= b1g1 + b2g2 + ...+bngn+e
where the 'b' terms are proportional to the regression coefficients estimated for each gene, the 'g' effects represent whether the '+' or '-' allele is homozygous, and e represents measurement and experimental error.
We can measure effects like these with relative ease in recombinant inbred line populations or
doubled haploid populations. In 1909, East and several others noticed that in maize, hybrids tend
to outperform the open pollinated populations from which they were derived. When he and his
students self-pollinated individual maize plants from these open pollinated populations, the
resulting inbreds were small and relatively non-productive. When independent inbreds were
intercrossed, their hybrid progeny dramatically exceeded their parents' performance. This hybrid
performance advantage was termed heterosis, and much of our quantitative genetics theory is
built around analysis of heterosis. As an example, if you a group of inbreds and intercross them in
all possible combinations, you find that some inbreds generally contribute more to progeny means
than the average, and some less (some parents are better than others). This is called "general
combining ability". You also find that some specific parental combinations produce better
progeny than you would expect. This is called "specific
combining ability". These phenomena are the observations which form the basis for the concept
'heterosis'. Below is a table showing how combining ability is estimated.
| Line 2 | Line 3 | Line 4 | Line Average | |
| Line 1 | 110 | 70 | 100 | 93.3 |
| Line 2 | 100 | 130 | 113.3 | |
| Line 3 | 90 (120) | 86.7 | ||
| Line 4 | 106.7 |
With this set of observations, one could hypothesize that Lines 1 and 3 showed negative general combining ability, while lines 2 and 4 showed positive general combining ability. If the L3 x L4 combination produced 120 bu/ac, then one could hypothesize that the L3 x L4 combination produced positive specific combining ability.
Two broad explanations were advanced to explain heterosis. The first, the overdominance
hypothesis, suggests that there exist a common set of genes in which heterozygotes outperform
either homozygote. The second, championed by Jones (1917) suggests that dominance is
important (i.e. the heterozygote is equal in performance to the better homozygote), but also that
repulsion linkage among genes is common. Thus, if dominance is related to productivity, then in
maize (and other crops in which heterosis, improved productivity of hybrids over parents,
is important) the best
bet is to maximize heterozygosity, thus maximizing net dominance. The U.S. seed corn industry
has exploited this basic idea remarkably well.
If Jones is right, then it should be possible to produce inbred maize lines which perform as well as Pioneer's best hybrid, if you can mitigate the problem of genes tightly linked in repulsion. One could argue that if as much effort had been directed toward the development of improved inbreds (and open pollinated varieties) as has been put toward hybrid maize production, we would have equivalent maize yields but without the seed costs.
The fundamental question is : Was Jones right? Maize is perhaps not the best organism to test this
hypothesis. Uncertainties regarding the impact of transposition on accumulation of variation
make maize less than a perfect model organism. Rice in this case serves as a better model.
Hybrid rice seed accounts for more than half of the total acreage in China, with heterosis the
reason for its success (Xiao, Li, Yuan and Tanksley, 1995: Genetics 745-754). The current best
hybrids in production derive from wide crosses between japonica and indica accessions. The
experimental approach is below:
Indica parent (9024) X Japonica parent (LH422)
F1
F2 (194 plants were randomly selected)
Advance by single seed descent to F7
9024 x 194 F7 lines x LH422
194 BC1F7 lines 194 F8 inbred lines 194 BC1F7 lines
So, they had a total of 388 BC1F7s and 194 single seed descent derived F8s. Sufficient seed was available to plant an RCB design with two reps. Parents and the F1 were included. A map was generated with 141 RFLP markers which had been previously mapped in other populations. Traits measured included plant height, panicle length, days to heading, days to maturity, panicles per plant, spikelets per panicle, grains per panicle, and spikelet fertility. Unfortunately, no followup paper has appeared to evaluate grain yield or adaptational characteristics over environments.
| Trait | 9024 | F1 | LH422 | BP% | MP% |
| plant ht | 94.2 | 114 | 104 | 9.9 | 15 |
| days to head | 83 | 86 | 86 | 0 | 1.8 |
| days to maturity | 118 | 129 | 125 | 3.2 | 6.2 |
| panicle length | 30 | 25 | 23.9 | 5.1 | 9.4 |
| panicles/plant | 11.4 | 10.8 | 8.6 | -5.2 | 8 |
| spikelets/panicle | 118 | 126.5 | 151.2 | -16.3 | -6 |
| grains per panicle | 84.2 | 93 | 105.9 | -12.1 | -2.1 |
| percent seed set | 71.4 | 73.6 | 70 | 3.0 | 4 |
| 1000 grain wt | 24.6 | 27.1 | 22.2 | 10.1 | 15.8 |
| spikelets per plant | 1346 | 1366 | 1300 | 1.5 | 3.3 |
| grain yield | 6.53 | 7.88 | 6.02 | 20.7 | 25.5 |
As this table demonstrates, heterosis for yield is real and obvious in rice. QTL analysis was performed based on the 194 RILs. So the question is: when you look at both backcross populations, do you see all of the genes for each trait segregating? If overdominance is the answer, then you should. If simple dominance is the answer, then you should only see segregation in the population whose parent is fixed for the unfavored allele. If overdominance occurs, the heterozygote should show an advantage in both backcross populations.
The critical components of this experiment are:
A couple of obvious points: the experiment was not sufficiently robust to address yield variation
effectively. However, for the higher heritability traits (e.g. plant height, flowering date, 1000
kernel weight) this experiment was excellent. I hope that Xiao and colleagues will put the grain
harvested from this experiment back in the field at multiple sites and do a good job of yield
evaluation. The general answer to the fundamental hypothesis is that no apparent overdominance
was detected. This is absolutely amazing- the amount of recombination available to scramble
repulsion linkages wasn't enormous, so one must conclude that either they didn't exist or the
resolution of the experiment was sufficiently low to miss them. What does this tell you about the
value of hybrid rice? How should we be developing improved rice varieties if this paper
accurately assesses the components of genetic variation that contribute to rice performance?
When evaluating potential sources of genetic gain,
wild relatives are of obvious importance.
Read and be prepared to discuss Tanksley's most
recent work mapping genes for yield from wild rice.
This is the end of heterosis, dominance and overdominance
Byrne and colleagues (PNAS 93: 8820-8825) evaluated the level of maysin in 285 F2 plants derived from a cross between the inbreds GT114 and GT119. Two major QTL were identified, one which cosegregated with the regulatory locus, p1, and another on chromosome 9. When you evaluate the genetic classes between these two classes, an interesting pattern emerges.
| P1 | umc105a | mean maysin content, % of fresh silk weight |
| A | A | .482 |
| A | H | .479 |
| A | B | .878 |
| H | A | .212 |
| H | H | .257 |
| H | B | .410 |
| B | A | .02 |
| B | H | .04 |
| B | B | .03 |
As an exercise, evaluate the average main effects for each gene, and determine whether it looks
like epistatic interactions are occurring (they are). Explain how P1 and the locus marked by
umc105a interact.
This analysis led to a flurry of activity from other labs, including one of our competitors who
supported our analysis. Unfortunately, their analysis was horribly flawed. This led another
student who was interested in marker assisted selection for dormancy to revisit the question. (See
Larson et al., 1996)
Back to the Table of Contents