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Definition

Heritability is a statistic relating the phenotypic variation among individuals of a given population, observed at a specific time in a specific environment, to the genetic differences among individuals in that population.The term originated in its modern technical sense in 1936.

Broad-sense heritability

Jay Laurence Lush distinguished "broad heritability" from "narrow heritability" in his early writings on heritability.

Illustrative quotations

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 659. ISBN 978-0-321-75435-6. Heritability values estimate the genetic contribution to phenotypic variability under specific environmental conditions. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 660. ISBN 978-0-321-75435-6. To further complicate the link between the genotype and phenotype, the genotype generated at fertilization establishes a quantitative range within which a particular individual can fall. However, the final phenotype is often also influenced by environmental factors to which that individual is exposed. Human height, for example, is genetically influenced, but is also affected by environmental factors such as nutrition. Quantitative (polygenic) traits whose phenotypes result from both gene action and environmental influences are often termed multifactorial, or complex traits. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 660. ISBN 978-0-321-75435-6. In addition to quantitative traits that display continuous variation, there are two other classes of polygenic traits. Meristic traits are those in which the phenotypes are described by whole numbers. Examples of meristic traits include the number of seeds in a pod or the number of eggs laid by a chicken in a year. These are quantitative traits, but they do not have an infinite range of phenotypes: for example, a pod may contain 2, 4, or 6 seeds, but not 5.75. Threshold traits are polygenic (and frequently multifactorial), but they are distinguished from continuous and meristic traits by having a small number of discrete phenotypic classes. Threshold traits are currently of heightened interest to human geneticists because an increasing number of diseases are now thought to show this pattern of polygenic inheritance. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 660–661. ISBN 978-0-321-75435-6. The question of whether continuous phenotypic variation could be explained in Mendelian terms caused considerable controversy in the early 1900s. Some scientists argued that, although Mendel's unit factors, or genes, explained patterns of discontinuous segregation with discrete phenotypic classes, they could not also account for the range of phenotypes seen in quantitative patterns of inheritance. However, geneticists William Bateson and G. Udny Yule, adhering to a Mendelian explanation, proposed the multiple-factor or multiple-gene hypothesis, in which many genes, each individually behaving in a Mendelian fashion, contribute to the phenotype in a cumulative or quantitative way. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 661. ISBN 978-0-321-75435-6. The multiple-gene hypothesis was initially based on a key set of experimental results published by Hermann Nilsson-Ehle in 1909. Nilsson-Ehle used grain color in wheat to test the concept that the cumulative effects of alleles at multiple loci produce the range of phenotypes seen in quantitative traits. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 662. ISBN 978-0-321-75435-6. The multiple-gene hypothesis consists of the following major points: 1. Phenotypic traits showing continuous variation can be quantified by measuring, weighing, counting, and so on. 2. Two or more gene loci, often scattered throughout the genome, account for the hereditary influence on the phenotype in an additive way. Because many genes may be involved, inheritance of this type is called polygenic. 3. Each gene locus may be occupied by either an additive allele, which contributes a constant amount to the phenotype, or a nonadditive allele, which does not contribute quantitatively to the phenotype. 4. The contribution to the phenotype of each additive allele, though often small, is approximately equal. While we now know this is not always true, we have made this assumption in the above discussion. 5. Together, the additive alleles contributing to a single quantitative character produce substantial phenotypic variation. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 666. ISBN 978-0-321-75435-6. The term heritability is used to describe what proportion of total phenotypic variation in a population is due to genetic factors. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 666. ISBN 978-0-321-75435-6. The concept of heritability is frequently misunderstood and misused. It should be emphasized that heritability indicates neither how much of a trait is genetically determined nor the extent to which an individual's phenotype is due to genotype. In recent years, such misinterpretations of heritability for human quantitative traits have led to controversy, notably in relation to measurements such as intelligence quotients, or IQs. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 667. ISBN 978-0-321-75435-6. When obtaining heritability estimates for a multifactorial trait, researchers often assume that the genotype-by-environment interaction variance is small enough that it can be ignored or combined with the environmental variance. However, it is worth remembering that this kind of approximation is another reason heritability values are estimates for a given population in a particular context, not a fixed attribute for a trait. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 667. ISBN 978-0-321-75435-6. Broad-sense heritability (represented by the term H²) measures the contibution of the genotypic variance to the total phenotypic variance. It is estimated as a proportion:

