Quantitative Genetic
Perspectives on Loss of Diversity
in Elite Maize Breeding
Germplasm
Jode W. Edwards
USDA ARS CICG
jode@iastate.edu
Outline
• Diversity
• Population genetics of maize
• Quantitative genetic processes
– Bottlenecks
– Selection
• Implications
What is diversity?
•
D = 1 – Spi2
– pi = allele frequency
•
•
At Hardy-Weinberg equilibrium D is an
estimator of heterozygosity, H
With population subdivision,
heterozygosity is related to Fst:
– Ht = (1-1/2N)tH0 = (1-Fst)H0
Sources: Nei, M, 1973, PNAS , 70:3321-3323; Wright, S., 1943, Genetics, 28:114-138
Diversity in Maize Inbreds and Landraces
Tenaillon, Sawkins, Long, Gaut, Doebley, and Gaut, 2001
• Estimated SNP diversity by sequencing
–
–
–
–
7 known genes,
6 cDNA clones
8 RFLP clones
All chromosome 1
• Germplasm
– 16 exotic landraces (1 inbred per landrace)
– 9 U.S. inbreds (B73, Mo24W, Mo17, W153R, Ky21,
NC258, Oh43, Tx601, T8)
• Inbreds contained 77% as much diversity as the
landraces (DI/DL)
Source: Tenaillon et al., 2001, PNAS, 98:9161-9166
Tenaillon et al. Conclusion
• ‘the U.S. inbred sample retains a high
proportion of diversity, which is difficult to
explain given that U.S. elite germplasm
has a narrow origin based largely on two
open-pollinated varieties, Reid yellow dent
and Lancaster (14)’
– [“(14)” is Major Goodman’s paper in Heredity]
Is 77% Hard to Explain?
E[1-Fst] = 0.89
• Subpopulation with
Fst = 0.87,
E[1-Fst] = 0.77
1
0.8
Heterozygosity
• 1 - Fst = 1 - 0.77
• For Fst of 0.23, N=2.2
If inbreds were:
• Sampled randomly,
0.6
0.4
0.2
0
0
25
50
Inbred lines
75
100
How should we measure diversity?
Heterozygosity (formally)?
Number of alleles?
Number of polymorphic loci?
Number of rare alleles?
JE thoughts:
Diversity is important, but we don’t know
how to measure it (or what it is)
Something else may be more important
Sustainable Selection Response
• Plant breeders’ main goal is selection
– Short term: Maximum response
– Long term: Sustainable response
• In order to address sustainability of
selection response, we need to understand
phenotype
– Population genetics of maize
– Quantitative genetics of population bottlenecks
– Quantitative genetics of selection with finite
size
Maize Population Genetics: BSSS
• Started with maize land races (O.P.) and
develop ‘first cycle’ inbreds
• 16 lines intermated to form BSSSC0
– Expected diversity = 87.5% of ancestor
• B14, B37 emerge from Cycle zero
– Expected diversity = .875 x .5 = 43.75%
• B73, B84 emerge from C5, C7
Corn Belt Maize Land Races
•
•
•
•
Outcrossing, monoecious populations
Large Ne (?)
Mass selected for visual characteristics (low h2?)
Corn belt dents existed 100+ generations, longer
for other groups
• Corn belt dents (Labate et al., 2003)
– Accessions: Fst = 0.15
– Varieties: Fst = 0.04
• “Almost” one large randomly mated population
Source: Labate, J.A. et al., 2003, Crop Science, 43:80-91
Maize Land Races
• Hardy-Weinberg equilibrium
• Linkage equilibrium
• Mutation-selection equilibrium
Haldane (1937) Principle
• Mutation frequencies determined by equilibrium
– New mutations are constantly added to the population
– Mutations removed by selection (and drift)
– Mutation rates estimated to be 0.4 – 1.0 per diploid
individual per generation
• At equilibrium
– Individuals carry many mutations
– Reduction in fitness due to mutations = “genetic
mutation load” (Muller)
Source: Haldane, J.B.S., 1937, The American Naturalist, 71:337-359;
Crow, J.F., 1993, Oxford Surveys in Evolutionary Biology, 9:3-42
Does Mutation Load Apply to Maize?
