#### Demographic monitoring

The bicolor damselfish (*S. partitus*) is an abundant species that inhabits coral reefs and lives in small social groups (≈2–20 fish) on distinct coral heads. This is an excellent model species for estimating genetic parameters in the field. Adults remain within a few meters of their home territory, permitting *in situ* monitoring of individual growth and reproduction. Males hold small breeding territories and will often mate with multiple females (schmale 1981). Females lay benthic eggs and will readily deposit eggs on artificial substrates that can be manipulated and brought back to the laboratory for analysis. We used artificial nests comprised of 15 cm lengths of 5-cm-diameter plastic pipe, lined with flexible transparent plastic that could be removed to access the attached eggs. Eggs hatch at twilight after 3.5 days of benthic development.

In 2006, we monitored reproduction at two sites near Lee Stocking Island, Bahamas. A total of 37 breeding territories with artificial nests were monitored daily for approximately 2 months. Adult fish at these sites (*n* = 65 and 35) were individually tagged as part of a broader long-term demographic study. Small tissue samples (fin clips) were taken from all adults in the study population to identify parent–offspring relationships. Most adults had been monitored periodically because settlement and their age, size, and growth rate were measured directly. Size-at-age of *S. partitus* is well described by a Von Bertalanffy growth function (Johnson and Hixon 2010), and maximum size of each adult (*L*_{max}) was expressed as the asymptotic size described by the growth function fit to individual size-at-age data. We used *L*_{max} in parent–offspring analyses because we believe that it is more useful and direct to predict correlated responses to changes in average values of *L*_{max} (a parameter that relates to growth trajectories) than to changes in average adult size (which also depends on age). Nonetheless, we also conducted parent–offspring analyses using current size, rather than *L*_{max} (see Supporting Information). However, because the adults in our study were within 86–99% of their estimated *L*_{max} values, genetic parameter estimates were very similar.

To quantify genetic covariance between larval and adult traits, we monitored breeding adults in the field, collected eggs immediately prior to hatching, and compared traits of both larvae and adults. We measured larval size and swimming performance as indicators of larval quality because both of these traits may influence larval survival (Vigliola and Meekan 2002; Fuiman and Cowan 2003). We sampled 55 larvae from each of 143 egg masses collected in the field. Thirty-five of these larvae were size-measured under a microscope, and 20 larvae were used to evaluate average swimming performance. Swimming performance was measured as the duration of time that fish could swim against a current of 3.2 cm/s within a swimming flume. Three larvae from each egg mass were individually preserved for genetic analysis.

Adults and larvae were genotyped at seven highly polymorphic microsatellite loci (Williams et al. 2003). This procedure provided multi-locus genotypes of all sampled adults and larvae, which we used to determine parentage (Appendix S1, also see Methods in Christie et al. 2010). Given the large numbers of alleles per locus, the probability of a single putative parent–offspring pair sharing alleles by chance was extremely low (*P* < 0.00457) (Christie 2010). Thus, we used simple Mendelian incompatibility to assign parentage. To cross-validate results as well as to fully account for genotyping errors, we also used likelihood-based methods as implemented in the program CERVUS (Marshall et al. 1998).

#### Genetic covariance among larval and adult traits

We examined the potential for a genetic relationship between *L*_{max} and larval traits by plotting offspring phenotype against the phenotype of the sire. All traits were expressed as phenotypic standard deviations from the population mean. If there is no environmental covariation between parent and offspring phenotype, then the slope of such a regression line estimates one-half the additive genetic covariance between traits (Lynch and Walsh 1998). For graphical display, we plotted mean values for all larval families (egg masses) sampled. However, because observations of multiple clutches of offspring from a single father were not independent, we regressed the mean standard length of all offspring of each sire on maximum total length of sire. In this analysis, each sire–offspring case was weighted by the number of clutches used to determine the average of larval traits. We also included effects of average water temperature, site, and average density of damselfish within breeding territories as covariates, because these factors may affect larval size (McCormick 2006; Appendix S2, Table B1). We acknowledge that because most of the offspring from sires in this study came from the same nest, this design confounded sire and nest effects. However, additional studies using our artificial nests within this system suggested that nest effects were small (accounting for <5% of the variation in larval traits) and unlikely to be correlated with sire asymptotic size (D. W. Johnson, unpublished data).

