Enhancing Gain from Long-Term Forest Tree Breeding while Conserving Genetic Diversity

ISSN 1401-6230, ISBN 91-576-5643-6 Long-term genetic diversity in a breeding population BP, and gain in production populations PP arising from it, were analysed by stochastic computer si

A CTA U NIVERSITATIS A GRICULTURAE S UECIAE

SWEDISH UNIVERSITY OF AGRICULTURAL SCIENCES

2

Enhancing Gain from Long-Term Forest Tree Breeding while Conserving Genetic Diversity

Ola Rosvall

Department of Forest Genetics and Plant Physiology

UMEÅ

Doctoral Thesis Swedish University of Agricultural Sciences

Umeå 1999

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A CTA U NIVERSITATIS A GRICULTURAE S UECIAE Silvestria 109

ISSN 1401-6230

ISBN 91-576-5643-6

 1999 Ola Rosvall, Sävar

Printed by: SLU, Grafiska enheten, Umeå, Sweden, 1999

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Rosvall, O 1999 Enhancing gain from long-term forest tree breeding while

conserving genetic diversity Doctor’s dissertation

ISSN 1401-6230, ISBN 91-576-5643-6

Long-term genetic diversity in a breeding population (BP), and gain in production populations (PP) arising from it, were analysed by stochastic computer simulation for different management strategies (population size and structure, selection and mating) and genetic parameters (variance components and inbreeding depression) The simulations were based on the infinitesimal genetic model and comparisons made over

a range of gene diversity The Swedish Norway spruce improvement program, featuring the use of clonal testing, was used as a baseline

It is suggested that the merit of a tree breeding strategy should be evaluated primarily

on the basis of the BP’s long-term capacity to supply improved material to PPs Under this objective, it is more important to conserve gene diversity in the BP, than when the objective is to improve the breeding value of the BP itself The level of acceptable inbreeding is dependent on test methodology and the type of PP to be supported When the effects of increased selection accuracy by clonal testing, positive assortative mating and inbreeding depression on PP net gain are considered together, balanced within-family selection appears favourable First, clonal testing considerably improves the response from within-family selection, while decreasing family variance under more aggressive index-selection scenarios Second, under within-family selection, the greatest family variance is maintained and the greatest enhancement of family variance

is reached by positive assortative mating, maximising additional gain from intensively selected PPs at maximum BP gene diversity Third, if inbreeding depression is considered, the net gain under within-family selection becomes even more equal to net gain under more aggressive selection strategies, since the lowest relatedness is also maintained Inbreeding depression is counteracted by mating designs with two crosses per parent instead of only one Fourth, the efficiency of clonal testing is greatest under low inbreeding depression Consequently, short-term genetic gain in PPs is enhanced

by methods that also conserve the greatest gene diversity for long-term breeding Under these conditions, the exploitation of the small additional gain available from among-family selection in the BP, involves a large loss of gene diversity per unit increase in net gain The optimal imbalance in parent contributions depends on the type of PP, but it usually seems worthwhile only to increase contributions from a small number of the very best parents In general, imbalance is best achieved by a restricted increase in contributions per parent, giving a structure similar to an open nucleus BP

Key words: artificial selection, breeding population, breeding strategy, effective

population size, gene diversity, genetic gain, genetic variance, inbreeding, inbreeding depression, status number, group coancestry, group-merit selection

Author’s address: Ola Rosvall, The Forestry Research Institute of Sweden, SkogForsk, SE-918 21 Sävar, Sweden

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Abstract _ 5 ContentS _ 7 Appendix 9 List of publications included 9 Introduction 7

Tree breeding strategies _7 Problems addressed 9 Objectives _10

theoretical context 10

The model system 10 Genetic diversity 11 Genetic response and gain 17 Selection for both genetic improvement and diversity 22

Conclusions _ 48

Practical implications 48

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Future research _49

Literature CITED 50 Acknowledgements _66

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In the thesis, publications are referred to by their roman numerals

