11 sustainable plant breeding

Key words:genetic improvement— BLUP selection — genetic selection — pedigree selection — genomic selection — genotype9 environment interaction This review considers the impact of evoluti

Sustainable plant breeding

WA L L A C E A CO W L I N G1, 2

1

The UWA Institute of Agriculture M082, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia;

2

Canola Breeders Western Australia Pty Ltd, Locked Bag 888, Como, WA 6952, Australia; Corresponding author, E-mail: wallace cowling@uwa.edu.au

With 1figure

Received August 1, 2012/Accepted October 18, 2012

Communicated by J L
eon

Abstract

Plant breeders disrupt Hardy –Weinberg equilibrium through selection,

non-random mating, drift, migration and mutation Sustainable plant

breeding can be de fined as productive and competitive breeding that is

achieved without loss of genetic diversity in the elite breeding

popula-tion during the professional career of the breeder Breeding is often

productive but not sustainable From 1974 to 2000, the animal breeding

programme Meatlinc in the United Kingdom had effective population

size of 95, population inbreeding of 0.19% per year and generation

interval of 2.15 years Genetic progress in Meatlinc tripled in the

8 years following introduction of best linear unbiased prediction

(BLUP) selection (based on the information from relatives) in 1992.

Canola breeding in Australia from 1970 to 2000 had longer generation

interval (6 years), smaller effective population size ( <11) and higher

rates of inbreeding ( >0.7% per year) BLUP selection in canola was

first reported in 2010 Neither programme replaced genetic diversity

lost through selection and drift Most breeding programmes violate

con-ditions of the infinitesimal model, thereby reducing predictability of

selection, but breeders can minimize these limitations to sustainable

plant breeding.

Key words:genetic improvement— BLUP selection — genetic

selection — pedigree selection — genomic selection —

genotype9 environment interaction

This review considers the impact of evolutionary forces that

dis-rupt Hardy–Weinberg equilibrium in plant breeding programmes

and affect the competitiveness and sustainability of plant

breed-ing Plant breeders influence evolutionary processes to develop

superior varieties from their elite breeding pools through

selec-tion, migraselec-tion, mutaselec-tion, random genetic drift (effective

popula-tion size) and designed mating systems In practice, either with

or without planned intervention, plant breeders add or gain new

alleles through migration and mutation, re-arrange alleles

through intermating and genetic recombination, and remove or

lose alleles through selection and random genetic drift How this

is done affects the competitiveness and sustainability of plant

breeding in the long term

Sustainable plant breeding can be defined as productive and

competitive breeding that is achieved without loss of genetic

diversity in the elite breeding population during the

profes-sional career of the breeder A sustainable plant breeding

pro-gramme will maintain or increase genetic diversity in the elite

breeding pool through migration and mutation The question

that many breeders (or their bosses) ask is ‘will a genetically diverse breeding programme be competitive?’ Breeders are reluctant to cross outside of elite pools, because migration from exotic germplasm into elite breeding pools is almost always accompanied by negative impacts on quantitative trait perfor-mance (Rasmusson and Phillips 1997) This does not have to

be the case A two-phase process of migration from wild or exotic germplasm into elite crop breeding pools was proposed

to avoid such negative impacts (Cowling et al 2009), and this two-phase process forms an integral part of the successful recurrent introgression population enrichment (RIPE) barley breeding system (Falk 2010) Migration from 2-row to 6-row barley through 3 cycles of crossing and selection improved yield in the elite 6-row breeding pool (Peel and Rasmusson 2000), and a back-crossing process (combined with marker-assisted selection) was used to successfully migrate alleles for grain yield from wild into cultivated rice (McCouch et al 2007) Clearly, valuable alleles exist in wild and exotic germ-plasm for complex traits such as yield and methods exist to assist migration of these alleles while minimizing the negative impacts of linkage drag

‘Prebreeding’ is a term often used in relation to plant breed-ing activities dedicated to enlargbreed-ing genetic diversity and enhancing genetic knowledge Often prebreeding is physically and genetically isolated from commercial breeding The focus of prebreeders is normally on the identification of major gene traits and molecular markers, while commercial breeders focus on introgression of these major genes into elite breeding pools by marker-assisted backcrossing Potentially valuable minor alleles for economic traits require special methods for incorporation into elite breeding populations from prebreeding or exotic sources, and such methods (discussed later in this review) are predicated on a direct link between prebreeding and commercial breeding

Plant breeders have powerful selection tools to improve response to selection, such as best linear unbiased prediction (BLUP) selection based on the information from relatives in the pedigree, or whole-genome marker data in the case of genomic selection Ironically, the cumulative effect of selection reduces effective population size because of fewer parents and also because parents tend to be close relatives (Walsh and Lynch 2012c) Therefore, breeders mustfind ways to replenish genetic diversity in elite breeding pools, as replenishment of genetic diversity at the elite level will be even more important as we

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move towards BLUP and genomic selection (Cowling et al.

