There can be some apparent paradoxes in the application of this strict definition. For example, the ‘heritability’ of the same characteristic could be near zero in one study, and close to 100% in another if, in one study, a group of army recruits (unrelated to each other) are all given identical training and nutrition, and their muscular strength is later measured, then those differences that are observed after the (identical) training will be largely ‘heritable’ – however, in another study, whose purpose might be to assess the efficacy of various workout regimes, or various nutritional programs, a group of subjects is chosen who match each other as closely as possible in prior physical characteristics, and then some of these are put onto Program A, and others onto Program B. Differences between the groups after being on the programs are then attributed to the differences in the program. They are environmentally-induced differences. They are not ‘heritable’.
In the case of scholastic ability, how well you do in the final school exams depends on both what and how well you were taught, how hard you have studied, how ‘naturally’ smart you are, and of course, a fair bit on luck. How ‘heritable’ it is depends on who is being compared with who, and in which circumstances.
Much the same goes for intelligence tests. However, the conclusions from studies involving intelligence tests often conclude that intelligence is highly heritable, because the tests are contrived so that it is (supposed to be) impossible to study so as to improve performance in them, and also because what ‘heritability’ actually means gets distorted in the re-telling in the popular media.
In human genetics, much use is made of twin studies in the analysis of heritability – monozygous (‘identical’) twins are clones of each other, and have effectively identical genotypes, and similarities between sets of monozygous twins can be compared with those between dizygous (‘fraternal’, or non-identical) twins, who have only a ˝ coefficient of relatedness to each other.