid et al. 2005; Keller et al. 2008).

Each year, the social parents of all offspring are identified as those incubating clutches or provisioning chicks within defended territories (Keller 1998; Sardell et al. 2010). Both sexes can breed at the age of one year and most recruited offspring survive one to three years (median 2, interquartile range 1–4). Females typically make one to three breeding attempts per year with mean clutch size 3.4 ± 0.6 (SD). Because the adult sex ratio is often male biased, a substantial proportion of males remains socially unpaired for whole breeding seasons (Hochachka et al. 1989; mean proportion of males that were unpaired during 1993–2008: 0.36 ± 0.19 [SD]). Although song sparrows show little morphological dimorphism, male song is a highly sexually dimorphic trait that functions in male–male competition and female mate choice (Arcese 1989; Reid et al. 2004).

PATERNITY ASSIGNMENT

During 1993–2008, blood samples (≤50 μl) were taken from 99.4% of all ringed offspring (2207/2221 from 811 breeding attempts), nearly all adults alive on Mandarte in 1993, and all subsequent immigrants (Sardell et al. 2010). All individuals were genotyped at 13 highly polymorphic autosomal microsatellite loci and parentage was assigned to all offspring using Bayesian full probability models that incorporated microsatellite data and the spatial location of offspring and potential sires (Sardell et al. 2010). All assigned dams had been correctly identified by social behavior. Sires were assigned to 99.2% of sampled offspring with ≥95% individual-level confidence and the estimated number of unsampled sires was approximately zero. Overall, 28% of offspring were assigned to an extra-pair male (Sardell et al. 2010), similar to the 24% estimated in a nearby mainland population (Hill et al. 2011). Because sires were assigned with high statistical confidence to nearly all offspring ringed during 1993–2008, and all independent and recruited offspring, the data provide a comprehensive record of the reproductive success of all adult males alive during 1993–2008.

ANNUAL AND LIFETIME FITNESS

For each adult male song sparrow alive on Mandarte during 1993–2008, apparent and realized ARS were estimated as the numbers of offspring reared and sired in each year. All males were classified as socially paired if they mate-guarded and/or provided paternal care, or socially unpaired if they remained unpaired for the entire season. Apparent ARS was by definition zero for socially unpaired males. ARS was calculated as the number of hatched offspring that survived to ringing (as in all previous studies, Table 1), independent offspring (surviving to independence from parental care), and recruited offspring (that survived to age one year). These measures were positively correlated across males (hatched vs. independent, r_S= 0.85; independent vs. recruited, r_S= 0.56; hatched vs. recruited, r_S= 0.47 based on male realized ARS). Mean male ARS was lower than mean female ARS due to the male-biased adult sex ratio.

Each male's apparent and realized LRS (a rate-insensitive measure of fitness) was calculated as the total number of offspring reared and sired over its entire life. For each male, apparent and realized λ_ind, a rate-sensitive measure of fitness that accounts for differential timing of reproduction, was calculated as the dominant eigenvalue of an individual age-structured projection matrix (McGraw and Caswell 1996). Matrices were parameterized using each individual's observed life span (with appropriate age-specific survival probabilities of 1 or 0) and age-specific reproductive success measured as hatched, independent, or recruited offspring. Because matrix fecundity elements describe the number of same-sex one-year-old offspring produced per year (McGraw and Caswell 1996; Brommer et al. 2002), elements parameterized in terms of an individual's observed number of hatched or independent offspring were multiplied by the mean population-wide proportions of hatched and independent offspring that survived to age 1 (0.187 and 0.283, respectively). All were multiplied by 0.5 because the hatching sex ratio is about 50:50 (Postma et al. 2011). λ_ind values do not predict population growth rate due to the male-biased adult sex ratio. Estimates of LRS and λ_ind could be biased if males that recruited on Mandarte subsequently emigrated to breed elsewhere. However, any such bias is probably very small because no such cases have been observed despite extensive study (Smith et al. 2006; Wilson and Arcese 2008).