• Inbreeding depression
– Severe in first cycle inbreds
– Less in germplasm with inbreeding history
(purging of recessives)
– If many loci carry mutations, complete purging
takes many generations
• Observation of major “lethal” mutations
• Empirical work in maize is needed!
Significance of Haldane Principle
• Mutation load provides a model of
quantitative genetic variation more realistic
than ‘infinitessimal theory’
• Provides a basis for understanding
quantitative genetic variation, and thus,
• Basis for predicting effects of bottlenecks
and artificial selection
Bottlenecks
• Population is formed from small number of
individuals
– Change allele frequencies
– Hardy-Weinberg and linkage disequilibria
• Under additive model
– ‘within subpoplation variance’, Vw = (1-Fst) s2A
– ‘among subpopulation variance’, Vb =2Fst s2A
• Non-additive model: effects of bottlenecks
are complex
Source: Wang, J., et al., 1998, Genetics, 150:435-447
Edwards and Lamkey (2003)
Within-Subpopulation Variances: BS13(S)C0
1.4
Vw (YLD)
Vw (PHT)
1.2
V
w
Variance
1.0
0.8
0.6
(MS
T)
VA (M
ST)
VA (YLD)
0.4
VA (PHT)
0.2
0.0
0.0
0.2
0.4
0.6
0.8
FST
Source: Edwards and Lamkey, 2003, Crop Science, 43:2006-2017
1.0
Garcia, Lopez-Fanjul, and Garcia-Dorado, 1994
D. melanogaster, Full-sib lines
160
Variance
120
80
40
0
0
0.25
0.5
Inbreeding Coefficient
Source: Garcia, N., et al., 1994, Evolution, 48:1277-1285
0.75
Gene Effect Sizes
Wang, Caballero, Keightley, and Hill, 1998
Percent of additive variance
80
70
60
50
40
30
20
10
0
0-50
50-100 100200
200300
300400
400500
>500 lethals
Effect size (Ne x s)
Source: Wang, J., et al., 1998, Genetics, 150:435-447
Gene Effects and Bottlenecks
• Genes of all sizes important in the base
• After a bottleneck: large recessives
become much more important (and hence
large increase in dominance)
• Explanation: Nonlinear relationship
between frequency and variance: small
increase in frequency = large increase in
variance
Limits to Selection Response
Robertson, 1960
• Max response = 2 Ne times initial response
• Half-life occurs at 1.4 Ne generations
• Total response is maximized at 50%
intensity (greater with linkage)
• Based on ‘infinitessimal’ theory
– Many genes of ‘infinitely’ small effect
– Can we understand ‘side effects’ of selection
under more realistic conditions?
Source: Robertson, A., 1960, Proc. Roy. Soc. London, Ser. B, 153:235-249
Selection Effects
• Loss of heterozygosity (diversity)
• Linkage disequilibrium
– Bulmer
– Hill-Robertson
• Epistasis
Linkage and Selection
• Bulmer effect
– Correlation between alleles induced by
selection
– Causes excess of coupling phase linkages
and reduced genetic variance
• Hill-Robertson effect
– Effect of repulsion phase linkages
– Unfavorable alleles become fixed because of
selection for favorable alleles linked in
repulsion phase
Sources: Bulmer, M.G., 1971, American Naturalist, 105:201-211;
Hill, W.G. and Robertson, A., 1968, Theor. Appl. Genet., 38:226-231
Zhang and Hill, 2005
• Simulated selection in cage populations derived
from ‘equilibrium natural populations’ of D.
