The “Bateman gradient” provides a means for estimating the strength of sexual selection. Although widely used for this purpose, this approach has not been applied to examine the covariance between mate numbers and offspring numbers among alternative mating strategies. Differences in this covariance could exist if the average fitnesses of different mating phenotypes were unequal, as has been suggested for “alternative mating tactics.” We tested this hypothesis in Paracerceis sculpta, a sexually dimorphic marine isopod in which three male morphs coexist. We found no significant differences in sexual competency and no significant differences in Bateman gradients among morphs, that is, the average morph fitnesses were equivalent. However, with data pooled among morphs, we found a significant sex difference in Bateman gradients, as expected for dimorphic species; females gained no additional fitness from mating with multiple males, whereas male fitness increased with increasing mate numbers. In nature, the fitnesses of the three morphs are variable due to differences in the availability of receptive females. Our results suggest that differences in mate availability, not differences in sexual competency, are responsible for observed variance in fitness within, and for the equality of fitnesses among, the three male morphs in this species.
- measuring sexual selection
- male polymorphism
By definition, females produce few, large ova, whereas males produce many, tiny sperm. This sex difference in initial parental investment is widely viewed as the primary cause of sexual selection and intersexual conflict [1, 2, 3, 4]. However, Bateman (, p. 363) also argued that, “Variance in number of mates is…the only important cause of the sex difference in the variance in fertility,” and therefore that a sex difference in the variance in fertility provides “a measure of the sex difference in intensity of selection.” This statement implies that selection within each sex, rather than between the sexes is responsible for sexual selection as well as for the evolution of sexual differences. The magnitude of the sex difference in fitness variance can be specifically quantified, not through proxies for selection intensity, such as the ratio of sexually mature males to receptive females at any time (the Operational Sex Ratio, OSR ) or the ratio of maximum potential reproductive rates for each sex (PRR; ), but rather from actual estimates of selection’s strength [7, 8, 9, 10, 11, 12].
Such measures include the opportunity for selection (
The Bateman gradient is among the more precise methods for measuring sexual selection because it measures the slope,
Polymorphisms in mating phenotype are considered by many researchers to provide examples of
The Gulf of California sphaeromatid isopod,
While the possible causes of variance in mating success within α-males are relatively well understood [27, 28, 29, 30, 31, 32], the causes of within-morph fitness variance for β- and γ-males are less clear. Here, we measured Bateman gradients for α-, β-, and γ-males, and females in
2. Materials and methods
2.1 Sexual receptivity, mating, and gestation in
Females are attracted to breeding sites in sponges when their ovaries and brood pouches mature . Sexual receptivity in these S1 females is initiated when they shed the posterior half of their cuticle and expose genital openings at the base of each fifth walking leg . Females in S2 (half molted) condition remain receptive for 24 h before shedding their anterior cuticles, ovipositing into internal brood pouches and becoming non-receptive (S3). Females do not feed during gestation (S4–S7; ). Males complete a mating sequence with receptive females by inserting their appendix masculina and ejaculating into one, and then into the other of their mate’s vaginas. Fertilization occurs and zygotes are brooded internally for 3 weeks before being released as fully formed juveniles (mancas; [27, 28, 29]).
2.2 Field collections
We collected several hundred isopods from the spongocoels of the intertidal sponge,
2.3 Matings for males
To examine the relationship between mate number and fertility for the three male morphs, and to compare the fertility of females mated to each of the three male morphs (see below), we allowed α-males (N = 14), β-males (N = 14), and γ-males (N = 13) to mate with 1–5 females in succession (Nfemales = 86). We allowed each male to remain with each female for the duration of her 24-h period of receptivity. We then separated individuals and placed them in separate 225-ml cups containing seawater. Males were then placed with another S2 female, allowed to mate for 24 h, and the sequence was continued until males either died or mated five times. All S3 females were maintained in containers until parturition when we counted all mancas and undeveloped zygotes, if present.