We evaluated sire–offspring relationships for a large sample of offspring from naturally breeding adults in 2006. Although significant relationships were observed (see Results section), they may have been caused by a combination of environmental, maternal, and/or additive genetic effects. To examine possible assortative mating and maternal influences, we used parentage analysis to identify mothers of each clutch and tested whether maternal size and/or age was correlated with paternal size. Finally, we separated genetic effects from any environmental effects that depended on paternal size (e.g. greater care of offspring) by conducting a cross-fostering experiment in the summer of 2007. Although the experiment was conducted in the same two study populations, there was very little overlap between individuals breeding in 2006 and 2007 because of high turnover in the population (only five sires and six mothers bred in both years). We monitored adult size and larval quality as before, except during this experiment; egg masses were swapped among nests for the duration of benthic egg development (3.5 day) by moving eggs on plastic collectors among nests. We compared offspring and sire phenotype for both biological and foster fathers.

Because our results indicated some assortative mating based on *L*_{max} but no environmental effects that depended on sire size (see Results), we pooled the data from both years (2006 and 2007) to calculate genetic covariances and size-dependent maternal effects. Additive genetic covariances (Cov_{A}), corrected for assortative mating, were calculated according to the following formula, derived from Lynch and Walsh (1998):

- (1)

where *b* is the slope of the sire–offspring regression, *r* is correlation between maternal and paternal size, and *m* is size-dependent maternal effect coefficient (Appendix S3). We estimated *m* as the difference between mother–offspring and sire–offspring regression slopes divided by (1 − *r*). Mean and 95% confidence intervals for estimates of size-dependent maternal effects and genetic covariances were generated using standard resampling procedures (Appendix S3).

We acknowledge that parental effects may depend on age (e.g. Berkeley et al. 2004a; Marteinsdottir and Steinarsson 1998) and that because of the correlation between age and size, our study (like many others) did not allow us to cleanly separate age-dependent effects from those that depend on size. However, because fishery selection is likely to reduce both the mean age of adults and the mean values of maximum length, our estimates of Cov_{A} and *m* should be robust and useful for predicting correlated responses of larvae.

#### Fishery selection, larval responses, and population replenishment

Using our genetic parameter estimates for *S. partitus*, we explored how larval traits may respond to fishery selection on adults. We predicted the response of larvae to a single (initial) generation of selective fishing by multiplying fishery selection differentials by the combined genetic covariance and size-dependent maternal effects. This approach provides a suitable approximation if one assumes no net selection in previous generations that would cause a lagged response arising from maternally transmitted effects (Kirkpatrick and Lande 1989). (Multi-generation responses to selection are much more complex and are considered further in the Discussion.) To describe fishery selection on adult body size, we used a range of standardized selection differentials (−0.05, −0.15, and −0.3) that were based on values estimated from several empirical studies (e.g. Rijnsdorp 1993; Law 2000; Swain et al. 2007). Importantly, these values served as estimates of the net selection differential (i.e. the total effects of fishery selection and natural selection on adults) and were used to predict correlated responses of SAH.

The effect of correlated larval response on relative survivorship (cumulative survival) throughout the larval and early juvenile phases was predicted by two different approaches. First, we used the method described by Munch et al. (2005) that uses information on growth and genetic covariance between adult size and size at younger ages to predict correlated changes in body length. This approach characterizes length-dependent mortality of larvae and juveniles by combining published estimates of daily, instantaneous mortality among species that varied in size. An advantage of this approach is that there are enough data available to describe overall patterns in mortality with reasonable precision across a broad range of sizes. Disadvantages are that this approach requires explicit information on growth rates and genetic covariance functions and that predictions may be sensitive to these inputs. Furthermore, this approach assumes that rates of size-dependent mortality within a single species can be approximated by comparing rates of total mortality across species that differ in size. By comparing total mortality among species, these estimates of size-dependent mortality may be confounded with species-specific differences in mortality that are attributable to other factors that may have strong effects on estimates of mortality rates (e.g. age, experience, catchability, life-history adaptations).

Our second approach to estimate the effects of changes in mean larval size on mortality rates was to synthesize information from studies of selective mortality on SAH. An advantage of this approach is that it can be used to compare mortality among cohorts of the same age and species and derive estimates of size-dependent mortality under similar field conditions. Disadvantages are that multiple estimates of selection have been made for relatively few species and that estimates of mortality are calculated indirectly using information on selection. Both methods of estimating size-dependent mortality assume that components of survival that do not depend on body size are the same for selected and unselected populations.

#### Larval size and relative mortality: approach 1

To predict survival consequences for a change in larval size, we followed the procedure described by Munch et al. (2005). In brief, we estimated expected survivorship of larvae after a single generation of selection on adults and compared this value as a fraction of expected larval survivorship in the absence of selection on adults. Relative survivorship of larvae and juveniles after a single generation of selection on adults was estimated as follows:

- (2)

where *t* is days posthatching, *L*_{t} is length at age *t*, *S* is the standardized selection differential on adult body size, *m* is the coefficient describing size-dependent maternal effects, and cov_{A(t)} is the genetic covariance function (see Appendix S4 for further details). We examined length-dependent mortality over the first 90 days posthatching (dph) to make these estimates comparable with our estimates of larval mortality derived from analyses of natural selection (90 days was the maximum duration of selection studies in our review.).

