Appendix S1. Additional details regarding the analysis of variability in selective mortality
To evaluate the survival cost associated with selective mortality, we compiled published
estimates of selective mortality associated with early life traits in fishes. In our literature
search, we considered only those studies that estimated selection on the same focal trait(s) for
two or more separate cohorts. In all of the studies in our review, fish were sampled before and
after a period of selective mortality. Within each of these samples, individual phenotypes were
measured (many phenotypes were derived from otolith measurements), and the distributions
of phenotypes in the before and after samples were compared to measure selective mortality.
We considered estimates to be comparable if they examined the same trait (or suite of
traits), and the replication was among, rather than within cohorts. For example, a study that
measured selective mortality associated with size at 10 days old and took measurements for
cohorts settling to the same site in three different months would be considered as three
replicate measurements. A study that measured selective mortality on body size during three
different periods for the same cohort (e.g., as recent settlers, then at 2 and 4 months post
settlement) would be considered a single replicate of three separate traits and would not be
included.
In cases where raw data are available (e.g., phenotypic values for each of the individuals
in the before- and after-selection samples are known), the functional form of selective
mortality (e-fz) can be estimated directly (see Anderson 1995, Johnson et al. 2012 for details).
However, in our meta-analysis we had access to summary data (means and variances), rather
than raw data, and therefore had to estimate fz indirectly. First, for each cohort of each species
we calculated selection differentials by subtracting the mean phenotypic value before selection
from the mean phenotypic value after selection. Selection differentials were then standardized
by dividing by the standard deviation of the before-selection sample. Next, we chose a
functional form of selective mortality (either truncation or a modified Gaussian; see below) and
solved for parameter values in fz that would have produced the observed selection differential
(see final equation in Box 1, also below). Once fz was estimated, we could calculate selective
mortality using the procedures outlined in Box 1.
To estimate selective mortality under truncation mortality, we assumed that
phenotypes were normally distributed before selection and that selection was generated by
truncation of the phenotype distribution (e.g., all individuals above a certain threshold survived
and all below died – this pattern was reversed in the cases where smaller phenotypic values
were favored). To calculate truncation mortality, we used a simple optimization routine to find
the truncation point on a standard normal distribution that would produce a truncated
distribution of “survivors” with a mean value that would produce the same standardized
selection differential as the observed one for each cohort. We then calculated selective
mortality as 1 minus the integral of the truncated distribution.
Truncation is the most efficient form of selection, and therefore provides the most
conservative estimate of selective mortality (Van Valen 1965). However, it was not clear how
our choice of the functional form of selection would affect our estimates of the degree to which
selective mortality varies among cohorts. To examine how the functional form of selection
might affect our conclusions about selective mortality, we repeated this analysis assuming that
selection can be described by a modified Gaussian function. Again, we assumed that
phenotypes were normally distributed before selection and solved for the parameter values of
a modified Gaussian function that would have resulted in the observed means and variances
after selection.
Within our dataset, 154 of our cohorts exhibited a reduction in estimated variance as a
result of selective mortality and 168 exhibited an increase. Because a Gaussian model of
survival can only produce a decrease in variance, we modified our model such that survival is
Gaussian in the case where variance in the after-selection sample was less than in the before−
(𝑧−𝜃)2
2𝜔2
selection sample (i.e., 𝑊𝑧 = 𝑒
). In cases where variance in the after-selection sample was
greater than in the before-selection sample, we modeled mortality as Gaussian (i.e., 𝑊𝑧 = 1 −
−
(𝑧−𝜃)2
𝑒 2𝜔2 ). If pz is a normal density function specified by the mean and variance observed before
selection, then the mean after selection can be described as
𝑧̅ ∗ =
∫ 𝑧𝑊𝑧 𝑝𝑧 𝑑𝑧
∫ 𝑊𝑧 𝑝𝑧 𝑑𝑧
,
(S1.1)
and the standard deviation after selection can be described as
2
2
̅̅̅̅ ∗ = √∫ 𝑧 𝑊𝑧 𝑝𝑧𝑑𝑧 − [∫ 𝑧𝑊𝑧 𝑝𝑧 𝑑𝑧] .