2011)

Genetic Diversity– The Impact of Small Effective

Population Size and Random Genetic Drift

Successful crop genetic improvement is demonstrated by corn

breeding in the USA Corn hybrids released around 2000 yielded

10 tonnes per hectare, more than twice the yield of hybrids

released in 1930s and 1940s, when tested in historical variety

tri-als (Duvick et al 2004) Modern corn varieties in the USA are

based on six founder genotypes, which contributed on average

90% of the pedigrees of maize hybrids developed for the

west-central USA corn belt around 2000 (Duvick et al 2004) Allelic

diversity, measured by the average number of alleles per locus at

298 simple sequence repeat (SSR) loci, was <1.5 in the male

and 2.0 in the female parents of hybrids released around 2000,

but averaged 4.0 at the same loci in male and female parents of

F1hybrids released in the 1930s and 1940s (Duvick et al 2004)

Genetic improvement in corn in the USA over 70 years has been

accompanied by a significant loss of genetic diversity at SSR

loci that are most likely selectively neutral This must be a result

of random genetic drift due to low effective population size (Ne),

which in turn is determined by the number of founder parents

(6) and low rates of migration or mutation during 70 years of

corn breeding in the USA Elite corn breeding populations in the

USA are becoming inbred The mathematical connection

between Neand population inbreeding is discussed below

The evidence confirms that many crop breeding programmes

in the past century have been carried out in populations with

very low Ne and high rates of inbreeding Soybean cultivars in

the USA were derived from relatively few soybean

introduc-tions early in the century, andfive introductions accounted for

55% of the pedigree of public cultivars in the 1990s (Gizlice

et al 1994) Chickpea experienced several bottlenecks during

and after domestication and consequently has very limited

genetic diversity in the crop gene pool (Abbo et al 2003)

Major international barley programmes were described as slow

recurrent selection programmes (long generation intervals) with

few founding parents and low migration (McProud 1979)

These and other examples cited by Kannenberg and Falk

(1995) were the stimulus for Falk (2010) to accelerate and

expand genetic diversity in the successful RIPE barley breeding

programme

Populations with small Neare subject to random genetic drift,

the dispersive evolutionary force that randomlyfixes alleles and

is a consequence of population inbreeding Following Falconer

and Mackay (1996), there is a link between the population

inbreeding coefficient (Ft) in generation t and Ne:

and

DF ¼ 1 2Ne

ð2Þ

That is, cumulative inbreeding increases as Ne decreases Ftcan

also be viewed as the cumulative effect of genetic drift (the

ran-dom loss of alleles as a result of fixation by chance), or the

probability alleles are identical by descent (Falconer and Mackay

1996) Population inbreeding is also the cause of inbreeding

‘depression’ (loss of viability and performance) in animal or

cross-pollinating plant species, although this is not a concern in most self-pollinating crop species

It is informative to compare and contrast evolutionary forces operating in two breeding programmes, one animal and one plant, over a similar time period from 1970 to 2000 Both were closed recurrent selection programmes without migration Thirty years is approximately equal to the duration of the professional career of one breeder; therefore, these two programmes can be compared for‘sustainability’ as defined in this review

In the animal breeding programme, Meatlinc sheep breeding

in UK, the average Ne was 95, there were 11 cycles of crossing and selection from 1974 to 2000; the average generation interval was 2.3 years, and in 2000, the cumulative population inbreed-ing coefficient at F11was 6.3% (DF = 0.5% per cycle or 0.19% per year) The rate of genetic progress tripled following the introduction of BLUP selection in 1993 (Avenda~no et al 2003) The rate of inbreeding was approximately constant before and after the introduction of BLUP breeding, with an indication of

an increase towards 2000 While Meatlinc is exceptional in the rate of genetic progress achieved with BLUP (Avenda~no et al 2003), the question should be asked – is this breeding pro-gramme sustainable?

As a comparison over a similar time period, canola (Brassica napus L.) breeding in Australia was also a closed recurrent selection population with Ne  11 based on pedigree informa-tion (Cowling 2007) Four founder parents made up more than 50% of the pedigrees of varieties released in 2000 The popula-tion underwent 5 cycles of crossing and selecpopula-tion between 1970 and 2000 with an average generation interval of 6 years, and in

2000, F5was 21% (DF = 4.5% per cycle or 0.7% per year) In other words, more than 21% of loci were fixed at random in Australian canola breeding during this 30-year period as a result

of genetic drift Nevertheless, the programme was successful in adapting canola to the winter–spring growing season of southern Australia and improving blackleg (Phoma) resistance for pro fit-able canola production (Cowling 2007)

