Estimating Trait Heritability in Highly Fecund Species

Abstract

Increasingly, researchers are interested in estimating the heritability of traits for nonmodel organisms. However, estimating the heritability of these traits presents both experimental and statistical challenges, which typically arise from logistical difficulties associated with rearing large numbers of families independently in the field, a lack of known pedigree, the need to account for group or batch effects, etc. Here we develop both an empirical and computational methodology for estimating the narrow-sense heritability of traits for highly fecund species. Our experimental approach controls for undesirable culturing effects while minimizing culture numbers, increasing feasibility in the field. Our statistical approach accounts for known issues with model-selection by using a permutation test to calculate significance values and includes both fitting and power calculation methods. We further demonstrate that even with moderately high sample-sizes, the p-values derived from asymptotic properties of the likelihood ratio test are overly conservative, thus reducing statistical power. We illustrate our methodology by estimating the narrow-sense heritability for larval settlement, a key life-history trait, in the reef-building coral Orbicella faveolata. The experimental, statistical, and computational methods, along with all of the data from this study, are available in the R package multiDimBio.

Keywords: binary variable traits; common garden; coral settlement; heritability; nonmodel organisms.

Figure 1

Diagram representing the design of the common garden experiment. First, independent fertilizations are completed for each sire and dam (in this case only one dam and nine sires are used). Second, equal quantities of fertilized embryos are pooled into one single common garden tank. This common garden is the split into three replicate tanks (N = 400 larvae per tank). Settlement slides are added to each experimental tank and after 4 days the settled larvae are collected and individually preserved. Larvae were then left for an additional 10 days and settled larvae were removed every few days. N = 50 larvae that remained swimming after 14 days were collected and individually preserved for genotyping, to compare their parentage to the parentage of the early-settling larvae.

Figure 2

Proportion of settled (successes) and swimming (failures) larvae belonging to each sire. The total number of genotyped larvae assigning to each sire is indicated at the top of each bar.

Figure 3

The cumulative distribution function for the actual (black solid), permutation (gray dashed), and theoretical (red dashed) nulls are compared. The permutation null is a closer match to the actual null and is less conservative than the asymptotic approximation. This suggests that asymptotic approximation to the true null distribution is inappropriate for our data set.

Figure 4

Power analysis for a varying number of sires. The offspring number was fixed, at μ = 4.63 and size = ${\mu }^2/\left(\sqrt{12.63}-\mu \right)$ respectively, and the number of sires was varied between 9 and 20. In (A), the power to reject the null hypothesis of h² = 0 is plotted as a function of narrow-sense heritability (h²), where the true value of h² > 0. (B) The power to fail-to-reject the null hypothesis when the true value of h² was equal to zero is plotted for varying numbers of sires.

Figure 5

Power analysis for a varying number of offspring. The mean number of offspring genotyped per sire, μ, was varied between 4 and 20, whereas the size parameter for the negative binomial distribution was ${\mu }^2/\left(\sqrt{\mu \left(12.63/4.63\right)}-\mu \right)$. The number of sires was fixed at 9. The power to reject the null hypothesis of h² = 0 is plotted as a function of narrow-sense heritability (h²), where the true value of h² > 0.