Principles of Plant Genetics and Breeding. George Acquaah

basis of phenotypic values to be used as parents in a cross, the success of such an action in changing the characteristics in a desired direction is predictable only by knowing the degree of correspondence (genetic determination) between phenotypic values and breeding values. Heritability measures this degree of correspondence. It does not measure genetic control, but rather how this control can vary.

      Genetic determination is a matter of what causes a characteristic or trait; heritability, by contrast, is a scientific concept of what causes differences in a characteristic or trait. Heritability is, therefore, defined as a fraction: it is the ratio of genetically caused variation to total variation (including both environmental and genetic variation). Genetic determination, by contrast, is an informal and intuitive notion. It lacks quantitative definition and depends on the idea of a normal environment. A trait may be described as genetically determined if it is coded in and caused by the genes, and bound to develop in a normal environment. It makes sense to talk about genetic determination in a single individual, but heritability makes sense only relative to a population in which individuals differ from one another.

       Types of heritability

      Heritability is a property of the trait, the population, and the environment. Changing any of these factors will result in a different estimate of heritability. There are two different estimates of heritability.

      1 Broad sense heritabilityHeritability estimated using the total genetic variance (VG) is called broad sense heritability. It is expressed mathematically as:It tends to yield a high value (Table 4.2). Some use the symbol H2 instead of H.

      2 Narrow sense heritabilityBecause the additive component of genetic variance determines the response to selection, the narrow sense heritability estimate is more useful to plant breeders than the broad sense estimate. It is estimated as follows:

Table 4.2 Heritability (broad sense) estimates of some plant architectural traits.

Trait	Heritability
Plant height	45
Hypocotyl diameter	38
Number of branches/plant	56
Nodes in lower third	36
Nodes in mid section	45
Nodes in upper third	46
Pods in lower third	62
Pods in mid section	85
Pods in upper third	80
Pod width	81
Pod length	67
Seed number per pod	30
100 seed weight	77

      However, when breeding clonally propagated species (e.g. sugarcane, banana), in which both additive and nonadditive gene action are fixed and transferred from parent to offspring, broad sense heritability is also useful. The magnitude of narrow sense heritability cannot exceed and is usually less than the corresponding broad sense heritability estimate.

      Heritabilities are seldom precise estimates because of large standard errors. Characters that are closely related to reproductive fitness tend to have low heritability estimates. The estimates are expressed as a fraction, but may also be reported as a percentage by multiplying by 100. A heritability estimate may be unity (1) or less.

       Factors affecting heritability estimates

      The magnitude of heritability estimates depends on the genetic population used, sample size, and the method of estimation.

       Genetic populationWhen heritability is defined as h2 = VA/VP (i.e. in the narrow sense), the variances are those of individuals in the population. However, in plant breeding, certain traits such as yield are usually measured on plot (not on individual plants) basis. The amount of genotypic variance present for a trait in a population influences estimates of heritability. Parents are responsible for the genetic structure of populations they produce. More divergent parents yield a population that is more genetically variable. Inbreeding tends to increase the magnitude of genetic variance among individuals in the population. This means that estimates derived from F2 will differ from, say, those from F6.

       Sample sizeBecause it is impractical to measure all individuals in a large population, heritabilities are estimated from sample data. To obtain the true genetic variance for a valid estimate of the true heritability of the trait, the sampling should be random. A weakness in heritability estimates stems from bias and lack of statistical precision.

       Methods of computationHeritabilities are estimated by several methods that use different genetic populations and produce estimates that may vary. Common methods include parent–offspring regression and variance component method. Mating schemes are carefully designed to enable the total genetic variance to be partitioned.

      4.2.10 Methods of computation

      The methods of estimating heritabilities have strengths and weaknesses.

       Variance ComponentsThe variance component method of estimating heritability uses the statistical procedure of analysis of variance. Variance estimates depends on the types of populations in the experiment. Estimating genetic components suffer from certain statistical weaknesses. Variances are less accurately estimated than means. Also, variances are unrobust and sensitive to departure from normality. An example of heritability estimate using F2, and backcross populations is as follows:Example:Using the data in the table below

	P1	P2	F1	F2	BC1	BC2
Mean	20.5	40.2	28.9	32.1	25.2	35.4
Variance	10.1	13.2	7.0	52.3	35.1	56.5

       Broad sense heritability