Valuable genetic improvements in quantitative traits were made in these two breeding programmes The animal breeding programme Meatlinc achieved very high rates of genetic pro-gress with high Ne and low rates of inbreeding and random genetic drift Addition of BLUP selection to Meatlinc in 1992 was a major stimulus to genetic progress The Meatlinc breeding programme was more sustainable than canola breeding, based on the definition in this review, but neither programme included migration during 30 years Both programmes suffered a loss of genetic diversity (more in canola than Meatlinc), and both pro-grammes need to consider how to use migration to replace genetic diversity that is lost through selection and drift

Information from Relatives and Models for Prediction

of Response to Selection

Predicting response to selection– the animal model Genetic progress under selection is defined in the general ‘breed-ers’ equation’ by Lynch and Walsh (1998) as:

whereDl is the change in the population phenotypic mean over one cycle of selection, b is the linear slope of the regression of offspring on parents, which is more specifically defined as nar-row-sense heritability h2 (Lynch and Walsh 1998), and S is the directional selection differential (the difference between the

selected group mean and the population mean, before

reproduction)

The breeder’s equation can be written in a form that includes

information from relatives (Simm 1998):

R¼irAr

where R is response to selection per year, i is selection intensity

in standard deviation units,rAis additive genetic standard

devia-tion or the standard deviadevia-tion of true breeding values, r is the

accuracy of selection based on records from the individual and

its relatives (the correlation between true and estimated breeding

values) and L is the generation interval in years Response to

selection increases when additive genetic variance and the

corre-lation between true and estimated breeding value increases, and

generation interval decreases

More accurate selection and more rapid breeding cycles are

the main motivations behind the development of the ‘animal

model’, which exploits information from relatives to estimate

breeding values of each measured individual in the pedigree

(Lynch and Walsh 1998) In the animal model, phenotypic data

from relatives in the pedigree, including historical data from

sev-eral generations before present, are updated and analysed every

year

The animal model is based on the solution of the general

mixed model for phenotypic values (y) of a trait measured in the

population:

where X and Z are incident matrices for a vector offixed effects

(b) such as treatment or location, and random effects (u) such as

additive genetic values, and e is the vector of residual deviations

(Lynch and Walsh 1998) The vectors of fixed and random

effects are estimated in parallel to covariance matrices G

(vari-ance due to random genetic effects) and R (vari(vari-ance due to

residual effects) For random genetic effects:

where A is the numerator (or kinship) relationship matrix, and

the elements of A are twice the coefficients of coancestry of

individuals (Mrode 2005), which may be estimated from

pedi-gree, marker or both pedigree and marker data (Stich et al

2008) Prediction of breeding values involves inversion of the

relationship matrix (i.e., A1), which works well for pedigree

information, but is problematic for some marker data when the

paternal or maternal origin of alleles is unknown, marker loci

are polyallelic or marker data are incomplete (Mrode 2005,

Maenhout et al 2009) Fixed effects are estimated by best

lin-ear unbiased estimators and random effects by BLUP General

mixed models allow for unbalanced data sets, selection,

non-random mating, unequal family sizes and extended pedigrees

Such data sets, typically produced in breeding programmes, are

unsuitable for analysis by general linear models with only

fixed effects (Lynch and Walsh 1998) BLUP provides less

biased estimates of breeding value when all the data upon

which selection is based are included in the analysis (Sorensen

and Kennedy 1984) Gomez-Raya et al (1992) provide a

ratio-nale for estimating heritability and genetic variances in the

base population when records are only available from later

generations

Genetic variances can be estimated by BLUP methodology from plant breeding data without the need for specific mating designs, which have been used in the past to estimate genetic variances in plant breeding populations Restricted maximum likelihood is most commonly used to estimate genetic and non-genetic variances from phenotypic data in plant breeding pro-grammes (Bernardo 2010) BLUP has not been adopted as widely in plant breeding and variety testing as in animal breed-ing, where it was developed to estimate breeding values (Piepho

et al 2008) Forest tree breeders have used BLUP methodology

to estimate breeding values for many years (White and Hodge 1989), but the methodology for self-pollinating crop species has been slower to develop Recent reports demonstrate BLUP appli-cation to canola breeding where information from relatives was used to estimate additive and non-additive genetic values in a framework of genotype9 environment (GxE) interaction (Beeck

et al 2010, Cullis et al 2010)

Selection with information from relatives is known as

‘genetic’, ‘pedigree’ or ‘BLUP’ selection, because parents are selected for crossing on the basis of predicted breeding value (PBV), which is calculated using information from relatives in the pedigree Selection on BLUPs has accelerated genetic pro-gress in animal breeding over traditional methods of selection based on total genetic value or phenotypic value (Avenda~no

et al 2003) BLUPs are calculated from phenotypic measure-ments of ancestors in the pedigree tree, sometimes going back several generations, collateral relatives and progeny records PBVs of progeny can be predicted from the parents through the following equation:

ai¼ ga i¼1

2asþ1

where the PBV of animal i (ai) or its additive genetic value (gai)

