Which of these statements about heritability is false? which of these statements about heritability is false? heritability for a given trait in a population can change if environmental factors change. heritability is high when much of the phenotypic variation is produced by genetic variation and little is contributed by environmental variation. heritability is not an indication of the mechanism by which genes control a trait. traits with high heritability are not very responsive to environmental changes. heritability values are accurate only for the environment and population in which they are measured.