DOI: 10.25349/d9660g
title: Data used in: Heritability and variance components of seed size in wild species: influences of breeding design and the number of genotypes tested

description: Seed size affects individual fitness in wild plant populations, but its
 ability to evolve may be limited by low narrow-sense heritability (h2). h2
 is estimated as the proportion of total phenotypic variance (s2P)
 attributable to additive genetic variance (s2A), so low values of h2 may
 be due to low s2A (potentially eroded by natural selection) or to high
 values of the other factors that contribute to s2P, such as extranuclear
 maternal effects (m2) and environmental variance effects (e2). 
 Here, we reviewed the published literature and performed a meta-analysis
 to determine whether h2 of seed size is routinely low in wild populations
 and, if so, which components of s2P contribute most strongly to total
 phenotypic variance. We analyzed available estimates of narrow-sense
 heritability (h2) of seed size, as well as the variance components
 contributing to these parameters. Maternal and environmental components of
 s2P were significantly greater than s2A, dominance, paternal, and
 epistatic components. These results suggest that low h2 of seed size in
 wild populations (the mean value observed in this study was 0.13) is due
 to both high values of maternally derived and environmental (residual) s2,
 and low values of s2A in seed size. The type of breeding design
 used to estimate h2 and m2 also influenced their values, with studies
 using diallel designs generating lower variance ratios than nested and
 other designs. e2 was not influenced by breeding design. For some breeding
 designs, the number of genotypes included in a study also influenced the
 resulting h2 and e2 estimates, but not m2. Our data support the view that
 a diallel design is better suited than the alternatives for the accurate
 estimation of s2A in seed size due to its factorial design and the
 inclusion of reciprocal crosses, which allows the independent estimation
 of both additive and non-additive components of variance.
description: Data search We performed a literature search
 to investigate published estimates of variance components for seed size in
 wild plant species. We used a query containing the following keywords:
 (“heritab*” or “variance component*”) and (“seed size” or “seed mass” or
 “seed weight”). We included only studies that examined the quantitative
 genetics of seed size of wild plant populations and excluded those that
 investigated agricultural or commercial species. We also excluded studies
 that pooled genotypes from multiple populations to estimate species-level
 heritabilities.  Studies included for analysis reported narrow- and/or
 broad-sense heritabilities from individual populations, the variance
 components (as raw values) used to estimate these parameters, or both. We
 performed our search using the Web of Science search engine.
 Data extraction From all selected studies, we
 extracted the following estimated parameters: 1) raw values of variance
 components of seed size (s2A, s2M, s2P, s2E, s2D, s2K; Table 1); and 2)
 narrow-sense heritability (h2 = s2A: s2P) when available. Whenever a
 reported value of a raw variance component was measured for the same
 population but in different year, we averaged them and reported a single
 value. When parameters were reported for more than one population, we
 included each estimate in our data set. In cases where seed size was
 measured in multiple ways (e.g., seed weight, seed length, or seed area),
 we used the value of seed weight and discarded the others.
 Additionally, for each published parameter we recorded the
 following: publication identity, breeding design, and the number of
 maternal and paternal genotypes used in the breeding design that generated
 the parameter estimate. Breeding design refers to the pattern by which
 controlled pollinations were performed or by which natural pollinations
 occurred in each study. Categories examined here include: diallel and
 nested designs, clonal replication (hereafter “clones”), and autogamously
 self-fertilizing genotypes (hereafter “selfing”). Studies that reported
 heritability estimates but no breeding design (e.g., naturally pollinated
 maternal lines) were also excluded because such estimates were derived
 from open-pollinated genotypes and were likely to be confounded by
 environmentally induced maternal effects. Data
 analysis Standardization of variance components. In
 order to compare the relative contributions to seed size of each type of
 variance component, in each published study used here, we standardized the
 raw variance components by calculating variance ratios, which were
 computed by dividing a given raw variance component by the total
 phenotypic variance in seed size (i.e., the sum of all reported variance
 components, including the focal raw variance component). h2, for instance,
 is equivalent to additive genetic variance divided by total phenotypic
 variance (s2A:s2P). In the same manner, we defined m2 as the maternal
 variance component divided by total phenotypic variance (s2M:s2P); and e2
 as the environmental (residual) variance component divided by total
 phenotypic variance (s2E:s2P). The same procedure was applied to the
 remaining components of seed size: paternal variance (Pat2 or s2Pat:s2P),
 dominance variance (d2 ors2D:s2P), and epistasis variance (k2 or s2K:s2P).