is equivalent to the sum of half the breeding value of the sire (as) plus half the breeding value of the dam (ad) plus an error term known as the Mendelian sampling term (mi) (Mrode 2005) The accuracy of genetic selection is limited by the Mendelian sampling term; there is a maximum correlation of 0.5 between the predicted and true breeding value for animals at birth (Goddard and Hayes 2009) Animal breeders face a dilemma when progeny reach reproductive age – which animals should they use for breeding? Most traits are not measured until after reproductive age – for example, it is not possible to assess genetic value of young potential sires for carcass weight or dams for milk production before puberty Therefore, the best parents are crossed based on their PBV (7), which is updated every year, and their progeny are raised and used for breeding until they have sufficient progeny records to estimate their PBV Relatives vary in the accuracy of their records: a single offspring record is double the value of a half-sib record, and offspring provide more accurate records than full-sibs (Simm 1998) As time passes, ani-mals with low PBV are culled from the system and those with high PBV are retained

The animal breeder is often forced to breed with families of sibs before knowing which sib has the best breeding value Nev-ertheless, selection on PBV has resulted in accelerated genetic improvements in some animal breeds, especially for lower herita-bility traits (Simm 1998, Avenda~no et al 2003), because BLUP selection allows breeders to cull poorer parents sooner and retain superior parents longer in the breeding programme (Simm 1998) Genomic selection may result in more accurate selection

of progeny for crossing and shorter selection cycles, because

genomic information from relatives can predict (in theory) which

are the best progeny to cross before progeny records are

avail-able (Goddard and Hayes 2009), although this hinges on the

accuracy of phenotyping and the size and relevance of the

‘train-ing population’ as well as the number of markers

Assumptions behind the prediction of response to selection–

the infinitesimal model

It is important to review the assumptions of the infinitesimal

model, which is the basis of predictions of selection response

The impact of violation on the assumptions of the infinitesimal

model is extensively reviewed by Walsh and Lynch (2012a,b,c)

and briefly summarized here Most models for selection

response, such as the breeders’ equation, assume that a trait is

controlled by an infinite number of loci each with infinitesimal

effect This satisfies the assumptions of normality and linearity

of parent–offspring regressions in models of selection response

The infinitesimal model allows for changes in the mean but not

in allele frequencies during selection; that is, the genic variance

(r2) is assumed to be constant and linkage disequilibrium (d)

contributes to changes in additive genetic variance (r2

A) under selection (Walsh and Lynch 2012a):

r2

In practical terms, for small populations or for traits controlled

by relatively few genes, selection response is affected by a

com-plex and often unpredictable interaction between linkage

disequi-librium and genic variance, as both affect estimates of additive

genetic variance

When the number of loci or effective population size isfinite,

selection causes a cumulative change in allelic frequencies,

which alters the outcome compared with predictions of the

infin-itesimal model Modelling with low effective population size

(Ne= 10) shows dramatic limitations to the cumulative selection

response after 25 generations compared with the infinitesimal

model (Ne= ∞) (Walsh and Lynch 2012a) Such low effective

population sizes are common in plant breeding – recall that Ne

in the Australian canola breeding programme from 1970 to 2000

was <11 (Cowling 2007), and soybeans in the USA until the

1990s had a low Ne(Gizlice et al 1994)

Violations of the infinitesimal model make it difficult to

pre-dict the outcomes of selection, as selection normally changes

allele frequencies and generates disequilibrium Many models

have been developed in an attempt to more accurately predict

outcomes from selection (Walsh and Lynch 2012a) In animal

breeding, the infinitesimal model is considered to adequately

describe most selection programmes where quantitative traits are

highly polygenic (Hill and Kirkpatrick 2010) In my view, the

infinitesimal model is akin to Hardy–Weinberg equilibrium – it

is based on conditions that are hardly ever met, but violations of

the assumptions provide unexpected surprises in evolution and

plant/animal breeding

Small populations violate an assumption of the infinitesimal

model and this imposes limits on response to selection For

com-plex traits such as yield, which are controlled by many loci, the

impact of small populations is more severe than for traits

con-trolled by few loci Most models of selection response assume

complete additivity of effects, but dominance and epistasis can

also change selection response The ‘take-home’ message for

plant breeders is given as: maintain as large an effective

popula-tion size as possible, recombine frequently and allow migrapopula-tion This will promote development of interesting new combinations

of alleles for complex traits through selection – even if this response cannot be accurately predicted due to violations of the

infinitesimal model High Nehelps to keep new beneficial muta-tions in the population (Walsh and Lynch 2012c) Low Ne in elite populations severely limits long-term response to selection

by eliminating low frequency valuable alleles through drift, whether they originate from the base population, migration or mutation

Long-term selection experiments support the optimistic view that response to selection for complex traits is possible in the long term, despite the difficulty we have in modelling this response as a result of violations of the infinitesimal model (Walsh and Lynch 2012b,c) The most famous long-term crop breeding experiment, the Illinois long-term selection experiment

on oil and protein content in maize, has been underway continu-ously since 1896 There is little evidence of a limit to the selec-tion for high oil after 100 years of annual cycles of recurrent selection in this closed population (Dudley and Lambert 2004) Mutation is probably a significant contributor to this long-term response to selection (Walsh and Lynch 2012c)