To determine whether the fertility of males differed or decreased with increasing mating frequency, as well as to determine whether the fertility of the females mated by α-, β-, and γ-males was statistically distinguishable, we first calculated the residuals for the regression of offspring number on female body size to account for the positive effect female body size has on fertility (F[1,85] = 98.14, P < 0.0001). Then, we analyzed these residuals using a two-way ANOVA to examine the influences of male morph (MORPH), the order of females in the mating queue (ORDER), and their interaction (MORPH*ORDER) on the number of offspring produced by individual females mated by α-, β-, and γ-males. We performed a similar analysis on the number of undeveloped zygotes per female but did not calculate residuals for this analysis because there was no significant relationship between female body length and the number of undeveloped zygotes (F[1,68] = 0.67, P = 0.42).
2.4 Matings for females
To examine the relationship between mate number and fertility for females, we allowed S2 females to complete one mating sequence each with either 1 (N = 2), 3 (N = 1), or 5 (N = 3) α-males in succession. Pairs of isopods were given a maximum of 20 min to begin mating. To prevent re-mating, we removed males after mating, changed the water in the cup, and allowed each female to recover for 5 min before the next male was introduced. The entire mating sequence for each female never exceeded 2 h. S3 females were maintained in their containers until parturition, when all mancas were counted. Again, the numbers of undeveloped zygotes, if present, were also counted.
To investigate whether the fertility of females who mated 1–5 times over 2 h, was different from each other as well as from the fertility of the 86 females, we allowed unlimited matings with males over 24 h (see “Matings for males” section), we first calculated the residuals for the regression of offspring number on female body size to account for the positive relationship between female size and fertility (F[1,5] = 15.98, P = 0.02). Next, because of the small sample size of females mated within 2 h (N = 6), we compared the residuals of the fertility of females mated 1, 3 and 5 times using a Kruskal-Wallis test. Because this test was non-significant (
Using two-way ANOVA, we then examined the influences of female body length (FBLENG), the time available for mating (DURATION; 1–5 matings in 2 h; unlimited matings in 24 h), and their interaction (FBLENG*DURATION) on the number of offspring produced by females. We performed a similar analysis on the number of undeveloped zygotes per female. As in the previous analysis of undeveloped zygotes, we did not calculate residuals for this analysis because there was no significant relationship between female body length and the number of undeveloped zygotes (F[1,73] = 1.27, P = 0.26).
2.5 Bateman gradients
We used two-way ANOVA to examine the influences of adult phenotype (ADULTP), mate number (NMATES), and their interaction (ADULTP*NMATES) on the number of offspring produced by α-, β-, and γ-males, and females. We then subdivided our data by sex and used two-way ANOVA to examine the influence of male morph (MORPH), mate number (NMATES), and their interaction (MORPH*NMATES) on the number of offspring produced by α-, β-, and γ-males. Because males were analyzed separately from females, we used a Bonferroni correction to reduce our criterion for significance, α = 0.05/2 = 0.025. Lastly, we pooled the data for all males and used two-way ANOVA to examine the influences of sex (SEX), mate numbers (NMATES), and their interaction (SEX*NMATES) on the number of offspring produced by all males and all females. For individual Bateman gradients, we calculated the least squares regression of offspring numbers on mate numbers for each adult morph .
Our two-way ANOVA of the residuals for offspring number on female body length, to determine whether the fertility of the three male morphs differed or decreased with increasing mating frequency, was non-significant overall (F[5,85] = 0.25, P = 0.94) with non-significant effects of male morph (F[MORPH] = 0.42, P = 0.66) and mate order (F[ORDER] = 2.21, P = 0.64) and a non-significant interaction between these factors (F[MORPH*ORDER] = 0.15, P = 0.86). This result indicated that the three male morphs did not differ in their sexual competency with multiple matings. This result also confirmed that there were no significant differences in the fertility of females mated with α-, β-, and γ-males, and confirmed that there were no significant differences in the numbers of undeveloped zygotes among females mated by α-, β-, and γ-males (F[5,67] = 0.18, P = 0.97; F[MORPH] = 0.31, P = 0.73; F[ORDER] = 0.01, P = 0.95; F[MORPH*ORDER] = 0.18, P = 0.83).