VARIANCE IN MALE FITNESS

There are multiple metrics of variation in fitness, with slightly different interpretations and utilities (Kokko et al. 1999). We used three metrics to quantify the effect of EPP on variation in male fitness, and assessed whether conclusions were consistent across these metrics (Kokko et al. 1999). First, we calculated the variance (Var) of male ARS, LRS, and λ_ind as the second moment of the observed distributions:

where n is the number of observations, x the individual fitness value (ARS, LRS, or λ_ind), and μ is mean fitness across all males. Second, we calculated the mean-standardized variance in male ARS, LRS, and λ_ind, which corresponds to the maximum opportunity for selection (I):

I equals the variance in relative fitness and is unambiguously interpreted as the maximum potential magnitude of selection as it is a selection differential on relative fitness (Arnold and Wade 1984; Shuster and Wade 2003). Third, we calculated Morisita's index (I_δ, Morisita 1962; Tsuji and Tsuji 1998) for male ARS and LRS:

I _δ measures clumping, adjusting the observed variance by the variance when reproductive success is equal across all observed individuals. It is independent of μ and equals 1 when fitness is uniformly distributed and >1 if the distribution is skewed. Morisita's index was not calculated for λ_ind because most values of λ_ind fell between 0 and 1, making the numerator negative.

Var, I, and I_δ were calculated for apparent and realized male fitness measured either annually (Var_ARS, I_ARS, and I_δARS) or over individuals’ life spans (Var_LRS, I_LRS, and I_δLRS). In each case, fitness was measured as hatched, independent, and recruited offspring. The relative change in variance due to EPP was then calculated as the ratios of Var, I, and I_δ calculated for realized versus apparent fitness (Var-ratio, I-ratio, and I_δ-ratio) at each offspring stage. Analyses of LRS and λ_ind were restricted to individuals hatched during 1993–2003 because some individuals hatched during 2004–2008 were still alive in 2009. Table S1 summarizes the nomenclature and definitions of all measures of fitness and variation.

Finally, to test whether the distributions of apparent and realized ARS and LRS differed more subtly than detected by the Var-, I-, and I_δ-ratios, categorical G-tests were used to determine whether the frequencies of males that produced specific numbers of apparent and realized offspring differed significantly. Males that produced ≥10 hatched, ≥10 independent, and ≥ 5 recruited offspring were pooled to provide sufficient sample sizes in each discrete category.

DECOMPOSITION OF THE OPPORTUNITY FOR SELECTION

A male's total realized reproductive success (T) is the sum of its WPRS and EPRS. The total variance in T (Var(T)) can therefore be decomposed into the variances in WPRS and EPRS (Var(W) and Var(E)) and their covariance (Cov(W,E)) where

This decomposition is valid for variables of any distribution as long as the components of interest are strictly additive (Arnold and Wade 1984). For ARS and LRS, Var(W), Var(E), and 2 × Cov(W, E) were calculated from the number of within-pair and extra-pair offspring sired by each male (Webster et al. 1995) measured as hatched, independent, and recruited offspring, both across all years and cohorts combined, and within each individual year and cohort. To facilitate comparisons with other studies, Var(T) and its variance components were standardized dividing by the squared mean T; thereby decomposing the realized opportunity for selection (I_T) into the opportunity for selection due to WPRS (I_W), EPRS (I_E), and the standardized covariance (CovI_W,_E). Ratios of each variance component to the total standardized variance in male reproductive success are reported. Linear regressions were used to quantify the relationship between CovI_W,_E and the I_ARS-ratios and I_LRS-ratios across 16 years for ARS and 11 cohorts for LRS.

