Mendel's laws hold when genes lie on different chromosomes and do not affect each other. In reality genes are often linked on one chromosome, some sit on the sex chromosomes, and one trait is frequently controlled by several genes. This lesson covers linked inheritance, sex genetics, gene interaction and the types of variation, with problems.
§1. Linked inheritance and the chromosome theory
T. Morgan and his students worked with the fruit fly Drosophila (a convenient organism: it breeds fast and has few chromosomes — 2n = 8).
Genes on the same chromosome are inherited together and form a linkage group. The number of linkage groups equals the haploid set (in humans 23 in women and 24 in men, because X and Y are separate groups).
With complete linkage a test cross gives 1 : 1 (only parental gamete types).
With incomplete linkage, crossing over (exchange of segments between homologous chromosomes) in prophase I of meiosis produces gametes with new combinations (recombinant gametes).
Crossing-over frequency is proportional to the distance between genes: 1% recombinants = 1 morganid (centimorgan).
The chromosome theory of heredity states: genes are arranged linearly on chromosomes; each gene occupies a specific locus; genes on one chromosome form a linkage group; linkage is broken by crossing over; the greater the distance between genes, the more often crossing over occurs.
Worked example
A dihybrid AB/ab was test-crossed with ab/ab. Offspring: AaBb — 42%, aabb — 42%, Aabb — 8%, aaBb — 8%. What is the distance between the genes?
The large classes (AaBb, aabb) are parental, non-recombinant offspring.
The small classes (Aabb, aaBb) are recombinants: 8% + 8% = 16%.
Answer: 16 morganids. If the genes were independent, each of the four classes would be 25%.
§2. Sex genetics
Sex is determined by the sex chromosomes; all the others are autosomes. The human karyotype is 46 = 44 autosomes + XX (female) or 44 + XY (male).
Females are homogametic (all eggs carry X); males are heterogametic (sperm carry X or Y). So a child's sex depends on the father's sperm, and the chance of a boy or a girl is 1 : 1.
In birds, butterflies and some reptiles it is the other way round: males are homogametic (ZZ), females heterogametic (ZW).
In some insects (for example grasshoppers) the male has a single X (X0).
Sex-linked traits are controlled by genes on the X chromosome. In humans haemophilia (failure of blood clotting) and colour blindness are recessive and X-linked.
A son receives his X chromosome only from his mother and his Y from his father. So an X-linked recessive disease is never passed from father to son.
A man has only one X, so a single recessive allele (XʰY) causes the disease — such diseases occur mainly in men.
A woman XᴴXʰ is a healthy carrier.
Y-linked traits pass only from father to son.
Worked example
The mother carries the haemophilia gene; the father is healthy. What is the chance of haemophilia in their children?
Answer: 25% of all children are affected; 50% of the sons; daughters are not affected, but half are carriers.
§3. Gene interaction
Non-allelic genes can jointly affect one trait. The 9 : 3 : 3 : 1 ratio in F₂ then changes, but the total stays 16.
Complementary genes — a new trait appears only when dominant alleles of both genes are present. In sweet peas A_B_ gives purple flowers and all others are white: 9 : 7. Other variants: 9 : 6 : 1, 9 : 3 : 4, 9 : 3 : 3 : 1 (comb shape in chickens).
Epistasis — one gene masks the effect of another, non-allelic gene. Dominant epistasis: 13 : 3 or 12 : 3 : 1; recessive epistasis: 9 : 3 : 4.
Polygeny (polymery) — a trait is controlled by several genes with similar effects; the more dominant alleles, the stronger the trait (cumulative). In humans: skin colour, height; also wheat grain colour. For two genes F₂ gives 1 : 4 : 6 : 4 : 1; non-cumulative polymery gives 15 : 1.
Pleiotropy — one gene affects several traits.
Worked example
Two different pure lines of white-flowered sweet peas were crossed; F₁ had purple flowers. How many of 320 F₂ plants will be white?
Purple F₁ is AaBb; the parents were AAbb and aaBB (each has only one dominant gene, so both are white).
Complementation: A_B_ is purple (9/16), the other 7/16 are white.
320 × 7/16 = 140.
Answer: 140 white plants.
§4. Variation
Modification (phenotypic) variation is caused by the environment; the genotype does not change, it is not inherited, it is group-wide and directed, and usually adaptive. Its limits are the norm of reaction, set by the genotype. Example: arrowhead leaves are ribbon-like under water, rounded at the surface and arrow-shaped in air; skin tanning in the sun. It is studied with a variation series and a variation curve; the average value is the most frequent.
Genotypic variation is inherited:
Combinative — independent assortment of homologous chromosomes in meiosis, crossing over, and random fusion of gametes at fertilisation. No new genes appear, only new combinations.
Mutational — sudden, random, undirected changes in the genetic material (the term was introduced by H. de Vries). The types of mutation are listed below.
Gene (point) mutations — changes in the nucleotide sequence (sickle-cell anaemia).
Chromosomal — deletion (loss of a segment), duplication (doubling of a segment), inversion (a segment turned through 180°), translocation (a segment moved to another chromosome).
Genomic — change in chromosome number: polyploidy (3n, 4n), aneuploidy (2n ± 1). Down syndrome is trisomy 21 (47 chromosomes); Klinefelter syndrome is XXY (47); Turner syndrome is X0 (45).
Methods of human genetics: genealogical (pedigrees), twin studies, cytogenetic (examining the karyotype under a microscope), biochemical, population-statistical.
Check yourself
The father is colour-blind and the mother is healthy (not a carrier). Can their sons be colour-blind?
How many linkage groups do humans have (in women)?
Two genes are 10 morganids apart. What fraction of AB/ab × ab/ab offspring are Aabb?
Which type of gene interaction does a 9 : 7 ratio in F₂ indicate?
What type of mutation is Down syndrome?
Why can modifications not serve as raw material for evolution?
Common mistakes
Saying haemophilia or colour blindness passes from father to son (the son gets Y from his father).
Assuming female birds are XX (in birds the female is ZW, the heterogametic sex).
Assigning the whole recombinant fraction to one class instead of splitting it in half.
Treating modification variation as heritable.
Thinking combinative variation creates new genes (it only creates new combinations).
Confusing inversion and translocation: inversion turns a segment within a chromosome; translocation moves it to another chromosome.