LIST OF PUBLICATIONS INCLUDED

I. ROSVALL, O., LINDGREN, D and MULLIN, T.J 1999 Sustainability

robustness and efficiency of a multi-generation breeding strategy based on

within-family clonal selection Silvae Genetica: 47(5−6), 307−321

II. ROSVALL, O., and ANDERSSON, E.W 1999 Group-merit selection compared

to conventional restricted selection for trade-offs between genetic gain and

diversity Forest Genetics 6(1):11−24

III. ROSVALL, O., and MULLIN, T.J 1999 Positive assortative mating with

selection restrictions on group coancestry enhances gain while conserving genetic diversity in long-term forest tree breeding Manuscript

IV. ROSVALL, O., MULLIN, T.J., and LINDGREN, D 1999 Controlling parent

contributions during positive assortative mating and selection increases gain

in long-term forest tree breeding Manuscript

All publications are reproduced with the publisher’s permission

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Tree breeding strategies

The design of an optimal breeding programme with selection over several generations must reconcile the trade-off between gains achieved in the short term and those subsequently possible in the longer term The conflict between short- and long-term gains occurs because genetic improvement is accompanied by a loss of genetic diversity (Robertson 1961; Dempfle 1975) and therefore less genetic variability is available for future improvement

A variety of breeding strategies and techniques addressing both genetic improvement and conservation are available for advanced-generation breeding (as reviewed by White 1993; Williams and Hamrick 1996; see also Burdon and Shelbourne 1971; Lindgren and Gregorius 1976; Burdon 1986; Kang and Nienstaedt 1987; Kang 1991), and described for a number of applied long-term tree breeding programmes, e.g.,

Chamaecyparis nootkatensis (Russell 1993); Larix decidua, L leptolepis (Li and

Wyckoff, 1994); Picea glauca (Beaulieu 1996); Picea mariana (Park et al 1993);

Picea sitchensis (Fletcher 1992); Pinus banksiana (Joyce and Nitschke 1993; Klein

1998); Pinus elliottii (White et al 1993); Pinus radiata (Cotterill 1984; Shelbourne et

al 1986); Pinus taeda (McKeand and Bridgewater 1998); Pseudotsuga menziesii (Woods 1993); and in Sweden for Pinus sylvestris, Pinus contorta, Picea abies, and

Betula pendula (Danell 1991a, 1993a)

Recent advances in long-term forest breeding strategies involve comparisons and optimisation with help from advanced analytical models and computer simulation (e.g., Mahalovich 1990; King and Johnson 1993; Bridgewater et al 1992; Kerr et al 1998; Gea et al 1997; McKeand and Bridgewater 1998; Borralho and Dutkowski 1998; Wei

et al 1998) Continuous development in biotechnology provides tree breeders with new means to domesticate, modify, propagate and conserve trees, offering new promises for resource management, but also potential threats to genetic diversity (van Buijtenen and Lowe 1989; Bonga et al 1997; Mullin and Bertrand 1998; Park et al 1998a, b)

Part of the solution to the built-in conflict in tree breeding is met by a structuring of the breeding population (BP), both physically and conceptually (Gullberg and Kang 1985) A hierarchical structure and sublining of the BP will keep selection intensity high, control loss of diversity, and reduce inbreeding in production populations (PP) (Burdon et al 1977; Danell 1993b; Williams et al 1995) The concept of dynamic gene conservation, based on consideration of evolutionary potential, has been proposed for tree improvement programmes concerned both with genetic improvement and with maintenance of adaptability to the changing environments and markets of an uncertain future (Namkoong 1984; Namkoong et al 1980; Eriksson et al 1993) With a multiple population structure, the genetic resource is maintained by using a large meta-population subdivided into a number of BPs for various environments and breeding objectives The inter-population variation assures future presence of genetic diversity,