Var(W), Var(E), and Cov(W,E) could be further decomposed into subcomponents of variance (i.e., the number of mates, number of offspring per mate, and proportion of offspring sired, Webster et al. 1995). This further decomposition was not implemented because the sum of these subcomponents cannot equal Var(T), rendering their interpretation unclear (Appendix S1).

The rate-sensitive measure of male lifetime fitness (λ_ind) is unlikely to equal the sum of λ_ind for individual age-structured projection matrices parameterized for male WPRS and EPRS separately. This is because the dominant eigenvalues of individual projection matrices are associated with eigenvectors whose directions are likely to differ. The variance in λ_ind could therefore not be simply decomposed as a function of the variances and covariance in WPRS and EPRS.

PAIRED VERSUS UNPAIRED MALES

To quantify the degree to which failing to identify socially unpaired males would have affected variance estimates and altered conclusions, we repeated all analyses across all males combined and across socially paired and unpaired males separately. Many unpaired males were one-year old and paired in subsequent years (Smith and Arcese 1989; Keller et al. 2008; Sardell et al. 2010). Males that were socially unpaired for their entire lifetime therefore primarily comprised males that survived only one year.

All analyses were run in R v.2.10.1 (R development Core Team 2009). All observations of ARS were retained even though many males were alive in more than one year. Any pseudo-replication does not affect the estimated variances that are our primary focus, and no individual contributed more than 1.3% of observations.

VARIANCE IN ARS, ALL MALES

Apparent and realized ARS were measured for 769 male-years comprising 310 individual adult males alive during 1993–2008 (Fig. 1). Across all observations, the median, interquartile range (IQR), mean, and variance in ARS decreased as ARS was measured as hatched, independent, or recruited offspring, whereas the proportion of males with zero ARS increased (Table 2A, Fig. 1). The precise distributions of realized ARS measured at each offspring stage differed from those of apparent ARS (Fig. 1, G-tests in Table 2A). However, the median, IQR, and mean apparent ARS were identical to those of realized ARS at all offspring stages, and the proportions of males with zero ARS were very similar (Table 2A). Across all data, the variances in realized ARS were greater than in apparent ARS at all offspring stages, but only by about 2–14% (ratios in Table 2A).

However, there was substantial among-year variation in the ratio of the variances in realized versus apparent ARS (I_ARS-ratio) at all offspring stages (Table 3B). Specifically, I_ARS-ratios ranged from 0.60 to 2.00 for hatched offspring, 0.78 to 1.75 for independent offspring, and 0.58 to 1.40 for recruited offspring with considerable differences between consecutive years (Table 3B).

Across all males and years combined, the opportunity for selection due to male WPRS (I_W) was much greater than the opportunity for selection due to EPRS (I_E) whether ARS was measured as hatched, independent, or recruited offspring (Table 3A). The standardized covariance between annual WPRS and EPRS was positive but smaller than I_E and substantially smaller than I_W (Table 3A).

Within each year, annual I_W was generally, but not always, greater than I_E (Table 3B). There was substantial among-year variation in the magnitude of these standardized variances, and in the magnitude and direction of the standardized covariances (Table 3B). The I_ARS-ratio increased significantly with the standardized covariance between WPRS and EPRS at all three offspring stages (Fig. 2).

VARIANCE IN ARS, SOCIALLY PAIRED VERSUS UNPAIRED MALES

A total of 186 adult males alive during 1993–2008 remained socially unpaired for at least one year, totaling 261 male-years. Socially unpaired males sired up to five extra-pair offspring per year (Fig. 3). However, about 85% of these males sired zero hatched or independent offspring, and 95% sired zero recruited offspring (Table 2B). Hence, although realized I_ARS and I_δARS for socially unpaired males were high, this primarily reflects their very low mean ARS rather than high variance (Table 2B, Fig. 3).