H² = ${\frac {V_{G}}{V_{P}}}$

Heritability values for a trait in a population range from 0.0 to 1.0. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. pp. 667–668. ISBN 978-0-321-75435-6. Narrow-sense heritability (h²) is the proportion of phenotypic variance due to additive genotypic variance alone. Genotypic variance can be divided into subcomponents representing the different modes of action of alleles at quantitative trait loci. As not all the genes involved in a quantitative trait affect the phenotype in the same way, this partitioning distinguishes among three different kinds of gene action contributing to genotypic variance. Additive variance, V_A, is the genotypic variance due to the additive action of alleles at quantitative trait loci. Dominance variance, V_D, is the deviation from the additive components that results when phenotypic expression in heterozygotes is not precisely intermediate between the two homozygotes. Interactive variance, V_I, is the deviation from the additive components that occurs when two or more loci behave epistatically. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 668. ISBN 978-0-321-75435-6. The partitioning of the total genotypic variance VG is summarized in the equation

$V_{G}=V_{A}+V_{D}+V_{I}$

and a narrow-sense heritability estimate based only on that portion of the genotypic variance due to additive gene action becomes

h² = ${\frac {V_{A}}{V_{P}}}$

Omitting $V_{I}$ and separating $V_{P}$ into genotypic and evnironmental variance components, we obtain