while the genetic management of a single population, can focus on maintaining genetic variance to persistently provide increased genetic gain in reforestation material Superimposed on either a large unstructured base population or over multiple populations, smaller groups of the best trees can also be managed as elite populations (Cotterill et al 1989; White 1993; Williams and Hamrick 1996) The idea originates from nucleus breeding and positive assortative mating (PAM) systems, developed primarily by animal breeders (James 1977; Shepherd and Kinghorn 1994; Roden 1995; Jorjani 1995a) In both systems, the trees are mated depending on their breeding values In such a hierarchical population structure, which is open for migration between the populations in one or both directions, the elite individuals provide for genetic gain, while the base population or lower tiers assure gene conservation (James 1978) Replicate populations or sublines represent a type of superimposed structure to control inbreeding in seed orchard progeny (van Buijtenen 1976; Burdon et al 1977, van Buitenen and Lowe 1979; Burdon and Namkoong 1983) The build-up of inbreeding within sublines can be released at any time by out-crossing among sublines The study of more accurate selection methods has given deeper insight into the trade-off between long- and short-term response in small populations (e.g., Lindgren 1986; Quinton et al.1992; Verrier et al 1993; Wei and Lindgren 1994; Andersson et al 1998) New methods to control loss of diversity, while maximising gain, or to optimise the conflicting targets have been investigated (e.g., Toro and Pérez-Enciso 1990; Grundy et al 1994; Wray and Goddard 1994; Brisbane and Gibson 1995; Lindgren and Mullin 1997; Villanueva and Wolliams 1997, Meuwissen 1997; Grundy et al 1998) However, it is not straightforward to find an optimal balance between genetic gain and diversity, due to the complexity of breeding programmes and the variety of methods and strategies available (Quinton and Smith 1995; Caballero et al 1996a) Vegetative propagation by rooted cuttings or new cloning technologies, i.e., micro-propagation and somatic embryogenesis (Högberg et al 1998; Park et al 1998a, b; Timmis 1998) can supply genetic test-material from juvenile trees through cloning without any time delay, and might change the way future forest regeneration material

is mass-produced Increased selection precision by cloning facilitates accurate family selection (Burdon and Shelbourne 1974; Shelbourne 1991; Russell and Loo-Dinkins 1993), which in combination with high selection intensity in the large offspring-families available from trees can substantially increase the response More precise estimates of clonal breeding values can be used to apply strong PAM, i.e., a high genetic correlation between mates to enhance genetic variance and the response to selection (Breese 1956; McBride and Robertson 1963; and see review by Jorjani 1995a)

within-Applying clonal testing to advance the BP towards new generations and to support mass propagation with tested clones provides strategy options that differ from those of

a programme counting on out-crossing in genetic testing and PPs (Libby 1969; Burdon and Shelbourne 1974; Chaperon 1984; Matheson and Lindgeren 1985; Burdon 1986; Carson 1986a; Foster 1986; Mullin and Park 1992; Högberg et al 1998; Park et al 1998a, b) It is a challenge to develop tree improvement programmes that enhance

short-term gain, while conserving long-term genetic diversity, and have enough flexibility to make the best use of current and future techniques (Kang 1979; Fowler 1988; Dale and Teasdale 1997)

Problems addressed

The starting point for these studies is that the optimal balance between genetic gain and diversity might differ, if evaluated from the standpoint of net gain realised from PPs rather than the mean additive response of the BP Some problems that affect the requirements for genetic diversity and the conditions for achieving genetic gain are outlined below

Defining and monitoring genetic diversity

Relevance and impact of various forms of genetic diversity must be identified for the different types of breeding and production populations (Lindgren et al 1997; Lindgren and Mullin 1998) What criteria and standards for variability are adequate in short- and long-term perspectives?