 Such standardized values are well-suited for comparisons among species,
 among independently conducted studies, and among different units of
 measurement (e.g., mass vs. linear measures) because standardized
 components are unitless. Model construction. Because
 the variance ratios analyzed here originate from publications that, in
 some cases, reported multiple estimates of the same variance component per
 publication, such estimates were not fully independent, thereby violating
 an assumption of ordinary least-squares methods. To account for variation
 among publications in the variance ratios of seed size, we analyzed the
 data with generalized linear mixed-effects models (GLMMs) that included
 publication identity as a random effect. We chose to include only
 publication identity as a random effect because most studies estimated
 variance components for a single species, making publication and species
 identity contain nearly the same information, such that their simultaneous
 inclusion in the model as random effects would be problematic.
 The number of maternal and paternal genotypes used to estimate
 each variance component varied greatly among published studies (range =
 2-170 genotypes; Table S1), and we reasoned that the number of genotypes
 contributing to a genetically determined parameter estimate might
 influence its estimated value.  Accordingly, we controlled for variation
 among studies in the number of genotypes sampled by including a weighting
 factor in the GLMMs. Weights were estimated as the number of
 genotypes—maternal or paternal genotypes, depending on the variance
 component—used in each study. Specifically, we used the number of paternal
 genotypes as weightings for models using estimates of h2 or Pat2 because
 these parameters are usually estimated using trait variation derived from
 the paternal lines. We used the number of maternal genotypes as weightings
 for models using estimates of m2 and e2 because maternal and environmental
 sources of variance in seed size are more likely to influenced by maternal
 than by paternal genotypes.  We used the number of maternal genotypes as
 weightings for models using estimates of d2 and k2 because these
 parameters may be influenced by the number of either maternal or paternal
 genotypes. Among the studies analyzed here, the number of maternal
 genotypes equaled or exceeded the number of paternal genotypes (Table S1),
 so using the higher number would take this into account.
 GLMMs are robust tools for the analysis of variables that vary
 over multiple levels and can be used with alternative distributional
 assumptions of the residuals. Because the variance ratios that we used as
 response variables have values in the closed interval from zero to one
 (with many zero values present), distributions commonly employed to model
 proportion data, such as the beta distribution, were inappropriate for our
 response variables. Because of this, we used a pseudo-likelihood approach
 where the variance structure between the mean and the variance of the
 observations, and the range of the response (but not its precise
 distribution), are assumed. Specifically, we used a quasi-binomial GLMM
 with a logit link function for all models, which uses the variance
 structure of a binomial distribution while allowing for continuous values
 in the [0, 1] range. We fitted all GLMMs with the ‘glmmPQL’ function of
 the R package ‘MASS’ version 7.3-58.1 , which uses penalized
 quasi-likelihood (PQL) for parameter estimation.
 Comparison of variance components of seed size.
 To compare the means of the distinct proportional variance
 component types (h2, d2, pat2, m2, e2, and k2), we used a quasi-binomial
 GLMM with the observed value of each variance ratio estimate as a
 response, and the type of variance ratio for each observation as a
 categorical predictor. Publication identity was included as a random
 effect, and each observation was weighted based on the number of paternal
 or maternal genotypes used in estimating the reported ratio. As described
 above, whether we used the number of maternal or paternal genotypes
 depended on the identity of the variance ratio to which each observation
 corresponded. Marginal means of each variance ratio type and pairwise
 statistical comparisons between ratio types were conducted using the
 ‘emmeans’ function of the ‘emmeans’ R package version 1.7.5, with Tukey
 contrasts used to assess the significance of pairwise differences, and a
 Tukey correction of p-values to account for multiple hypothesis
 testing. Heritability and variance components of seed
 mass in relation to breeding design and number of genotypes. To determine
 whether breeding design and number of genotypes influenced h2, m2, and e2
 of seed size, we fitted quasi-binomial GLMMs using each of these variance
 ratio types as a separate response variable. These models included
 breeding design as the main explanatory variable, and the number of
 genotypes (maternal or paternal as assigned above) and the interaction
 between breeding design and number of genotypes as control variables. The
 model also included publication identity as a random effect. Number of
 genotypes were also included as a weight in order to assign more
 information value to estimates obtained from a greater number of
 genotypes. In each model, we used the ‘emmeans’ package to estimate the
 marginal means for each breeding design, using Tukey multiple comparisons
 tests to assess the significance of differences in mean ratios between
 breeding designs. In each model, p-values obtained from pairwise
 comparison of breeding designs were adjusted for multiple hypothesis
 testing using the Tukey method. Significance testing for the effects of
 breeding design and genotype number were obtained using Type III ANOVA as
 implemented in the ‘car’ package version 3.1-0 in R.
description: RStudio was used to create the Rmd file that contains the code
 used to create the output included in the Results section of the
 manuscript (including the Figures and Tables in the main text and in the
 Supplemental Materials).