melanogaster
• Conditions
– Genetic model: mutation-selection balance under
joint pleiotropic and stabilizing selection
– 40% intensity
– Recombine 40 individuals
– VG0 = 0.5 VE
– 3 chromosomes of varying length
Source: Zhang, X.S., and Hill, W.G., 2005, Genetics, 169:411-425
Selection and Linkage
Zhang and Hill, 2005
Source: Zhang, X.S., and Hill, W.G., 2005, Genetics, 169:411-425
Gene Numbers and Effects
Zhang and Hill, 2005
• Distribution of gene effects
– 90% of genes have a<0.1sp and account for
27% of genetic variance
– 10% of genes have a>0.1sp and account for
the rest of the genetic variance
• Estimated that 103 – 104 loci are
polymorphic in a cage population
Source: Zhang, X.S., and Hill, W.G., 2005, Genetics, 169:411-425
Evidence of Linkage in Maize
• Degree of dominance, d, can
be estimated as a ratio,
sD2/sA2, in F2-derived
populations
• Linkage disequilibrium causes
a bias called ‘associative
overdominance’
• Random mating breaks up
linkage and reduces bias
Aa -> d=2
AA
Aa -> d=1
Aa -> d=0
aa
Maize NCIII Experiments
1.8
Average degree of dominace
1.6
1.4
1.2
Gardner
Lonnquist
1
0.8
0.6
0.4
0
3
6
9
12
15
Generations random mated
Lonnquist, J.H., 1980, Anal. Acad. Nac. Cs. Ex. Fis. Nat., 32:195-201;
Gardner, C. O., Personal communication to E.T. Bingham
Epistasis
• Favorable epistatic interactions are increased by
selection
• Lamkey, Schnicker, and Melchinger, 1995
– Began with BSSS lines B73 (cycle 5) and B84 (cycle
7)
– Formed the F1, F2, BC1 (to both parents) and
intermated F2
– Testcrossed all generations onto Mo17
– With additive model (no epistasis) there is a linear
relationship among generations
Source: Lamkey, K.R., et al., 1995, Crop Science, 35:1272-1281
Epistasis in B73 and B84
Lamkey, Schnicker, and Melchinger, 1995
Source: Lamkey, K.R., et al., 1995, Crop Science, 35:1272-1281
How did we get here?
• Bottleneck followed by 5 and 7 cycles of
selection
• During selection
– Linkage disequilibrium increases
– Epistatic combinations become more important
– Selection may be dominated by genes of large effect
• Slow increase in frequency of many small
favorable alleles is not a good model
– For positive effects, i.e., response
– For negative effects
Sustainable Response is a
Function of More than Diversity
• Loss of alleles (diversity)
• Increase in linkage disequilibrium (reduced
variance)
• Increased dependence on specific
epistatic combinations
• Shift in size of genes that contribute to
genetic variance (small to big)
Implications for Elite x Exotic Crosses
• Genetic variance within a single population is
due mostly to genes of large effect
• Linkage disequilibrium within the cross may
reduce genetic variance
• Any new alleles from the exotic parent are
preferentially lost if:
– Linked to negative alleles at physiologically selected
loci, e.g., photoperiod
– There are favorable epistatic interactions among elite
alleles
What can be done?
• Map major genes (especially photoperiod) and
use markers to break linkages
• Recycle lines from different crosses
• Enhance or improve land races directly to
maintain more variation and reduce
disequilibrium
– If major genes were identified, could speed up with
markers
– Preserve more variation due to genes of small effect
• Random mate individual crosses
Basic Research Questions
• How differentiated are maize land races from
each other and from elite lines?
– At neutral loci
– At selected loci
• Can we identify major genes that
– Differentiate elite lines from ancestral varieties
– Corn belt dent from tropical races
• Genetic architecture
– Can we estimate mutation load parameters?
– Can we distinguish purging of recessive load from
selection for physiological effects
We can succeed doing what we
are already doing
However, can we be more
successful?