Managing within- and among-family variance for different purposes

Long-term advancement of the BP will rely primarily on within-family additive variance, since it is re-established by Mendelian sampling each generation, while PP gain can also use among-family variance without affecting the long-term breeding potential (Burdon 1986) However, during the first rounds of selection, among-family

variance is reduced as a consequence of the selected parents being more alike, “the

Bulmer effect” (Bulmer 1971) Consequently, there will be a substantial decrease both

in BP response over the first generations and in the additional gain available from PPs What breeding and selection strategies under PAM can counteract the decrease in among-family variance? What are the implications for the optimal BP effective size?

Net gain depends on inbreeding depression

Inbreeding will reduce additive variance in the long term, but can also negatively affect tree performance by inbreeding depression in the short term (Williams and Savolainen 1996) Besides the expected reduction in productivity of deployed families

or clones, trees suffering from depression make genetic testing, selection, and seed production more complicated (Frampton and Foster 1993; Lindgren and Gregorius 1976) What implications will this have on clonal selection efficiency, breeding strategy and population effective size?

Computer simulation was used to study conditions for maximum gain and diversity, with the Swedish Norway spruce programme used as a baseline First, efficiency, sustainability and robustness of the baseline strategy were investigated for different population sizes, and at various levels of non-additive genetic and environmental variance Second, the effects of conservative within-family selection was compared to more aggressive selection and mating strategies under clonal testing and positive assortative mating, while accounting for different levels of inbreeding depression

• Evaluate sustainability of long-term tree breeding programmes using new quantitative analysis methods, with special emphasis on the Swedish Norway spruce breeding programme

• Evaluate methods to improve the efficiency of tree breeding programmes in the long- and intermediate-term perspectives

• Evaluate mating and selection strategies that both increase genetic response and conserve genetic variance over generations, at levels where the highest possible additive and dominance gain can be realised in the PPs with acceptable diversity now and in future generations

THEORETICAL CONTEXT

The model system

These studies were made for a model system of a tree improvement program,

illustrated in Figure 1 Genetic variance is re-established in successive generations in

a recruitment population generated by mating among a fixed number of selected individuals, the breeding population (BP), while additive effects accumulate Production populations (PP) that can exploit various components of the genetic variance are more intensively selected to supply seed or vegetative propagules for production of reforestation planting stock As genetic improvement accumulates, genetic diversity is compromised

VA

VD

VA

Seed orchard Clone mix

variance are managed within the breeding population to support high net gain in future seed orchard and clone mix production populations

Simulation

Deterministic simulations are based on algebraic equations that predict the likely outcome of sampling, while stochastic (Monte Carlo) simulation models mimic random processes Stochastic simulation is particularly suitable for genetic systems, as meiosis and genetic recombination are random processes Although well developed and rapid, deterministic prediction and simulation cannot deal with the same level of complexity over many generations as can stochastic simulation (Lacy, 1987; Mullin and Park 1995) Stochastic simulation is commonly used to verify accuracy when prediction equations are developed (e.g., Verrier et al 1990; Shepherd and Kinghorne 1994) Monte Carlo simulation can easily handle cumulative changes in variances and mean values, and can cope with departures from normality Sampling distributions for the outcome make it possible to perform statistical comparisons to study robustness This type of simulation model can also easily accommodate any management practice, which may not be readily accomplished by mathematical analysis

Stochastic genetic models may mimic events at individual loci, so-called finite loci or allelic models, or may be parameter based, describing average genetic effects according to quantitative genetics theory The choice between using allelic- or parameter-based models depends on assumptions regarding the nature of gene action and on the objective of the study (e.g., Jorjani et al 1997a) Whatever the choice, models are necessarily simplifications of a real system Simulation has long been used

in theoretical as well as applied genetics, e.g., conservation genetics (e.g Lacy 1987) and in animal breeding (e.g Harris, 1982; Verrier et al 1993; de Boer and van Arendonk 1994; Quinton and Smith 1995), and has come into practice in recent years for the evaluation of long-term tree-breeding strategies (e.g., Mahalovich 1990; King and Johnson 1993; Mullin and Park 1995; Bridgwater et al 1993; McKeand and Bridgewater 1998; Andersson et al 1998; Wei et al 1998)