Application of the animal model in plant breeding Plant breeders have been slow to adopt BLUP selection (Piepho

et al 2008), although the potential advantages of BLUP selec-tion in plant breeding are great (Heffner et al 2009) Plant breeders have a major advantage over animal breeders for effi-cient BLUP selection– plant varieties can be ‘cloned’ and tested

in replicated plots over space and time, and potentially plant breeders can select progeny for breeding as soon as they are phenotyped Consequently, plant breeders do not have to wait for progeny records before eliminating poor parents Unlike ani-mal breeders, however, plant breeders generate unique predic-tions of genetic value in each environment, and therefore, GxE must be taken into account for selection With BLUP selection based on pedigree information, unique estimates are generated for additive, non-additive and total genetic value for each breed-ing line in each environment (Cullis et al 2010)

A practical application of BLUP selection in a canola breeding programme was developed by Beeck et al (2010) based on fac-tor analytic modelling of the variance structure of the genetic effects, that is, GxE effects Selection occurred for yield and seed oil content in multienvironment trials (METs) over 2 years Factor analytic modelling of GxE in METs was developed by Smith et al (2001), and Oakey et al (2007) included indepen-dent modelling of additive and non-additive genetic effects based

on information from relatives GxE can be considered as a multi-variate problem as suggested by Falconer and Mackay (1996):

‘A character measured in two different environments is to be regarded not as one character but as two’ This approach allows the breeder to capitalize on genetic correlations for yield in dif-ferent environments to improve the power of the analysis The prediction of genetic value of individuals is enhanced by correla-tions between these‘traits’ The power of the analysis was also improved by modelling of within-trial spatial heterogeneity (Beeck et al 2010)

Factor analytic modelling of yield in the canola breeding METs revealed different patterns of GxE for additive (PBV), non-additive and total genetic effects (Cullis et al 2010) Factor analytic modelling revealed two macroenvironments for additive genetic effects for yield (Cullis et al 2010) Selection of parents

for crossing (ranking on additive genetic effects), or lines for

promotion (ranking on total genetic effects), was unique to the

macroenvironments identified in the METs (Cullis et al 2010)

Genome-wide or genomic selection is being developed in

ani-mal breeding (Meuwissen et al 2001) Genomic selection may

help to identify superior future parents before they reach

repro-ductive age, rather than breeding with unselected sires and dams

and waiting for progeny tests to cull inferior animals (Goddard

and Hayes 2009) Genomic selection may thereby shorten the

generation interval and improve the efficiency of breeding

Sim-ulation studies in animals showed that accuracy of the genomic

breeding value, or the correlation between the genomic and true

breeding value, was around 0.85 (Meuwissen et al 2001),

although actual values in practice have been lower than this

(Goddard and Hayes 2009) This improvement in accuracy

(greater than the maximum correlation of 0.5 in genetic

selec-tion) is the greatest motivation for genomic selection This of

course depends on the number of animals phenotyped and

genotyped in the reference population, and the accuracy of

phe-notyping The reference population numbered 6700 dairy bulls

in the USA dairy breeding programme, each genotyped with

many tens of thousands of SNP markers (Goddard and Hayes

2009)

Reference populations, also called training populations, are

used to predict the value of molecular markers on the breeding

population (Meuwissen et al 2001, Heffner et al 2009, 2011)

Training populations are valuable if the predictive power of

markers is sufficient across years and environments to

accu-rately select in the breeding population (Heffner et al 2009,

2011) However, training populations will need to be large, and

phenotyped in several years and environments, to mimic the

effect of GxE on the main breeding population If GxE for

both additive and non-additive genetic variance is large, as was

reported by Cullis et al (2010), and heritability is low (e.g for

grain yield), then the training population will have to be very

large to get full benefits from genomic selection (Heffner et al

2011)

Results from maize, barley and Arabidopsis indicate that

gen-ome-wide prediction of breeding value by BLUP is more

accu-rate than by multiple regression (Lorenzana and Bernardo 2009)

At least in the short term, genomic selection via BLUP should

outperform testcross phenotypic selection (Bernardo 2010)

Crossa et al (2010) reported a greater predictive ability in

mod-els with marker information than pedigree-based modmod-els in both

wheat and maize, but also warned that the effects of markers

varied across environments Heffner et al (2011) report a

two-stage BLUP analysis across two years for genomic selection in

wheat, where GxE effects were apparently small, and genomic

selection outperformed marker-assisted selection

BLUP selection is based on a relationship matrix developed

from the coefficient of coancestry between pairs of individuals

in the pedigree It is also possible to develop pairwise

related-ness from molecular markers, but estimation of coefficient of

coancestry from marker data is upwardly biased because

alike-ness in state does not necessarily mean the alleles are derived

from a common ancestor In one study, the pedigree-based

esti-mate of coefficient of coancestry was superior to several

marker-based alternatives (Maenhout et al 2009)