A total of 219 males were socially paired for at least one breeding attempt within any single year, totaling 508 male-years. Across these males, the precise distributions of apparent and realized ARS differed to some degree (Fig. 3, G-tests in Table 2C). However, the median, proportion of zeros, IQR, and mean apparent ARS were very similar to those for realized ARS (Table 2C). Across all years and offspring stages, the variances in realized ARS exceeded those in apparent ARS by about 4–42% (ratios in Table 2C). The Var_ARS-, I_ARS-, and I_δARS-ratios were consistently greater across socially paired males than across all males at analogous offspring stages (Table 2A, C).

I_ARS-ratios and the decomposition of realized I_ARS for socially paired males in each individual year are presented in Table S2. In summary, standardized variances in WPRS, EPRS, and their standardized covariance (I_W, I_E, and CovI_W,E) were smaller across socially paired males than across all males, both across all years and in each individual year (Tables 3 and S2). However, the ratios of each variance component to the total realized I_ARS were similar across socially paired males to those estimated across all males both overall (Table 3A, C) and in individual years (Tables 2B and S2B).

VARIANCE IN LIFETIME FITNESS, ALL MALES

LRS was measured for 183 males hatched during 1993–2003 (Fig. 4). Across all observations, the median, IQR, mean, and variance in LRS decreased as LRS was measured as hatched, independent, and recruited offspring, whereas the proportion of males with zero LRS increased (Table 4A, Fig. 4). The distributions of realized LRS differed from those of apparent LRS (Fig. 4, G-tests in Table 4A). Across all cohorts and offspring stages, realized Var_LRS, I_LRS, and I_δLRS were about 11–27% greater than apparent Var_LRS, I_LRS, and I_δLRS (ratios in Table 4A). The variances in LRS were greater than the variances in ARS at analogous offspring stages, except for I_LRS measured as recruited offspring (Tables 1 and 3). Furthermore, the Var-, I-, and I_δ-ratios for LRS were about 4–17% higher than those for ARS across analogous offspring stages (Tables 1 and 3).

However, there was substantial among-cohort variation in I_LRS-ratio at all three offspring stages (Table 5B). Specifically I_LRS-ratios ranged from 0.89 to 2.14 for hatched offspring, 0.85 to 2.34 for independent offspring, and 0.23 to 1.89 for recruited offspring, with considerable differences between consecutive cohorts (Table 5B).

Across all males and cohorts, the opportunity for selection due to lifetime WPRS (I_W) was substantially greater than that due to lifetime EPRS (I_E) whether LRS was measured as hatched, independent, or recruited offspring (Table 5A). The standardized covariance between lifetime WPRS and EPRS was positive (Table 5A) and substantially greater than the standardized covariance between annual WPRS and EPRS (Tables 2A and 4A).

Within each cohort, lifetime I_W was generally, but not always, greater than lifetime I_E (Table 5B). The standardized covariance between lifetime WPRS and EPRS was generally positive but varied substantially in magnitude and direction (Table 5B). The I_LRS-ratio did not vary significantly with the standardized covariance between lifetime WPRS and EPRS at any of the three offspring stages (Fig. 5).

Across all 183 males, the mean and variance in realized λ_ind (the rate-insensitive measure of lifetime fitness) were similar to those for apparent λ_ind (Table 4B). Estimates of I_λ were slightly greater for realized λ_ind than apparent λ_ind at all three offspring stages, but by ≤13% (ratios in Table 4B).

VARIANCE IN LIFETIME FITNESS, SOCIALLY PAIRED VERSUS UNPAIRED MALES

A total of 65 males remained socially unpaired for their entire life (median life span: 1 year, range: 1–3). These males sired up to three hatched extra-pair offspring (Fig. 6) but very few sired any recruited offspring (Table 4C). Their apparent and realized LRS therefore remained very low (Table 4C, Fig. 6).