#### Larval size and relative mortality: approach 2

Selective mortality of larval and juvenile fish is likely to be a mix of both ‘soft’ selection (i.e. frequency-dependent selection in which selective mortality is substitutable with nonselective, background mortality) and ‘hard’ selection (i.e. frequency-independent selection which generates survival variation in addition to any background mortality; Wallace 1975). Because measurements of selection are likely to reflect both frequency-dependent and frequency-independent components and because frequency-dependent selection may not have direct effects on population dynamics (Saccheri and Hanski 2006), we used the following procedure to estimate both frequency-independent and frequency-dependent components of selection on size-at-hatching.

We obtained overall estimates of size-dependent mortality by estimating the amount of selective mortality required to generate the observed changes in the distribution of trait values between initial samples of fish (i.e. the before selection sample) and samples of fish that survived to a later date. We assumed that before selection, the distribution of phenotypic values in the *i*th cohort, , is normal with mean and variance specified by and , respectively. We also assumed that the expected value of relative fitness (defined in this case as daily survival) can be described as a smooth function of phenotypic value, *W*(*z*), Given known values for , , , and for each cohort, parameter values defining *W*(*z*) can be obtained by finding the best solution to the following inverse problem, where

- (3)

and

- (4)

where *t*_{i} is duration of the study (in days) for the *i*th cohort. We estimated the relationship between SAH and survival under selective mortality by numerically solving for parameters in *W*(*z*) that minimized the sum of absolute differences between predicted and observed values of and . This analysis assumes that there is a component of the selective surface that is constant and that sampling multiple cohorts across a range of phenotypic values can reveal the constant selective surface underlying any independent variation in selection (e.g. owing to environmental variation). *W*(*z*) may be described by a number of different functional forms. Following earlier studies that model hard and soft selection on quantitative traits (e.g. Wade 1985; Goodnight et al. 1992), we modeled hard selection as a component in which individual fitness depends on absolute phenotypic value, and soft (frequency-dependent) selection as a component in which fitness depends on relative phenotypic value (deviations from the cohort mean). Specifically, we modeled fitness as

- (5)

The first term describes how phenotype affects expected individual fitness, regardless of the frequency of other phenotypes in the cohort. The second term describes how individual fitness depends on *relative* phenotypic value (i.e. value relative to the group mean). This added term describes the expected (average) value of soft selection. Note that in the absence of hard selection (i.e. when the first term in eqn 5 is constant with respect to phenotypic value), the relative survival of cohorts would be equal. Because both hard and soft selection may take several functional forms (i.e. directional, stabilizing, or disruptive), our approach was to start by fitting a relatively complex model to the data (i.e. eqn 5 in which each component of selection was described by a flexible, three-parameter logistic function). Variation in our parameter estimates was assessed by a bootstrapping procedure. For each of 200 iterations, 37 cohorts were sampled with replacement and parameters defining *W*(*z*) were estimated. If appropriate, we simplified the model by dropping those parameters whose bootstrapped 95% confidence intervals included zero.

To obtain an overall estimate of *W*(*z*), we pooled data from all eight species. Phenotypic values for each species were standardized by dividing by the average phenotypic standard deviation within the initial samples and expressed as deviations from the overall mean for that species. Although selective surfaces are unlikely to be exactly the same across species, this approach matched our goal of describing an average pattern of selective mortality based on size-at-hatching. Our estimate of *W*(*z*) was then used to predict how a given shift in mean SAH would change the average value of survival. However, we were interested in comparing survival of cohorts of larvae produced after a generation of selection on adults to the average survival of larvae in the absence of such selection. We therefore calculated relative survival by dividing the mean survival of a cohort of larvae whose mean SAH shifted in response to selection on adults, , by mean survival for a cohort of larvae whose mean SAH was equal to the overall mean before selection on adults (i.e. ). Relative survivorship (cumulative survival at time *t*) was therefore calculated as follows:

- (6)

where *W*(*z*) is as described above and *t* is days posthatching (see Appendix S6 for details). We evaluated relative survivorship at 90 days posthatching (90 day was the maximum duration of selection studies in our review). Distributions of larval SAH were assumed to be normal, and variance in SAH was assumed to be equal before and after selection on adults.