BLUP selection tends to select close relatives, thereby

reduc-ing Ne (Heffner et al 2009, Walsh and Lynch 2012c) Methods

of replenishing lost genetic variation and increasing Ne are

nec-essary for long-term sustainability in plant and animal breeding

programmes Mutation is a minor contributor to genetic

varia-tion in the short term, although it could be very significant in the long term or in large populations (Walsh and Lynch 2012b) Migration is therefore the key to sustainable plant breeding

Migration– Adding New Genetic Diversity

Normally, the performance of elite breeding populations is nega-tively affected when exotic germplasm is introduced (Rasmusson and Phillips 1997) Sewall Wright’s shifting balance theory (Wright 1931) suggests that crossing between a locally adapted genotype and a distant genotype will result in inferior progeny

in the local environment Elite breeding populations are well adapted to the target agricultural environment, but exotic germ-plasm (by definition) is not adapted to the same environment To avoid the negative effects of linkage drag in wide crossing, breeders have used multiple backcrosses to reconstruct the per-formance of the original elite parent and have focussed on intro-gression of major genes from the exotic parent Incorporation of beneficial minor alleles for quantitative traits from exotic parents requires strict adherence to quantitative genetics theory, because the value of such alleles may not be known until the incorpora-tion is almost complete (Spoor and Simmonds 2001) Three cycles of crossing and selection were necessary to find useful improvements in the yield in 6-row barley after introgression of alleles from 2-row barley (Peel and Rasmusson 2000) This sug-gests that yield benefits can be obtained from incorporation of relatively small doses of donor alleles while maintaining favour-able gene combinations in the adapted population

A two-phase process was proposed to move valuable alleles for quantitative traits from wild donors into the elite breeding pool (Cowling et al 2009, Falk 2010) In phase 1, the F1of the elite9 donor cross was backcrossed to an elite parent, and six

BC1 plants were backcrossed to produce 36 BC2 plants This provided 95% confidence of transmission of a potentially valu-able donor quantitative allele into the BC2while permitting the reselection of major domestication genes during the backcrossing process (Cowling et al 2009) The 36 BC2plants were selfed to

fix potentially valuable migrant quantitative alleles In phase 2, fixed BC2-derived selections with interesting attributes were crossed back into the elite breeding pool (Cowling et al 2009, Falk 2010) Modelling of similar backcrossing procedures in wheat confirmed that the BC2was the most appropriate stage to stop backcrossing when the donor lines were poorly adapted or distantly related (Wang et al 2009) Despite these guidelines, incorporation of valuable quantitative alleles from exotic germ-plasm into elite breeding programmes has not yet been widely adopted by crop breeders (Spillane and Gepts 2001)

There are excellent prospects to use genomic methods to assist the incorporation of valuable quantitative alleles via BC2 from exotic germplasm into elite gene pools The concept of

‘advanced backcross QTL’ was based on whole-genome markers

to aid incorporation of useful quantitative alleles into elite breed-ing programmes (Tanksley and Nelson 1996), and this approach was used to move yield-enhancing quantitative alleles from wild

to cultivated rice in BC2-derived progenies (McCouch et al 2007) Genomic methods may help to identify valuable quantita-tive alleles during the migration process

‘Successful’ migration, which results in incorporation of valu-able minor alleles for quantitative traits into elite breeding pro-grammes, is made more difficult by low effective population size and genetic drift Modelling in conservation genetics has shown that populations which suffer a low effective population size

(Ne= 20) for a brief period of time (a genetic ‘bottleneck’)

experience a reduction in frequency of alleles at selectively

neu-tral loci if the allele frequency before the bottleneck is below 0.1

(Luikart et al 1998) Migration into elite plant breeding

popula-tions is therefore more difficult, and incorporation of migrant

alleles is reduced, when Neis 20 or less As was discussed

ear-lier, many plant breeding programmes have effective population

size much lower than 20

In the RIPE system in barley, the number of parents used in

crossing each year is very high through the use of a male sterility

system (Falk 2010) Migration is undertaken on a regular basis

in the RIPE breeding system, and generation interval is short

(2–3 years) Several improvements in quantitative traits including

yield, stem strength, seed size and disease resistance have arisen

during 20 years of recurrent selection, based on population

breeding principles, which included migration via BC2 methods

of exotic barley strains and wild Hordeum spontaneum (Falk

2010)

Mating Design and Genetic Diversity

Mating design has a large impact on Ne, in addition to the

effects of the number of founder parents, variation in family size,

the ratio of males to females, the number of parents in each

gen-eration, the number of migrants and whether mating is

assorta-tive or disassortaassorta-tive (Falconer and Mackay 1996)