h² = ${\frac {V_{A}}{V_{E}+V_{A}+V_{D}}}$ {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 669. ISBN 978-0-321-75435-6. The longest running artificial selection experiment known is still being conducted at the State Agricultural Laboratory in Illinois. Since 1896, corn has been selected for both high and low oil content. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 669. ISBN 978-0-321-75435-6. h² values vary, but heritability tends to be low for quantitative traits that are essential to an organism's survival. Remember, this does not indicate the absence of a genetic contribution to the observed phenotypes for such traits. Instead, the low h² values show that natural selection has already largely optimized the genetic component of these traits during evolution. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 670. ISBN 978-0-321-75435-6. Another possible error source is interactions between the genotype and the environment that produce variability in the phenotype. These interactions can increase the total phenotypic variance for DZ twins compared to MZ twins raised in the same environment, influencing heritability calculations. Overall, heritability estimates for human traits based on twin studies should therefore be considered approximations and examined very carefully before any conclusions are drawn. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 671. ISBN 978-0-321-75435-6. Progressive, age-related genomic modifications may be the result of MZ twins being exposed to different environmental factors, or from failure of epigenetic marking following DNA replication. These findings also indicate that concordance studies in DZ twins must take into account genetic as well as epigenetic differences that contribute to discordance in these twin pairs. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 680. ISBN 978-0-321-75435-6. Behavior is a complex response to stimuli that is mediated both by genes and by the environment. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 680. ISBN 978-0-321-75435-6. The behavior-first and gene-first approaches have been successfully used to dissect behavioral responses in Drosophila, making it a useful model organism for the study of nervous system function and the mechanisms that underlie human behavioral disorders. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 681. ISBN 978-0-321-75435-6. By the early 1900s, clear-cut cases of genetic influence on behavior had been identified, but at the time, behavior was primarily of interest to psychologists, who were concerned with learned or conditioned behavior. Such behaviors were thought to reflect the influence of the environment to the exclusion of the genotype. The difference between these two approaches to studying behavior was the starting point for what has been called the nature versus nurture debate. In this simplistic (and false) dichotomy, behavior is controlled entirely either by genes or by the environment. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 681. ISBN 978-0-321-75435-6. In humans, twin studies and adoption studies have provided evidence for the role of heredity in behavioral responses. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 681. ISBN 978-0-321-75435-6. Two different approaches have been used to study the genetic control of behavior, to define the interactions between genotype and environmental factors, and to dissect the pathways leading from genes to a behavioral phenotype. One of these approaches is a top=down, or behavior-first, method in which a specific behavior is identified in an organism, and then, genetic crosses are used to produce strains that bred true for either a high level or a low level of this behavioral response. Once these strains are established, further crosses identify and analyze the genetic components of the behavior. The second approach is a bottom-up, or gene-first, approach in which mutagenesis followed by screening is used to identify single-gene mutations associated with variant or abnormal behaviors. Analysis of the molecular mechanism of gene action in these mutant strains often provided a direct explanation of the behavior. Each approach has its advantages and shortcomings, but in spite of their differences, both share the same goals: to establish the inherited nature of a specific behavior, to identify and enumerate the genes or gene systems involved in the behavior being studied, to map these genes or gene systems to specific chromosomes, and to elucidate the molecular mechanisms by which these genes influence a behavioral response. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 681. ISBN 978-0-321-75435-6. The prevailing view today is that most behaviors are complex traits involving a number of genes, as well as interactions between and among these genes and environmental influences. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 688. ISBN 978-0-321-75435-6. The genetic control of behavior has proven more difficult to characterize in humans than in other organisms, partly because the types of responses considered to be the most interesting forms of human behavior, including aspects of intelligence, language, personality, and emotion, are difficult to study. Two problems arise in studying such behaviors. First, these traits are difficult to define objectively and to measure quantitatively. Second, they are affected by environmental factors and there is a wide range of individual variation in the responses to these factors. In each case, the environment is extremely important in shaping, limiting, or facilitating the final phenotype. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 688. ISBN 978-0-321-75435-6. Historically, the study of human behavior genetics has been hampered for other reasons as well. Many early studies of human behavior were conducted by psychologists with limited training in genetics. Second, traits involving intelligence, personality, and emotion have great social and political significance. Consequently, research findings concerning these traits are likely to be distorted by sensationalism when reported to the public. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 688. ISBN 978-0-321-75435-6. In lamenting the gulf between psychology and genetics in the study of human behavior, C. C. Darlington wrote in 1963, 'Human behavior has thus become a happy hunting ground for literary amateurs. And the reason is that psychology and genetics, whose business it is to explain behavior, have failed to face the task together.' Since 1963, some progress has been made in bridging this gap, but the genetics of human behavior remains somewhat controversial. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 691. ISBN 978-0-321-75435-6. The evidence from GWAS on schizophrenia indicates that no single gene or allele makes a significant contribution to this disorder. Instead, the results point to the involvement of hundreds of genes that each contributes only a small amount to schizophrenia. GWAS are based on the assumption that common gene variants (present in more than 5 percent of the population ) contribute to disease risk (the common disease/common variant hypothesis, abbreviated as CDCV). In this case, common variants identified by GWAS contribute only about 4 to 30 percent of the risk for schizophrenia. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 698. ISBN 978-0-321-75435-6. The rediscovery of Mendel's work in 1900 began a 30-year effort to reconcile the concept of genes and alleles with the theory of evolution by natural selection. As twentieth-century biologists applied the principles of Mendelian genetics to populations, both the source of variation (mutation) and the mechanism of inheritance (segregation of alleles) were explained. We now view evolution as a consequence of changes in alleles and allele frequencies in populations over time. This union of population genetics with the theory of natural selection generated a new view of the evolutionary process, called neo-Darwinism. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 700. ISBN 978-0-321-75435-6. The finding that populations harbor considerable genetic variation at the amino acid and nucleotide levels came as a surprise to many evolutionary biologists. The early consensus had been that selection would favor a single optimal (wild-type) allele at each locus and that, as a result, populations would have high levels of homozygosity. This expectation was shown conclusively to be wrong, and considerable research and argument has ensued concerning the forces that maintain such high levels of genetic variation. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 700. ISBN 978-0-321-75435-6. The neutral theory of molecular evolution, proposed by Motoo Kimura in 1968, proposes that mutations leading to amino acid substitutions are usually detrimental, with only a very small fraction being favorable. Some mutations are neutral, that is, they are functionally equivalent to the allele they replace. Mutations that are favorable or detrimental are preserved or removed from the population, respectively, by natural selection. However, the frequency of the neutral alleles in a population will be determined by mutation rates and random genetic drift, and not by selection. Some neutral mutations will drift to fixation in the population; other neutral mutations will be lost. At any given time, a population may contain several neutral alleles at any particular locus. The diversity of alleles at most loci does not, therefore, reflect the action of natural selection, but instead is a function of population size (larger populations have more variation) and the fraction of mutations that are neutral. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 703. ISBN 978-0-321-75435-6. One way to establish whether one (or more) of the Hardy-Weinberg assumptions does not hold in a given population is to determine whether the population's genotypes are in equilibrium. To do this, we first determine the frequencies of the genotypes, either directly from the phenotypes (if heterozygotes are recognizable) or by analyzing proteins or DNA sequences. We then calculate the allele frequencies from the genotype frequencies, as demonstrated earlier. Finally, we use the allele frequencies in the parental generation to predict the offspring's genotype frequencies. According to the Hardy-Weinberg Law, the genotype frequencies are predicted to fit the p² + 2pq + q² = 1 relationship. If they do not, then one or more of the assumptions are invalid for the population in question. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 708. ISBN 978-0-321-75435-6. The phenotype is the result of the combined influence of the individual's genotype at many different loci and the effects of the environment. Selection for these complex traits can be classified as (1) directional, (2) stabilizing, or (3) disruptive. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 708. ISBN 978-0-321-75435-6. In directional selection (Figure 25-10) phenotypes at one end of the spectrum become selected for or against, usually as a result of changes in the environment. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 708. ISBN 978-0-321-75435-6. Stabilizing selection tends to favor intermediate phenotypes, with those at both extremes being selected against. Over time, this will reduce the phenotypic variance in the population but without a significant shift in the mean. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 708. ISBN 978-0-321-75435-6. Disruptive selection is a case where selection acts against intermediate phenotypes and in favor of both phenotypic extremes. It can be viewed as the opposite of stabilizing selection because the intermediate types are selected against. This will result in a population with an increasingly bimodal distribution for the trait, as we can see in Figure 25-12. In one set of experiments using Drosophila, after several generations of disruptive artificial selection for bristle number, in which only flies with high- or low-bristle numbers were allowed to breed, most flies could be easily placed in a low- or high-bristle category. In natural populations, such a situation might exist for a population in a heterogeneous environment. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 710. ISBN 978-0-321-75435-6. In small populations, significant random fluctuations in allele frequencies are possible by chance alone. The degree of fluctuation increases as the population size decreases, a situation known as genetic drift. In addition to small population size, drift can arise through the founder effect, which occurs when a population originates from a small number of individuals, whose gene pool may not reflect that of the larger population from which the founders are drawn. Although the population may later increase to a large size, the genes carried by all members are derived only from those of the founders (assuming no mutation, migration, or selection, and the presence of random mating). Drift can also arise via a genetic bottleneck. Bottlenecks develop when a large population undergoes a drastic but temporary reduction in numbers. Even though the population recovers, its genetic diversity has been greatly reduced. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 712. ISBN 978-0-321-75435-6. violations of the first four assumptions of the Hardy-Weinberg Law, in the form of selection, mutation, migration, and genetic drift can cause allele frequencies to change. The fifth assumption is that the members of a population mate at random; in other words, any one genotype has an equal probability of mating with any other genotype in the population. Nonrandom mating can change the frequencies of genotypes in a population. Subsequent selection for or against certain genotypes has the potential to affect the overall frequencies of the alleles they contain, but it is important to note that nonrandom mating does not itself directly change allele frequencies. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 719. ISBN 978-0-321-75435-6. Perhaps the most unexpected finding in this analysis is that the genomes of present-day humans in Europe and Asia, but not Africa, are composed of 1–4 percent Neanderthal sequences. Interbreeding with Neanderthals may have occurred somewhere in the Middle East, before humans migrated into Europe and Asia. No Neanderthal contributions to African genomes were detected, but it is possible that a larger sampling of African populations will determine whether some Africans carry Neanderthal genes. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Klug, William S.; Cummings, Michael R.; Spencer, Charlotte A.; Palladino, Michael A. (2012). Concepts of Genetics (Tenth ed.). Pearson. p. 719. ISBN 978-0-321-75435-6. Assuming that chimpanzees and humans last shared a common ancestor about 6.5 million years ago, the tree shows that Neanderthals and humans last shared a common ancestor about 706,000 years ago and that the isolating split between Neanderthals and human populations occurred about 370,000 years ago. From these studies, several conclusions can be drawn. First, Neanderthals are not direct ancestors of our species. Second, Neanderthals and members of our species may have interbred, but from the results available, it appears that Neanderthals did not make major contributions to our genome. As a species, Neanderthals are extinct, but some of their genes survive as part of our genome. Third, from what we know about the Neanderthal genome, we share most genes and other sequences with them. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)

Bibliography

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• Gottfredson, Linda S. (2003). "Chapter 3: The Science and Politics of Intelligence in Gifted Education". In Colangelo, Nicholas; Davis, Gary A. (eds.). Handbook of Gifted Education. Julian C. Stanley (Guest Foreword). Boston: Allyn & Bacon. ISBN 978-0-205-34063-7. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)
• Keller, Evelyn Fox (21 May 2010). The Mirage of a Space between Nature and Nurture. Duke University Press. ISBN 978-0-8223-4731-6. {{cite book}}: Unknown parameter |lay-date= ignored (help); Unknown parameter |lay-url= ignored (help)
• Manuck, Stephen B.; McCaffery, Jeanne M. (2014). "Gene-Environment Interaction". Annual Review of Psychology. 65 (1): 41–70. doi:10.1146/annurev-psych-010213-115100. ISSN 0066-4308. PMID 24405358.