Genetic diversity

Genetic variability can be understood in several ways, for example:

(i) the allelic richness that can be identified by biochemical methods and expressed for individuals or populations (e.g., proportion of polymorphic loci, number and frequency of alleles in these loci, proportion of heterozygous loci) (Berg and Hamrick 1997);

(ii) quantitative variation in metric characters, assessed by a statistical analysis of variance; and

(iii) effective population size based on relatedness within and among individuals and populations

Allelic diversity and genetic variance

The genetic diversity of the gene pool in terms of gene frequencies determines the quantitative genic variance, assuming perfect Hardy-Weinberg (H-W) and gametic

phase or linkage equilibrium, which should be distinguished from how the individuals

of the population carry this pool, determining the genotypic (or genetic) variance

(Bulmer 1976; Falconer and Mackay 1996)

The genetic information is re-combined at generation shifts and renewed by mutations Under natural conditions, changes in the gene pool generally occur slowly over an evolutionary time scale, and the pool ordinarily contains a huge allelic variability if assessed by the number of alleles (Ledig 1986; Williams et al 1995) Also, lethal and deleterious mutant alleles, which constitute the “genetic load”, are carried in individuals if the complementary allele in the homologous pair is functional These genes contribute to inbreeding depression when they appear in homozygous genotypes (Ritland 1996)

While long-term maintenance of genetic variance in a population under selection is more dependent on the alleles present in the population than on heterozygosity

(Robertson 1960), the number of alleles at a locus (allelic diversity) has a low impact

on heterozygosity and thus current genetic variance (Allendorf 1986) Alleles that are initially rare must increase in frequencies by chance and selection, before they will influence genetic variance

For a commercial forest stand to cope with temporal and spatial variation in the environment and to resist biotic stresses, it is the heterozygosity within individuals, i.e loss of heterozygosity due to inbreeding, as well as the genotypic variation from tree

to tree that is of prime importance (Lindgren and Gregorius 1976; Ledig 1986; Lesica and Allendorf 1992) Roberds and Bishir (1997) discuss models for risk analysis to guide plantation diversity in clonal forestry, where genetic uniformity can be brought

to its extreme However, if planted stands are not harvested or naturally regenerated, the quality of their gene pools will influence the following generation, both on the site and in the population as a whole (Ryman and Laikre 1991)

Management of genetic diversity

Sampling of alleles and population size

Since the transmission of alleles between generations is a sampling phenomenon, population size is fundamental to several aspects of genetic diversity and its maintenance in small populations (Robertson 1960; Nicholas 1980; Franklin 1980; Lande and Barrowclough 1987; Kang 1991) First, the size and quality of the sample from the natural forest population determines the initial allelic diversity of a BP (Gregorius 1980; Nienstaedt and Kang 1987; Danell 1993b) Second, the structure and effective size of the BP determines the sampling from generation to generation The smaller the population, the larger is the random genetic drift in gene frequencies, which eventually will result in the total loss or fixation of alleles, and the larger is the measurement error variance due to the sampling of a limited number of individuals for testing (Aggrey et al 1995) Third, the size of the BP, together with the mutation

frequency, determines the total number of new mutations that are potentially available for selection In the long term, mutations will contribute to genetic diversity and variance also in a managed population (Hill 1982; Lynch 1988)

The non-random selection of BP founders can itself increase genetic variance through heterosis and release from linkage (Falconer and Mackay 1996) Increase in variance may also occur from the reduction in population size when there is dominance and epistasis, by changes in gene frequencies and departure from H-W and linkage equilibria, analogous to the changes in variance after a bottleneck (Wang et al 1998)