In plant breeding, several mating designs have been developed

to assist measurement of genetic variances in the breeding

popu-lation, such as one-factor design, factorial design, diallel and

nested design (Bernado 2010) Valid estimates of variance

require that parents are random members of a single

random-mating population, and there is no linkage

These restrictions of mating designs for the assessment of

genetic variance explain why plant breeders do not estimate

genetic variances before choosing parents, as they prefer to grow

progeny for selection rather than for estimating genetic variances

(Bernardo 2010) With BLUP selection, the PBVs are estimated

from the entire breeding population rather than from a specific

mating design experiment The general mixed model is flexible

and provides estimates of genetic variances from any type of

mating design (Lynch and Walsh 1998), but plant breeders

should use mating designs that promote high Ne

The effective population size is closely linked to the number

of parents used in crossing each year Assuming that a breeding

programme can undertake just 64 crosses per year, based on

bio-logical andfinancial limitations, this number of crosses can be

‘invested’ in a full diallel design (total number of parents = 8),

an 89 8 MxN design (total number of parents = 16), or 64

pairwise crosses (total number of parents= 128) Among these

choices, pairwise mating is the most efficient design to increase

effective population size

In practice, there will be other issues that influence the mating

design, for example, the breeder may wish to use one or more

parents in several crosses due to their superior performance, to

minimize coefficient of coancestry between potential parents, to

maximize genetic distance with molecular markers or to restrict

parents according to their pattern of adaptation to the

environ-ment (GxE) The breeder should aim to maximize the number

and diversity of parents that are crossed in each generation to

increase Ne, and to use moderate selection pressure so that more

ancestors are represented in the pedigree The RIPE system in

barley is a good example of breeding with large numbers of

par-ents and crosses each year (Falk 2010)

Genetic Recombination– The Importance of Short Generation Intervals

Genetic recombination is the driver of genetic improvement in plant breeding Recurrent selection cycles with short generation intervals (defined in plant breeding as the average time between crossing among parents and crossing among their progeny) are important to increase the opportunities for recombination during

a breeder’s professional career Recombination may reveal latent variation for quantitative traits that is‘hidden’ by repulsion link-ages in different parents (Falk 2010), or masked by epistasis and unadapted backgrounds

An exercise in an advanced plant breeding course at the Uni-versity of Guelph (D E Falk, personal communication) high-lights the importance of recombination for long-term response

to selection (Fig 1) The exercise requires the students to find the minimum number of crossing cycles to recombine eight

‘favourable’ alleles into one progeny, when the favourable alleles are present at eight distinct loci distributed among eight different founder parents (assuming simple dominant/recessive gene action and no linkage or epistasis among the genes) The students apply Mendel’s laws to segregation of unlinked genes

In this version of the exercise (Fig 1), the F1 and F2 genera-tions are grown in growth rooms, and the F2 are selected and crossed before flowering, with each cycle completed in one year The total number of F2 individuals is limited to 336 from all crosses in any one year based on growth room space available The students need to know that a two-gene recombi-nant can be selected from among 48 F2 progeny with 95% probability, when the parents differ only at two loci, based on binomial statistics With one cycle per year (generation interval

1 year), it takes seven years to recombine and accumulate eight alleles from eight different inbred parents into a single superior progeny line – assuming that selection for the homozygous rec-ombinants in F2 progeny in each cycle is perfect!

If one assumes a generation interval of six or more years, the recombination exercise translates into 42 years for seven cycles (Fig 1) This exercise has surprised professional plant breeders

in several training courses on population plant breeding over the past 10 years (D E Falk and W A Cowling, unpublished) Most breeders seek ways of achieving this relatively simple goal,

of bringing 8 genes together in seven cycles, within their profes-sional career - andfind it difficult to do so

Breeders may ‘self’ progeny to improve heritability, which increases the probability of finding a rare recombinant and the number of target genes potentially fixed in each cycle, but sel-fing also extends the duration of each cycle compared with annual cycles (Fig 1) Efficient selection schemes such as infor-mation from relatives (BLUP and/or genomic selection) may help to select progenies sooner in the selfing process Genomic

or molecular marker selection may help to identify heterozygotes (when target homozygotes are very rare), but the number of progeny tofind a target recombinant from a heterozygous parent increases exponentially compared with crossing among homo-zygotes It is paramount that breeders maintain high Ne as drift may eliminate one or more of these eight valuable quantitative alleles during the seven cycles Breeders should use mating designs that ensure that the eight founder parents are represented

in pedigrees as soon as possible, and target alleles are not elimi-nated by drift Accurate phenotyping in relevant environments is essential for effective BLUP or genomic selection, as genotypes may have positive breeding value in some environments and negative in others (Beeck et al 2010, Cullis et al 2010)