Our two-way ANOVA to compare the fertility of females who mated 1–5 times over 2 h vs. the fertility of females allowed unlimited matings over 24 h was significant overall (F[3,81] = 34.56, P < 0.0001) with a significant effect of body length (F[FBLENG] = 7.34, P = 0.008), but no significant effect of the time available for mating (F[DURATION] = 1.03, P = 0.31) and no significant interaction between female body length and the time available for mating (F[FBLENG*DURATION] = 0.35, P = 0.55). This result indicated that the size-adjusted fertility of females allowed to mate 1–5 times was no different from those of females allowed unlimited access to matings over 24 h. This result was corroborated by our finding that there were no significant differences in the numbers of undeveloped zygotes among females mated 1–5 times compared with females allowed unlimited matings over 24 h. (F[3,73] = 0.63, P = 0.60; F[FLENG] = 1.07, P = 0.30; F[DURATION] = 0.04, P = 0.84; F[FBLENG*DURATION] = 0.33, P = 0.57).
Our two-way ANOVA comparing the relationship between mate numbers and offspring numbers for each of the three male morphs and females (Figure 2) was significant (F[7, 39] = 8.71, P < 0.001), with a significant effect of adult phenotype (F[ADULTP] = 5.13, P = 0.004), a significant effect of mate numbers (F[NMATES] = 32.60, P < 0.0001), and with a significant interaction between adult phenotype and mate numbers (F[ADULTP*NMATES] = 3.25, P = 0.032). This result indicated that a phenotype difference in Bateman gradients does exist for
That source was revealed by two successive tests. Our two-way ANOVA of males alone, to identify the source of the difference in Bateman gradients among the adult phenotypes, was significant overall (F[5, 35] = 8.91, P < 0.0001), with a significant effect of mate numbers (F[NMATES] = 40.66, P < 0.0001). However, we found no significant effect of male morph (F[MORPH] = 1.59, P = 0.22) and no significant interaction between male morph and mate numbers (F[MORPH*NMATES] = 0.17, P = 0.85), indicating that Bateman gradients for the three male morphs were indistinguishable. This result justified pooling all males for re-analysis of the relationship between mate numbers and offspring numbers for males and females.
This pooled-male analysis was significant overall (F[3,38] = 19.09, P < 0.001) with a significant effect of sex (F[SEX] = 11.81, P = 0.001), a significant effect of mate numbers (F[NMATES] = 10.14, P = 0.003), and a significant interaction between sex and mate numbers (F[SEX*NMATES] = 9.26, P = 0.004), a result confirming that a sex difference in Bateman gradients exists for
Our results showed that although they appear to invest different amounts of energy toward somatic and gametic functions [27, 28], the three male morphs in
Our results further showed that while the three male morphs do not exhibit distinct Bateman gradients, a sex difference in Bateman gradients does exist for
In contrast, within each of the three morphs, male fitness increased linearly with increasing numbers of matings (Figure 2). The large difference between the sexes in the number of offspring produced with increased numbers of mates suggests that intersexual conflict (c.f., [1, 2, 3, 4, 12])
The significant sex difference in Bateman gradients for
If this is indeed the case, then as is widely acknowledged, the number of matings individual males acquire need not translate linearly toward that male’s overall fitness. More specifically, in nature, multiple Bateman gradients among male morphs may exist that each depend on the number of available mates
For this reason, we recommend, when male polymorphisms exist, that the fitness for a large number of males of each morph be measured, and their relative fitness outcomes be considered in proportion to the average fitness that all males in the population achieve. This approach is consistent with studies of this and other species [26, 40], in which equal average fitnesses exist among male morphs over multiple generations.
This research was supported by NSF REU Site grant DBI-0552644, Research Experience for Undergraduates in Behavioral and Conservation Sciences at Northern Arizona University, and by NSF grants DEB-9726504 and OCE 84-01067 to SMS. We are grateful to D. S. Smith, R. Beresic-Perrins, and J. C. Boothroyd for their comments on earlier drafts of this manuscript. We also thank the summer 2007 REU students and G.P. Shuster for help in collecting