# The design and analysis of binary variable traits in common garden genetic experiments of highly fecund species to assess heritability

## TL;DR

This paper introduces a new method to estimate heritability for binary traits in highly fecund species, using coral larval settlement as an example.

## Contribution

The study presents a novel empirical and computational methodology for estimating heritability of binary traits in species with high fecundity.

## Key findings

- The methodology was applied to estimate heritability of larval settlement in the coral Orbicella faveolata.
- The approach includes a permutation test to calculate significance values and power calculations.
- The methods and data are available in the R package multiDimBio.

## Abstract

Many biologically important traits are binomially distributed, with their key phenotypes being presence or absence. Despite their prevalence, estimating the heritability of binomial traits presents both experimental and statistical challenges. Here we develop both an empirical and computational methodology for estimating narrow-sense heritability of binary 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 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, were deployed in the R package multiDimBio.