𝑆𝐷
𝑊 𝑝 𝑑𝑧
𝑊 𝑝 𝑑𝑧
∫
𝑧 𝑧
∫ 𝑧 𝑧
(S1.2)
For each cohort we estimated parameters of W(z) numerically by minimizing the squared
differences between the observed and expected values of the mean and SD after selection.
This procedure was carried out using a Nelder-Mead algorithm using the optim function in R
version 3.0.1 (R Development Core Team 2013). Once parameters defining Wz were estimated,
we calculated selective mortality as 1 − ∫ 𝑊𝑧 𝑝𝑧 𝑑𝑧.
As expected, assuming a modified Gaussian form for Wz resulted in greater selective
mortality (Fig. S1a). However, assuming a different functional form did not produce a major
change in our overall estimates of the degree to which selective mortality varied among cohorts
within a species. The median values for the ranges of selective mortality were practically
indistinguishable (0.401 vs. 0.402) and the distributions of the estimated ranges of selective
mortality were qualitatively similar (Fig. S1b). This was because the two estimates (truncation
and modified Gaussian) of the range of selective mortality within species were highly correlated
(r = 0.67, p = 1.7 x 10-5) and centered on a 1:1 line (data not shown).
Selection on multiple traits
Often, studies reported changes in means and variances for multiple traits. We could
therefore calculate multiple selection differentials for each cohort. We could also estimate
selective mortality associated with each selection differential. However, within our review,
studies that examined multiple traits usually examined traits that were correlated (see
discussion of selection on multiple traits in Lande & Arnold 1983, Johnson et al. 2012). In such
cases, selection differentials are not independent, and mortality that drives selection on one
trait can also drive selection on other traits. When selection was measured for multiple traits,
we used the trait with the largest absolute value for the selection differential as the basis for
calculating truncation mortality. This method provides a conservative estimate of selective
mortality. However, in the absence of more detailed information (e.g., none of the studies
reported changes in the covariances among traits before and after selection), these
conservative estimates are the best available.
One final caveat is that any estimate of the amount of selective mortality a cohort
experiences is conservative in the sense that we can only evaluate mortality that is selective
with respect to the traits that were measured. Because no study is capable of measuring every
trait that has the potential to be important for survival, some of the “non-selective” component
of mortality may include mortality that is selective with respect to unmeasured traits.
Does selective mortality vary among species type?
We were interested in whether there were systematic differences in the amount of
selective mortality experienced by different types of species and at different stages. We divided
species within our dataset into to two categories: fished species (which tend to be large and
mobile), and non-fished species (which tend to be small and reef-associated). Similarly, studies
within the dataset could be separated based on the stage in which selection was measured (i.e.,
studies that measured selection during the planktonic larval phase, during the benthic juvenile
phase, or during both). To test for differences among these groups, we used t-tests or analyses
of variance. The amount of selective mortality was logit-transformed to meet the assumptions
of these statistical tests.
The average amount of selective mortality within cohorts was similar for groups of
fished and non-fished species (t-test on logit-transformed mortality: t = 0.997, df = 32, P =
0.326). Similarly, no differences were found among groups that measured selection during the
planktonic larval phase, during the juvenile phase, or both (ANOVA on logit-transformed
mortality: F2,31 = 0.264, P = 0.770). No difference in the range of mortality was detected
between groups of fished and non-fished species (t test on logit-transformed range of
mortality: t = 0.258, df = 32, P = 0.798). Similarly, no differences were found among groups that
measured selection during the planktonic larval phase, during the juvenile phase, or both
(ANOVA on logit-transformed mortality: F2,31 = 0.705, P = 0.502).
Figure S1
Figure S1. Distributions of estimated values of selective mortality for 33 species of fish.
Selection was assumed to follow a modified Gaussian form (see appendix text) (a) Values of
average selective mortality observed for each species. (b) Ranges of selective mortality values
observed among cohorts within each species.