Conservation of alleles

The conservation of the gene pool of a BP is influenced by how the natural processes within the population (random genetic drift, as well as directional forces on gene frequencies: mutation, natural selection and migration) are affected by management: (i) how the population is structured; (ii) the methods of breeding (mating and selection); and (iii) introduction of new genes These actions also influence how the alleles are arranged into genotypes and, thus, the genotypic and phenotypic variance among trees, i.e., the quantitative variance

In a random mating BP of constant size, without substructure and with unrelated founders, genes are best conserved by balanced within-family selection, and balanced mating, giving equal gene contributions from each founder (Ballou and Lacy 1995; Lindgren et al 1996) When the loss of diversity is minimised in this way, random genetic drift sets the limit for gene retention Conservation is even greater in a sub-structured population as drift can change gene frequencies in different directions among the sub-groups (Robertson 1960; Lande and Barrowclough 1987; MacKeand and Bridgewater 1998) The extreme case of this phenomenon is regular inbreeding, e.g., repeated selfing (Lindgren 1976; Falconer and Mackay 1996) Consequently, any form of imbalance in parental contributions will accelerate the loss of genetic diversity

If desirable, a balance can sometimes be re-established from an unbalanced situation

by genetic management of the population to minimise average coancestry (i.e., average mean kinship) (Ballou and Lacy 1995)

The loss of diversity by drift in a small population results in a loss of allelic variants and lower heterozygosity, while inbreeding due to non-random mating only changes the level of heterozygosity Genetic drift and inbreeding affect both target traits and neutral alleles, while selection will only affect target and linked genes Directional or disruptive selection will ultimately fix one allele and thereby deplete genetic variation For traits where heterozygosity has an advantage, due to whatever cause (inbreeding depression, overdominance), natural and artificial balancing selection slows down the loss of allelic variation due to drift over what neutral models predict (Lesica and Allendorf 1992) In addition, selection and assortative mating cause gametic phase disequilibrium, without changing the gene frequencies of the loci affecting the character and for linked loci (Bulmer 1976; Jorjani et al.1997b,c)

Measuring loss of genetic diversity

Group coancestry and inbreeding

Given an initial pool of unrelated founder genes, the potential changes and losses of genetic diversity can be assessed by the increase in relatedness, i.e., the increase in

genetic similarity due to genes being identical by descent Group coancestry (Θ) is the probability that two genes taken at random from the gene pool, with replacement,

are identical by descent (Cockerham 1967) Similarly, pair-wise coancestry (θij) (coefficient of kinship) is the probability that genes sampled from each of two

individuals i and j are identical by descent The inbreeding coefficient (F i) is the

probability that the two homologous genes within an individual i are identical by

descent Self coancestry, i.e., the coancestry of an individual with itself is 0.5(1+F i )

(i=j) (Falconer and Mackay 1996; Lindgren and Mullin 1998) Thus, Θ of a population

with N individuals is the average of all self- and pair-wise coancestries, including

reciprocals,

2

)1()

=

where θ is the average of all pair-wise coancestries; and F is the average inbreeding

As Θ includes the repeated sampling of the same gene, Θ depends on population size

by 1/2N, which is well-known from other formulations of the effect of genetic drift (Falconer and Mackay 1996)

The loss of genetic diversity within an individual, due to inbreeding and drift, results

in decreased heterozygosity, which is measured by the inbreeding coefficient (F) Selection against inbreeding depression may change the average F of the population,

while other possible changes in individual heterozygosity by selection, including

changes in gene frequencies, are not seen in F Pair-wise coancestry between two

mates becomes inbreeding of their progeny, and group coancestry in one generation becomes the expected average inbreeding in the next, following random mating

Population structure

Some forms of non-random mating, like local inbreeding within sub-groups or lines of

a population, can cause an excess of homozygotes While the expected gene frequencies are not changed in a separate sub-population, the genotype frequencies are not what would be expected under H-W equilibrium (Falconer and Mackay 1996) If the population reverts back to random mating, expected genotype frequencies would return to H-W proportions However, in a small population, assumed to mate at random, deviations occurs by chance (e.g., “unconscious” assortative mating, Wright 1921); there is a random departure from H-W equilibrium and change in gene frequencies due to genetic drift (Wang 1996)