Across 118 males that were socially paired for at least one breeding attempt during their life, the median, IQR, proportion of zeros, and mean for apparent LRS were similar to those for realized LRS (Table 4D). Across all cohorts and offspring stages, realized Var_LRS, I_LRS, and I_δLRS were 14–38% greater than apparent Var_LRS, I_LRS, and I_δLRS (ratios in Table 4D, Fig. 6). For the rate-sensitive measure of lifetime fitness, the variances and opportunity for selection (Var_λ and I_λ) were 2% smaller to 57% greater for realized λ_ind than for apparent λ_ind.

Lifetime I_W, I_E, and CovI_W,E were smaller across males that were socially paired at least once than across all males and cohorts (Tables 4C and 5A). However, the ratios of each standardized variance component (I_W, I_E, and CovI_W,E) to the total I_LRS among socially paired males were similar to those estimated across all males and cohorts (Tables 4C and 5A). I_LRS-ratios and the decomposition of the realized I_LRS in each individual cohort for socially paired males are presented in Table S3. In summary, standardized variances and covariances in WPRS and EPRS were consistently smaller across socially paired males than across all males, but the ratios of each variance component to the variance in male LRS across paired males were similar to those estimated across all males (Tables 4B and S3b).

VARIANCE IN ARS

Across all males and years, three measures of variation in male ARS (Var, I, and I_δ) remained relatively similar whether estimated as apparent or realized ARS. This result was broadly consistent whether ARS was measured as hatched, independent, or recruited offspring (range of ratios: 2–14%). Thus, despite the relatively high EPP rate of 28%, EPP had a relatively small effect on the variance in ARS in song sparrows. There was therefore qualitative but only limited quantitative support for the hypothesis that EPP will substantially increase the variance in male fitness. These results contrast with previous (less-comprehensive) studies of socially monogamous but genetically polygynandrous bird populations, which report that EPP substantially increased male I_ARS. Indeed, the median ratio of realized to apparent I_ARS for hatched offspring across 17 published studies is 2.9, compared to 1.1 in song sparrows (Table 1).

However, there was substantial among-year variation in I_ARS-ratio in song sparrows, ranging from 0.57 to 2.00 across all years and offspring stages. EPP therefore approximately doubled or halved I_ARS in different years. Because most previous studies covered few years (Table 1), it is not yet clear whether substantial among-year variation in I_ARS-ratio is common, and hence whether effects estimated by short-term studies may simply reflect individual study years rather than any consistent or average effect.

VARIANCE IN LRS

Individual fitness is commonly measured as ARS (Kingsolver et al. 2001). However ARS may inaccurately predict fitness if there are cross-season trade-offs among fitness components, potentially providing misleading conclusions regarding the effect of EPP on the variance in total fitness. In song sparrows, variance in apparent LRS was substantial (see also Hochachka 2006) and consistently greater than the variance in ARS at all offspring stages. However, as with ARS, variation in realized LRS was only slightly greater than the variation in apparent LRS (11–27% measured as Var, I, or I_δ). This result is broadly consistent with the only other study that quantified variation in male apparent and realized LRS in a socially monogamous but genetically polygynandrous species; realized I_LRS was 12% greater than apparent I_LRS in splendid fairy wrens (Malurus splendens, Webster et al. 2007). This study and ours also report the lowest I_ARS-ratios published to date (Table 1), and both indicate that I_LRS-ratios slightly exceed I_ARS-ratios. The effect of EPP on the variance in male fitness might therefore be greater when integrated over each individual's life span than over individual breeding seasons. Furthermore, the I_LRS-ratio varied substantially among song sparrow cohorts, from 0.23 to 2.34 across all offspring stages. EPP therefore more than doubled I_LRS or reduced it by a factor of four in different cohorts, showing that the true lifetime realized opportunity for selection may be substantially larger or smaller than the apparent opportunity in any individual cohort.