Successful implementation of this ‘simple’ student exercise

(Fig 1) in commercial breeding programmes invokes all of the

core elements of sustainable plant breeding

Conclusions

This review highlights the importance of managing

evolution-ary forces to achieve sustainable plant breeding While plant

breeding can be made more efficient and competitive through

BLUP selection and (potentially) genomic selection, sustainable

plant breeding will replenish genetic diversity lost through

selection and genetic drift Migration can, under appropriate

conditions, be accomplished without loss of elite performance

and without losing valuable donor alleles through drift Large

effective population size is important to achieve sustainable

plant breeding

Methods for BLUP selection in plant breeding build on the

animal model The general mixed model was combined with

fac-tor analytic modelling and pedigree information to independently

estimate additive, non-additive and total genetic variance and

patterns of GxE for each component in a canola breeding

pro-gramme (Beeck et al 2010, Cullis et al 2010) Unlike animal

genotypes (Avenda~no et al 2003), most plant genotypes are

rep-licated within experiments and across environments and this

results in unique genetic estimates (both additive and

non-addi-tive) for traits in each environment PBVs for yield show

geno-typic correlations across sites (Beeck et al 2010, Cullis et al

2010) – this is equivalent to finding correlation among traits for

breeding value in animals (Falconer and Mackay 1996)

How-ever, to date, this type of BLUP analysis in plant breeding has

been limited to several sites over two years (Beeck et al 2010),

rather than decades of data as achieved in the animal model

(Av-enda~no et al 2003) The scale and complexity of BLUP analysis

is much larger in plant breeding

Correlation between pairs of traits (for example, correlation between PBV for grain yield in two environments) improves the power of estimation of PBV for yield in the presence of GxE This is further strengthened by adding information from rela-tives, which allows independent estimates of additive, non-addi-tive and total genetic variance in MET data sets (Oakey et al

2007, Cullis et al 2010)

Population breeding has been advocated for breeding of stable polygenic resistance to plant disease and insects (Robinson 1995) The focus in population breeding is on large effective population size, migration, moderate selection pressure and rapid cycles Population breeding was used to improve yield, stem strength and disease resistance over 20 years in the successful RIPE system in barley (Falk 2010)

Migration is essential to maintain or increase genetic diversity, and methods have been developed to incorporate minor alleles from exotic sources into elite breeding pools during two phases

of breeding (Cowling et al 2009, Falk 2010) Large effective population size promotes effective migration and incorporation

of rare donor alleles for quantitative traits into the elite breeding pool (Cowling et al 2009), as well as the retention of rare posi-tive mutations (Walsh and Lynch 2012b) Genomic information may assist this migration process for quantitative traits

Sustainable plant breeding can be achieved with efficient but moderate selection pressure using BLUP or genomic selection, short generation intervals and high effective population size with migration and/or mutation to replenish genetic diversity While plant breeding will always violate the assumptions of the in fini-tesimal model, these violations can be minimized by the approaches suggested in this review, and this may result in unex-pected outcomes such as new gene combinations and new epi-static interactions (Walsh and Lynch 2012c), which could give rise to valuable future genotypes By following the approaches suggested in this review, successful plant breeders may enhance

AAbbccddeeffgghh

AABB…

… AABBCCDD…

GGHH aabbccddeeffggHH

Totals

No genes to recombine in g

Selec on ra o F2 (perfect

No F2's per cross to find one

Fig 1: Student exercise in recombination (modifed with permission from the original developed by D Falk, Univ of Guelph, Canada): what is the minimum number of cycles to recombine eight genes into one descendant, when eight ancestors each have one gene to contribute to a valuable quanti-tative trait? In each cross, progeny are selected for rare recombinants according to Mendelian expectations in the F 2 from parents, which differ in two genes According to binomial theory, about 48 F 2 progeny (or approximately 3 9 the number of progeny in the perfect population in the F 2 ) must be tested to find one rare recombinant with 95% probability In this example, biological, financial and physical restraints limit the number of F 2 progeny that can be evaluated to a maximum of 336 at any one time, and there is a maximum of 48 plants per cross in the F 2 so that 7 cycles of crossing are required to complete the process Crosses are made in a pattern where each line is crossed to its half-sibs with which it shares one gene in common but differs in two other genes, to form a ‘chain’ through the pedigree The process could be accelerated by combining four genes per cross, but this would result in unacceptable numbers of F 2 plants in each cross (768) to find one rare recombinant with 95% probability.

rather than diminish genetic diversity in their elite breeding

pools during their professional careers

Acknowledgements

This review developed from an invited talk of the author at The German

Society for Plant Breeding (GPZ) Conference in March 2012 at Justus

Liebig University, Giessen, Germany I thank GPZ for financial support.

I acknowledge the contribution of many colleagues to the ideas written

in this paper, especially Duane Falk, University of Guelph, Canada, who

provided permission to modify and reproduce his graduate-level class

exercise in Fig 1 I thank my family who supported me during the long

period required to read background literature and prepare this paper This

paper was written as part of the author ’s part-time role as a research

aca-demic at The University of Western Australia The author is also

Research Director on the Board of Canola Breeders Western Australia

Pty Ltd.

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