Clearly there must be a cause for variance and we have found two main components controlling it. These are the environment and the genes.

Variance due to the environment (V_e) results from the action of the environment due to differences from place to place and even in an environment that appears to be very uniform, like the uterus of a pregnant mammal, there could be slight variations within it which may cause different effects upon individuals growing there. Because plants are generally fixed in one place they must cope with local environmental variations which animals may avoid by moving and hence they show a greater phenotypic plasticity. An example of this is dandelions of the same genotype growing in trampled and untrampled areas, one type grows in a dwarfed form while the other is tall with bigger leaves and longer flower stems. This may be due to environmentally sensitive switching genes.

Variance due to genotypes (V_g) results from the different combinations of alleles found in the population of organisms within the area. The different gene combinations in different individuals will have some influence upon the phenotypes we observe in the population.

The genetic component of variance (V_g) can be split into two main parts: Additive genetic variance (V_a) which results from the action of additive gene systems upon the phenotype. Non-additive genetic variance (V_na). This is the part of the genetic not caused by additive gene systems. The non-additive component can be split into two parts, variance caused by epistatic gene systems (V_i) and variance caused by dominance effects (V_d).

For a biochemical pathway to work efficiently a number of enzymes are needed to perform each stage in the operation. If one of the enzymes is missing then the pathway stops at the point before the missing enzyme. For example take a series of three genes which produce enzymes which work in a linear biochemical pathway. If gene¹ fails then enzyme¹ is not produced and therefore the other two enzymes cannot work even though they are present because they will not be receiving the substrate they need. We say that gene¹ is epistatic to gene² and gene³. We call gene² and gene³ hypostatic to gene¹.

Clearly we cannot make B, C or D if Enzyme¹ is not present since there is nothing to turn A into B! Therefore Gene² and Gene³ cannot do anything even though they are there and are churning out the necessary enzymes. They are dependent upon the presence of a working Gene¹ if they are to have any affect. Epistasis has two forms called dominant and recessive. These have different affects upon the phenotypes produced by the organism. If we consider a phenotype controlled by two gene loci we can see how the two types differ.

Crossing two dihybrids AaBb we get the familiar table:

From this type of cross we normally expect our 9:3:3:1 ratio of phenotypes but if we have a case of recessive epistasis in which gene A is epistatic to gene B then if the alleles aa are present in the offspring allele B cannot work, so we can't get the BB or Bb phenotype to show itself. Thus the offspring marked * in the table all appear the same as aabb and we get a 9:3:4 ratio and only three phenotypic classes.

If the epistasis is dominant, then the genotype aa will allow the normal dominant allele B to function, but the dominant allele A will stop it from working, so for the same dihybrid cross we would get a similar table of genotypes but a different range of phenotypes. The following table gives the results of a dominant epistasis cross.

Any offspring with the allele A in its genotype will be of the same phenotype regardless of the B alleles present. Therefore all those marked * are identical giving a 12:3:1 ratio.

The other component of non-additive genetic variance is the result of dominance interactions and is referred to as Vd which is the contribution to variance made by a series of genes which show complete dominance. Many genes have variants which do not work at all in terms of affecting the phenotype, while the dominant allele causes a complete affect even if there was only one of it. If you have the alleles aa then you develop the recessive phenotype and if you have the alleles AA or Aa then you develop the complete dominant phenotype even though you may only have 1 dominant allele in you. Thus the homozygous and heterozygous dominant genotypes develop exactly the same phenotypes and thus there is no additive effect, which explains why this is included as part of the non-additive component of Vg. The deviation of the heterozygous phenotype from the mid-point of the phenotype range is a measure of the degree of dominance shown by the allele.

The term hybrid has many meanings, we use it to refer to organisms which are heterozygous for a particular phenotype, but it has other interpretations.

Intraspecific hybrids: These are crosses within a species usually between different strains (used for animals and bacteria) or varieties (used for plants). This leads to heterozygous types.

Interspecific hybrids: These are the results of crosses between different species and result in allopolyploid types with a mixture of chromosomes from the two species.

Intergeneric crosses: These are the results of crossing organisms from two genera, since the chromosomes tend to be markedly different in each genus such crosses often result in interference between genetic systems which prevents normal development, although sometimes with chromosome doubling the system does work.

Chimera: On occasions tissue from two species is mixed, but the chromosomes of each species are in separate cells. This gives rise to a mosaic of tissues from the two species which can give rise to interesting effects. It is known to have occurred in plants.

Hybrids occur naturally in many groups of organisms and the process has been employed in breeding programs to introduce new genetic combinations in many inbreeding plant types. In an inbreeding population of plants there will be many different homozygous lines and by hybridising between these lines we can produce new combinations of genes. The technique employed is to remove the female parts from some developing flower buds and the male parts from others. The flowers are covered to prevent entry of foreign pollen and when the anthers are ripe, the pollen is transferred by brush or by rubbing the pollen coated anthers against the receptive stigmas on the other flowers. The flowers are then covered again to prevent foreign pollen from entering. Some flowers like the pea, which appears to be an insect pollinated out breeder, are in fact self fertilising whilst the flower bud is developing, and therefore this technique must be employed early in development.

The degree of genetic determination, or broad sense heritability is the proportion of phenotypic variance resulting from the overall genetic variability of a given population and we calculate it using the equation:

Narrow sense heritability is used much more by animal breeders because its the proportion of variance resulting from the additive genetic component. It is worked out as:

Most of the important crop animal traits have a strong additive genetic component. There are various ways of calculating heritability values for organisms. It has been done for lots of crop organisms.

If we calculate the mean value of a phenotype in a given population (m_t) and we then select a particular group of individuals from this population and calculate the mean of this selected group (m_s), we can then breed from the selected stock and calculate the mean of these progeny (m_p). Having done this we can calculate h² by the formula:

h² = (m_t - m_p) / (m_t - m_s)

We can calculate H by doing a crossing experiment: If we have a pure breeding plant variety whose seed mass has a mean value of 2.3g and a variance of 0.5 and another pure breeding plant variety with mean seed mass 3.4g and variance 0.9, both of which were growing in the same basic environment then we cross these plant to produce a hybrid variety with seed mass 2.9g and variance 0.6 then we can calculate broad sense heritability as follows. Since all of the plants were either pure bred strains or F₁ hybrids we know that the genetic variance was zero.

Then when we cross these F₁ plants we get the F₂ type seeds which have a mixture of genotypes (try it if you dare!) and then we find that the seeds are more variable in mass so we get values such as mean 2.8 and variance 1.1.

By applying our formulae for H we can calculate heritability like this:

Pure bred strains: V_g = 0

therefore average: V_e= (0.5+0.9) ÷ 2 = 0.7

F₁strain: V_g = 0

therefore V_e = 0.6

Thus the average V_e is (0.7+0.6) ÷ 2 = 0.65

F₂ strain V_p = V_g + V_e = 1.1,

and since V_e = 0.65,

therefore V_g = 1.1 - 0.65,

thus V_g = 0.35.

From the equation: H = Vg ÷ Vp

we get H = 0.35 ÷ 1.1 = 0.32.

There are other ways of measuring heritability, especially where breeding programmes aren't possible such as with humans. Here we can find monozygotic, or identical twins useful because they can be scored for concordance, or sameness, and disconcordance, or differentness. And comparing these figures with dizygotic twins gives a measure of heritability. We can also use regression analysis and correlation coefficients which relate offspring phenotype to parental phenotype.