VARIANCE IN RATE-SENSITIVE LIFETIME FITNESS

A male's ability to sire within-pair and/or extra-pair offspring could vary with age, for example if young males lose paternity to older males (Richardson and Burke 1999; Schmoll et al. 2007). Rate-insensitive measures of fitness such as LRS do not incorporate any such age-specific paternity loss or gain. However, the effect of EPP on the variance in rate-sensitive measures of lifetime fitness, such as λ_ind, has not previously been estimated.

In song sparrows, variances in λ_ind were consistently lower than variances in LRS measured at analogous offspring stages. This may be because although variation in life span increases the variance in LRS compared to ARS, it increases the variance in λ_ind to a lesser degree because the value of offspring produced later in a male's life is discounted (Brommer et al. 2002). Furthermore, the slight increase in the variance in male LRS due to EPP was even less evident when fitness was measured as λ_ind. Indeed, the variance in realized λ_ind even decreased slightly relative to the variance in apparent λ_ind when λ_ind was estimated as recruited offspring. Analysis of λ_ind therefore suggests that, on average, EPP increased the variance in adult male fitness slightly or not at all in song sparrows.

MECHANISMS

The fact that EPP increased the variance in male fitness less in song sparrows than reported in other populations (Table 1) may primarily reflect the less-comprehensive paternity assignment in those studies and the consequent inflation of estimated I_ARS-ratios. This bias is well documented (Downhower et al. 1987; Freeman-Gallant et al. 2005). However, the distribution of EPP on Mandarte is skewed across males and repeatable within males among years (Reid et al. 2011), two conditions that underpin the potential for EPP to increase the variance in fitness (Webster et al. 1995). The observation that EPP did not substantially increase the overall variance in male fitness therefore requires further explanation.

The small overall effect of EPP on the variance in male fitness may result from the presence of socially unpaired males with zero apparent reproductive success. These socially unpaired males sired few extra-pair offspring (Sardell et al. 2010), and so also had very low realized reproductive success. The presence of socially unpaired males therefore dampens the effect of reallocation of paternity among socially paired males on the total variance in fitness. Indeed, EPP increased the variance in male ARS by 4–42% when socially unpaired males were excluded (compared to 2–14% across all males). These results support Shuster's (2009) suggestion that studies that fail to sample socially unpaired or otherwise unsuccessful males may overestimate the effect of EPP on the total variance in male fitness.

However, even after excluding socially unpaired males, the overall increase in the variance in realized versus apparent fitness was still relatively small on average. Small effects of EPP on the I-ratio might be expected if reproductive success gained through EPP is offset by reduced WPRS due to cuckoldry (Webster et al. 1995). The I-ratio is therefore expected to reflect the magnitude and direction of covariance between male WPRS and EPRS (Webster et al. 1995; Jones et al. 2001). Across all years and cohorts, the covariances between male annual and lifetime WPRS and EPRS were positive, showing that males that successfully sired within-pair offspring also sired more extra-pair offspring. However, the magnitude and direction of the covariance between annual WPRS and EPRS varied substantially among years, and explained approximately a third of the among-year variation in I_ARS-ratio. The covariance between lifetime WPRS and EPRS also varied substantially among cohorts, but explained only 0–28% of the among-cohort variation in the I_LRS-ratio. The hypothesis that variation in I-ratio reflects the covariance between WPRS and EPRS was therefore somewhat supported with respect to ARS, but less so with respect to LRS, and substantial proportions of variation remained unexplained.

In general, limited effects of EPP on the I-ratio are expected if the variance in male WPRS is large and depends primarily on components of fitness that are not influenced by EPP. Following from the decomposition of variance in male realized reproductive success, the I-ratio (I_T/I_Ta) can be rewritten as

where μ_r and μ_a are the mean realized and apparent reproductive success, and Var(RS_a) is the variance in apparent reproductive success. Variation in I-ratio therefore reflects not only variation in Cov(W,E) but also variation in Var(W), Var(E), and Var(RS_a) (Webster et al. 1995), and in the ratio of μ_r to μ_a (Downhower et al. 1987). In song sparrows, the mean apparent and realized ARS were identical (i.e., μ_r/μ_a= 1) both across all years combined and within each individual year, as must be true in the absence of measurement error because all offspring have one sire. Mean apparent and realized LRS were similar but not identical across all cohorts and within individual cohorts (mean μ_r/μ_a= 1.02, range: 0.93–1.30). These small discrepancies between μ_r and μ_a for LRS arose because some offspring reared by males from one cohort were sired by males from cohorts not included in the study and vice versa. However, such small variation in μ_r/μ_a is unlikely to cause substantial among-cohort variation in I-ratio.

