Tests for associations between sexual dimorphism and patterns of quantitative genetic variation in the water strider, Aquarius remigis

The evolution of sexual dimorphisms requires divergence between sexes in the evolutionary trajectories of the traits involved. Discerning how genetic architecture could facilitate such divergence has proven challenging because of the difficulty in estimating non-additive and sex-linked genetic variances using traditional quantitative genetic designs. Here we use a three-generation, double-first-cousin pedigree design to estimate additive, sex-linked and dominance (co)variances for 12 traits in the water strider, Aquarius remigis. Comparisons among these traits, which have size ratios ranging from 1 to 5 (larger/smaller), allow us to ask if sexual dimorphisms are associated with characteristic patterns of quantitative genetic variation. We frame our analysis around three main questions, derived from existing theory and empirical evidence: Are sexual dimorphisms associated with (1) lower additive inter-sex genetic correlations, (2) higher proportions of sex-linked variance, or (3) differences between sexes in autosomal additive and dominance genetic variances? For questions (1) and (2), we find weak and non-significant trends in the expected directions, which preclude definitive conclusions. However, in answer to question (3), we find strong evidence for a positive relationship between sexual dimorphism and differences between sexes in proportions of autosomal dominance variance. We also find strong interactions among the three genetic components indicating that their relative influence differs among traits and between sexes. These results highlight the need to include all three components of genetic (co)variance in both theoretical evolutionary models and empirical estimations of the genetic architecture of dimorphic traits.


A. Sex-linked variance estimates
: Studies reporting sex-linked genetic variance. Columns show the percentages of phenotypic variance ascribed to autosomal additive variance ( %), X-or Z-linked variance ( %), and autosomal dominance variance ( %). Data obtained using a search of web of science with keywords "sex-linked variance", "dominance variance", "heritability" and variants of these. These papers were themselves searched for additional relevant references. Simple means were calculated using all the reported estimates in each paper.  Zhu and Weir (1996). Figure S1. Plots of male versus female genetic (autosomal and X-linked) variances as a percentage of the phenotypic variance. The diagonal is the 1:1 line. Note that male and female autosomal variances covary whereas X-linked variances show no such pattern. Different colors show the individual data for the relevant studies shown in Table S1. Cowley et al. (1986, black), Mezey and Houle (2005, red), Evans et al. (2014, blue), Cowley and Atchley (1988, green), Pan et al. (2007, yellow), Kosova et al. (2010, purple)

C. Dominance and maternal variances
Most methods cannot estimate both autosomal dominance and additive X-linked which, given question 3, makes such approaches inappropriate for testing hypotheses concerning sexual dimorphisms. Unmanipulated pedigree designs can, in principle, estimate both autosomal additive and autosomal dominance genetic variances. However, in practice, the number and variety of relationships that arise are generally not sufficient for models with dominance to converge or provide accurate estimates (Wolak and Keller 2014). Thus, dominance variances have been typically omitted in studies of sex-linked variances (see Table S1).
Maternal effects are also frequently omitted. Maternal effects are most frequently found during juvenile or larval stages but not in adults (Mousseau and Dingle 1991;Fox 1994;Fox and Savalli 1998;Cotter et al. 2004;Roff and Sokolovska 2004;Keena et al. 2007). This effect is shown in Figure S1, where estimates of maternal effects from the studies in Table S1 Figure S4: Cumulative frequency plot of maternal variance as a percentage of the total phenotypic variance for juvenile versus adult traits. Data are from those studies given in Table  S1 that provide maternal estimates (12 studies, 58 adult traits, 18 juvenile traits) Data sources are indicated in the reference list by "*".

D. Characteristics of the founding populations.
The founders for each replicate were adult A. remigis collected from Rattlesnake Creek (latitude 34.459683°N, longitude 119.692105°W), a small, rocky, permanent stream in Santa Barbara, County, California. The founding animals for replicates 1 and 3 were collected during consecutive peak reproductive seasons (Table S2) and the following day were placed in the experimental protocol. The founders for replicate 2 were collected the intervening October (Table S2) and were maintained in stream tanks until the onset of reproduction (approximately 3 months) before being placed in the experimental protocol.  (Calabrese 1974;Fairbairn 1986;Fairbairn and Desranleau 1987). However, winged individuals are more common in California than in other regions (Calabrese, 1974;Polhemus and Chapman, 1979;Kaitala and Dingle, 1992;Fairbairn and King, 2009). Winged adults differ slightly from wingless forms in both size and shape (Fairbairn, 1992), and to avoid this potentially confounding effect, we used only wingless adults to initiate our breeding populations.

