Of Meiosis
4.1 Genes lie on chromosomes #
4.1.1 Sutton–Boveri #
Sutton and Boveri, about 1902–1903, matched Mendel’s segregation to meiosis: homologues pair and then separate, one of each pair to each gamete. Boveri’s sea-urchin embryos developed abnormally when particular chromosomes were missing or extra, so chromosomes are not interchangeable. Independent assortment of unlinked genes is the independent orientation of different pairs. Cell Biology owns the spindle.
Bridges (1916) made the location direct. Rare Drosophila progeny broke the X-linked colour rule and were XXY or XO, from nondisjunction in the mother. The gene and the chromosome mis-segregated together. Chapter 5 uses nondisjunction as a source of aneuploidy. Here it is evidence of address.
4.1.2 Linkage as the exception to independent assortment #
Genes on one chromosome do not assort independently. Bateson and Punnett saw too many parental sweet-pea combinations for 9:3:3:1. Morgan’s reading: alleles that enter together tend to leave together.
Each locus still segregates 1:1. What fails is independence. In a coupling test cross AB/ab × ab/ab, parentals exceed Ab and aB. Coupling means the two dominants arrived on the same chromosome; repulsion means they arrived apart. Recombinant is defined against that input. A recombinant fraction near 50% means the loci are not observably linked. They may still share a chromosome if they are far apart.
4.1.3 Crossing over #
Recombinants between linked genes come from an exchange between one chromatid of each homologue in meiosis I. Creighton and McClintock (1931) used maize chromosomes marked both by genes and by a knob and a translocation: genetic recombinants had exchanged the cytological marks. Stern showed the same accompaniment in Drosophila that year. The break-and-repair chemistry is Molecular Biology.
One exchange yields two recombinant chromatids out of four, so the recombinant fraction has a ceiling of one half even if an exchange always occurs. That ceiling, and the 50% from free assortment, is why a single distant pair cannot build a long map.
4.2 Map distance #
4.2.1 The centimorgan #
Sturtevant set RF = recombinants / total, and defined one centimorgan as 1% recombinants, assuming crossover chance rises with distance and loci lie in a line. Order is more robust than spacing. A test cross shows every gamete; an intercross hides double heterozygotes.
Short intervals are the honest ones, because doubles are then rare. Maps add short intervals. A centimorgan is not a fixed number of base pairs: rate per megabase varies along the chromosome and often between the sexes.
4.2.2 What a double crossover does to the observed distance #
Two exchanges between outer markers restore the parental combination of those markers. Watched only at the ends, the chromatid looks non-recombinant, and the exchanges are missed. Observed RF therefore underestimates map distance, more so as the interval grows.
In the constructed cross below, 16.4 centimorgans of additive distance appear as only 15.6% recombinants. The missing 0.8 percentage points are twice the double-crossover frequency, because each double is counted in both component intervals and in neither outer recombinant class. RF drifts toward 50% and stalls while the additive map keeps growing. Genes 80 map units apart can look unlinked in a two-point cross.
4.3 A three-point testcross #
4.3.1 Which gene is in the middle, and the distances #
A triple heterozygote test-crossed to a triple recessive shows every gamete. These counts are constructed so the arithmetic is exact. They are not data. Loci are written in the arbitrary order r u s. One thousand progeny:
| Genotype (r u s) | Count | Class once order is known |
|---|---|---|
| + + + | 415 | Parental |
| r u s | 425 | Parental |
| r + + | 32 | Single crossover, r–u |
| + u s | 28 | Single crossover, r–u |
| + + s | 46 | Single crossover, u–s |
| r u + | 50 | Single crossover, u–s |
| + u + | 2 | Double crossover |
| r + s | 2 | Double crossover |
Parentals are the largest classes, so the input chromosomes were + + + and r u s. Doubles are the smallest. Compare + + + with + u +: they differ only at u. So do r u s and r + s. The locus a double crossover flips is the middle one. Order is r–u–s.
Singles in r–u total 60 and singles in u–s total 96. Doubles enter both intervals, so r–u = (60 + 4) / 1,000 × 100 = 6.4 centimorgans and u–s = (96 + 4) / 1,000 × 100 = 10.0 centimorgans.
Additive distance r to s is 16.4. Observed RF for the outers drops the four doubles, which look parental at r and s: 156/1,000 = 15.6%. The gap is 2 × 0.4 percentage points.
4.3.2 Interference and the coefficient of coincidence #
Independence would predict double crossovers at 0.064 × 0.100 = 0.00640, or 6.40 per 1,000. Four were seen. The coefficient of coincidence is S = 0.004 / 0.00640 = 0.625. Interference is I = 1 − S = 0.375: about three eighths of the expected doubles did not occur.
Positive interference, I > 0, is usual over a few to a few tens of centimorgans. I = 1 would mean no doubles; I = 0 would mean independence. S > 1, negative interference, appears in some very short intervals and is not the ordinary result.
4.4 Key terms, summary, and self-check #
Key terms. Chromosome theory; linkage; coupling; repulsion; centimorgan; crossing over; double crossover; three-point testcross; coefficient of coincidence; interference.
Summary. Genes lie on chromosomes; Bridges’s exceptions carried exceptional sex chromosomes. Linkage is the failure of independent assortment; crossing over, a physical exchange, produces recombinants. One centimorgan is 1% recombinants, and doubles make a long RF too short because they restore the outer markers. The rarest three-point classes name the middle gene. Interval distance includes singles and doubles. S is observed doubles over the product of the interval fractions, and I = 1 − S.
Self-check.
1. What did Bridges observe together that the Mendel–meiosis parallel only suggested?
2. Give two chromosomal reasons for a recombinant fraction of about 50%.
3. Which comparison in the constructed cross shows that u is in the middle?
4. Why do the four double-crossover progeny enter both map distances and not the outer RF?
5. If S = 0.2, what is I, and are doubles rarer or more common than independence predicts?