From the above expression, it is clear that the I-ratio will be close to 1 if the variance in WPRS is large relative to the variance in EPRS and is relatively unaffected by EPP. Indeed, the variance in WPRS integrates the variances in social pairing success, female fecundity, and the proportion of within-pair offspring sired (Webster et al. 1995). The occurrence of EPP is expected to influence the variance in the proportion of within-pair offspring sired, but not necessarily the variances in social pairing success or social female fecundity. How to quantify the relative contribution of these fitness components to the total variance in male realized reproductive success is unclear (Appendix S1). However, social pairing success is a major component of male fitness in Mandarte sparrows because a substantial proportion of males remains socially unpaired and have low EPRS (Sardell et al. 2010). Furthermore, there is substantial variation in female fecundity; females rear zero to four broods in a season (Smith et al. 2006, p. 34), and the number of offspring hatched per female varies substantially (median female ARS: 5, IQR: 3–6). The small difference in the variances in realized and apparent fitness in song sparrows may therefore result from the substantial variance in male WPRS that is unaffected by EPP.

Finally, the overall effect of EPP on the I-ratio across all years may be small because it combines substantial among-year variation in the variance and covariance in annual WPRS and EPRS (Table 3). This among-year variation could itself reflect among-year variation in population state such as density, breeding synchrony, operational sex ratio, or age structure (Richardson and Burke 1999; Westneat and Stewart 2003; Shuster 2009), all of which vary markedly on Mandarte (Hochachka et al. 1989; Arcese et al. 1992; Smith et al. 2006; Keller et al. 2008). The degree to which among-year and among-cohort variation in I-ratio reflects these extrinsic and intrinsic processes remains to be investigated.

IMPLICATIONS

In song sparrows, EPP increased the overall variance in male fitness by only 0–27%, but caused much larger changes in individual years and cohorts. Whether these changes are sufficient to influence evolutionary processes, however, depends on the particular process of interest.

The variance in fitness influences effective population size (Nunney and Elam 1994). However, because EPP does not affect the variance in female fitness, a small increase in the variance in male fitness due to EPP is unlikely to substantially affect effective population size or consequent rates of inbreeding and genetic drift. Indeed, previous analysis of four years of song sparrow data showed that the ratios of effective to total population size were 0.66 and 0.65 when estimated using variances in apparent and realized ARS, respectively (O’Connor et al. 2006).

However, even though EPP did not substantially increase the variance in reproductive success, it could still affect the variance in mating success. This could in turn explain the evolution of sexual dimorphism in social monogamous but genetically polygynandrous species, in terms of morphology and other traits such as song (Webster et al. 2007). Furthermore, EPP altered the distributions of male ARS and LRS in more subtle ways than detected by measures of population-wide variance. Such small changes in the distribution of fitness, if linked to heritable attributes of males that gain or lose reproductive success through EPP, could affect phenotypic variation over time (Shuster and Wade 2003). Furthermore, subtle changes in the distribution of reproductive success could also affect patterns of relatedness by changing the frequencies of full and half siblings, and hence influence inbreeding risk and kin selection and competition (Cornell and Tregenza 2007; Cornwallis et al. 2010). In summary, although EPP did not greatly alter the variance in male fitness in song sparrows, it could still influence major evolutionary processes through more subtle redistribution of paternity.