E. Rearing regime for Aquarius remigis
All rearing and adult maintenance was done in plastic 'shoe-box' cages (34 x 24 cm) partially filled with water, or in oval-shaped, stream tanks (140 cm x 45 cm) with circulating water, under 14hL:10hD, and at room temperature (laboratory) or 25 o C (environmental chambers), as noted. Differences in sample sizes and seasons necessitated minor alterations to the protocol for the different replicates, but the same general protocol was followed for all.
To maintain A. remigis nymphs and adults in laboratory culture, the water surface must be kept moving. Survival is poor on stagnant water. A circulating current was maintained in the stream tanks by means of submerged pumps controlled with rheostats. The water was also filtered through aquarium pumps and aerated with aquarium air stones (bubblers). In the smaller, 'shoebox' rearing cages, surface movement was maintained by an aquarium bubbler in each cage. Cages and stream tanks were also provided with floating Styrofoam pieces as resting and oviposition sites. To prevent escapes, all tanks and cages were covered with cheesecloth or screen which is sealed around the edges with double-sided tape.
We used the following feeding protocol, which has been shown to produce maximum survival under our rearing conditions: a minimum of one D. melanogaster per day for each first and second instar nymph, supplemented with one medium-sized, nymphal house cricket, Acheta domestica, per day for every two third or fourth instar nymphs. Fifth instar nymphs and adults were fed at the rate of one adult A. domestica per day for every four individuals plus twice weekly supplements of one D. melanogaster per individual. All food items were previously frozen. The old crickets were removed from the water surface daily to prevent lipids from the decomposing bodies from compromising the water surface tension. Similarly, the Drosophila carcasses are removed at least twice a week. See Blanckenhorn et al (1995) for more information.

F. Experimental Protocols
To initiate each replicate, the field-caught adults from Rattlesnake Creek (Table S2) were distributed among laboratory stream tanks. The founders for replicates 1 and 3 were evenly distributed among four tanks, with equal sex ratios within tanks and total population sizes of 200 and 210 respectively. Replicate 2 had only two stream tanks with 25 females/42 males in one, and 21 females/36 males in the other (total N = 124). After tank set-up, all eggs laid in the first seven days were discarded. This minimized possible environmental maternal effects on egg quality and increased the probability that eggs harvested from each tank were sired by males in that tank. Eggs were subsequently harvested daily and used to seed cages for rearing the GP generation. Within each replicate, equal numbers of cages were seeded from each founder tank (total number of cages: 128, 148, and 144 cages for replicates 1, 2 and 3 respectively). This ensured that each tank contributed equally to the GP generation within each replicate (see below). The cages were distributed in randomized blocks in two environmental chambers to avoid confounding any environmental variation within chambers with possible sampling variation among founding tanks. Nymphs were reared using standard protocols (see above) and eclosing adults were removed from the cages within 24h, marked with unique numbers, separated by sex and held in stream tanks for at least seven days until formation of GP breeding units.
To form the breeding units called for in our experimental design, we adopted a stratified random sampling protocol that minimized the probability of sib matings in the P generation and ensured that the GP generation captured the variance in the source population. Our protocol ensured that each GP adult came from a unique rearing cage, the founding tanks were equally represented within each breeding unit and overall, and within each pair, the male and female came from different founding tanks.
For replicates 1 and 3, the GP generation consisted of 15 breeding units for a total of 60 mating pairs. All individuals were selected based upon their unique numbers using the following stratified random sampling scheme. We first randomly selected one number from each rearing cage, with the restriction that the final set of sampled individuals had to contain equal numbers of males and females. From this set, we formed each breeding unit by randomly selecting one male and one female originating from each of the four founding stream tanks. The resulting four males and four females were then paired such that the males and females within each pair derived from different founding stream tanks. Thus, each breeding unit consisted of eight adults from eight different rearing cages, of which one male and one female were from each of the four founding stream tanks.
For replicate 2 the GP generation consisted of six breeding units with a total of 24 mating pairs. Because we only had two founding stream tanks for GP adults, each breeding unit was set up with four males from one tank and four females from the other (all selected at random from different rearing cages as above), alternating which tank contributed which sex among the breeding units.
Each GP mating pair was maintained in a cage at room temperature. Eggs were harvested and used to seed three or four cages per female with 20 -30 eggs each. After hatching, nymphs were redistributed among cages within dams to achieve approximate densities of 20 nymphs per cage per female. Nymphs were reared to eclosion using standard protocols as for the GP generation, and newly eclosed adults were separated by sex and held in the laboratory for a minimum of seven days before formation of parental (P) mating sets.
Each breeding unit required four structured parental (P) mating sets consisting of three females and a single male. To maximize the probability that the male would fertilize the eggs of each of his three females, each P female occupied her own cage and the male was rotated among his three females by being transferred sequentially from one cage to another every second or third day. The egg collecting and rearing protocols for the offspring (F1) were identical to that used for the GP and P generations.
All adults were preserved in 70% ethanol prior to being photographed for measurement.
F1 adults were preserved as soon as their cuticles had hardened sufficiently (typically one day post-eclosion).

G. Measurement Protocols
Our measurement protocols followed those established in previous studies of body size variation in this species (e.g., , Preziosi et al,1996, Fairbairn, 2005Bertin and Fairbairn 2007). Each preserved individual was placed in a glass-bottomed box with a scale bar fixed to the glass. The strider was arranged with ventral side against the glass and legs spread to the sides, and held in place with a Styrofoam plug made to fit snugly into the box.
The plug gently pressed the water strider against the glass. This protocol ensured that each specimen was held in a standard position with the dorso-ventral axis perpendicular to the glass and with all landmarks clearly discernable. With the specimen thus secured, the box was inverted and placed under a Leica Wild M3c dissecting microscope so that the specimen was viewed in ventral aspect for photographing. The microscope was equipped with a 0.5 reducing lens and an attached Spot Insight 3.2.0 color camera. The entire strider was photographed at 10x magnification and the posterior region was photographed again at 25x magnification.
All measurements were made from these photographs using the digitizing software SigmaScan Pro 5.0. Photographs in which landmarks were unclear were retaken. Except where noted, lengths were taken along the ventral midline. Measures of the head, thorax, abdomen and femora were taken from the photo of the entire animal ( Figure S2). We measured only the right three femora unless one or more of those legs were missing or damaged (as occasionally happened during handling), in which case we substituted the three left femora. The remaining measures were taken from the more magnified photograph of the genital region ( Figure S3). The length of the margin of segment 7 was taken as the linear distance between the right lateral (outer) end of the suture between segments 6 and 7 and the tip of the connexival spine on the right side of the body. Measurements from each photograph were transformed to mm based on measurement of the included scale bar.
Unlike the somatic body components, whose lengths are fixed as adults (e.g., see Preziosi and Fairbairn, 1997), the genital segments of both sexes are mobile to facilitate copulation and oviposition (Fairbairn et al., 2003). These changes could influence our genital measures, introducing error variance and reducing heritabilities. To guard against this, all photographs of the posterior region were carefully evaluated and measurements were included only for specimens whose genitalia were fully retracted. As an additional precaution, regressions of genital measures on thorax length were used to identify outliers in which genital measures were high. In these cases, the photograph was re-evaluated and the measurement was discarded if any sign of genital extrusion was evident.
To determine our accuracy taking measurements from our photographs, we conducted a repeatability analysis for an initial set of photographs from 73 males and 167 females (n = 3 per individual. The mean intraclass correlation coefficient over all traits and both sexes was 0.966 (SD = 0.034), with a maximum of 0.996 for hind femur length in males, and a minimum of 0.878 for segment 8 length in females. The latter was the only measurement with a repeatability less than 0.9.

H. Correlations among traits
To determine if the 12 measured traits could be legitimately considered as different traits at the genetic level, we estimated the pairwise additive genetic correlations among traits within each sex using an additive-only model, with generation and replicate as fixed effects and the variance components as random effects.
All pairwise correlations in both sexes differed significantly from ±1.0, and hence none is an absolute constraint on independent evolutionary response to selection (Tables S3, S4). The magnitudes of the correlations were generally low: for male traits the mean absolute value of the 66 pairwise correlations was only 0.470 (SD 0.220), and for female traits it was only 0.324 (SD 0.258). Only five of the 132 correlations exceeded 0.8, and all of these were among the lengths of the leg femora. Although relatively high, even these correlations were significantly less than 1.0. Many of the pairwise correlations were low (<0.3) and not significantly different from zero. This is particularly true for correlations involving SpineDist, L.Seg8 and L.Seg9.10, all traits of the terminal abdominal and genital segments. Based on these results, we included all 12 traits in our subsequent analyses. Table S3: Between-trait additive genetic correlations within each sex (males above the diagonal, females below). Bold values differ significantly from 0. All estimates differ from ±1.0 by more than 2SE a . Traits are listed in the same order as in Table 1    Estimates for males are above the diagonal, females below. Traits are numbered as in Table S3.

I. Genetic variances (as proportions of phenotypic variance) and between-sex genetic
correlations for the 12 measured traits. Table S5. Genetic variances (as proportions of the total phenotypic variance) and between-sex genetic correlations (rA, ra, rd). Bold font: estimates significantly different from zero a . For the correlation estimates, italic font indicates significantly different from ±1. Other cases: see footnotes. Traits are numbered as in Tables S3 and S4. a. Significance assessed as > 2 SE above 0 or at the boundary of 1.0 (see Table S6). b. = (Va + Vx)/Vp, similarly contains both autosomal and sex-linked components. c. 0.00 = estimate < 10 -6 and set to 0. d. We used the asreml approach that directly estimates the genetic correlation rather than attempting to separately estimating the covariances and variances. Because it uses restricted maximum likelihood the correlation cannot exceed ±1. The asreml program calculates jointly the variances and the correlations, which tends to be more stable than estimating the variances and covariances and then estimating the correlations from these. Note that the genetic correlations are based only on the genetic variances and covariances and therefore it is possible to have high genetic correlations in spite of low heritabilities (which express the genetic variances as proportions of phenotypic variances), as in these examples. e. U: the estimated value is too small for a reliable standard error estimate. f. NA: standard errors not estimated because correlation values were fixed at the boundary of 1.  Table S6. Standard errors for the genetic variances and correlations given in Tables S5. Traits are  numbered as in Tables S3 and S4.