To measure population structure, distinction should be made between the inbreeding

due to non-random mating and that due to finite population size Wright´s F-statistics describe the genetic structure of a subdivided population (Wright 1969) F-statistics

can be interpreted in terms of inbreeding coefficients, probability of gene identity,

correlation between gametes and variance of gene frequencies (Wright 1969; Cockerham, 1967, 1969; Weir and Cockerham 1984; Caballero 1994; Wang 1997a), and in terms of heterozygosity or gene diversity (Nei 1973, 1977) in relation to various

hierarchical levels of a structured population The relationship among the F-statistic

coefficients of a subdivided population is

)1)(

subpopulation F IS is the probability that two homologous genes in an individual are

identical by descent, relative to the sub-population to which it belongs F IT is the overall probability of identity for two homologous genes in an individual and is a composite of the other two, measuring the absolute decrease in heterozygosity in the

population By the comparison of average probability of gene identity within ( F) and

among (θ)individuals, F IS measures the deviation in inbreeding (or heterozygosity) due to non-random mating in a sub-population, and thus departure from H-W equilibrium (Nei 1977; Cockerham 1967; Wang 1997a; Caballero 1994)

Proportional gene diversity

Gene diversity (GD) is the variance in allele frequencies at a locus, and is equal to the

heterozygosity expected in a population with random union of gametes, i.e., in H-W equilibrium (Nei 1973, 1977; Lacy 1995)

∑

−

=1 p i2

where p i is the frequency of allele i and summation is over all alleles at that locus GD

reflects both the number of alleles and the uniformity of their frequencies GD can be arranged over loci to provide a genome wide measure of genetic variation, i.e., the probability that two alleles sampled from the gene pool are different by descent The rate of decay in GD is independent of initial gene diversity or allele frequencies (Crow and Kimura 1970) However, it is essential that the baseline population used for the comparison be explicitly understood (Lacy 1995) Here the BP at time 0 is the founders, which can be considered as a sample from the source population Gene

diversity of the BP in generation t is designed GD t and the group coancestry Θt Setting the gene diversity of the source population to 1, i.e., all alleles are unique,

proportional gene diversity in generation t is

t t

in Θ (Cockerham 1977), N eV considering generations 0 to t is

The inbreeding effective population size N eF is the size of an ideal population that

accumulates F at the same rate as the population under study (exchange Θt for F t in [6]) The two effective sizes depend on the increment of Θ and F, respectively If the

population is in H-W equilibrium (random mating) after the first breeding cycle, variance and inbreeding effective population sizes are expected to be identical Under non-random mating they will differ, but eventually converge to the same asymptotic value (Wang 1997a) Developments in predicting the effective population size are reviewed by Caballero (1994) and in particular for subdivided populations by Wang and Caballero (1999)

Lindgren et al (1996) defined status effective number

to be the effective size of a population, equivalent to the census size of a population

with the same gene diversity, but without any pair-wise coancestry or inbreeding N s is identical to the concept “Founder Genome Equivalents” (FGE), in the form it was re-defined by Lacy (1995) It can be understood as the allele-carrying capacity in terms of the expected number of founders that would be required to provide the same level of genetic diversity, if the founders were equally represented and if no genetic drift had occurred (no change in gene frequency and no alleles lost) (Ballou and Lacy 1995;

Lindgren et al 1997; Lindgren and Kang 1997) In contrast to conventional N eV and

N eF, status number refers to the accumulated relatedness in the gene pool, and is

therefore the effective size at a particular state of development In generation t, the

measures are related as follows

eVt t

s t

112

11

The term 1-1/2N indicates that a different baseline population (the founders, which can

be, considered the initial breeding population) is used for N eV

The decrease in N s is non-linear and reflects the sampling process of founder genes, being proportional to the probability that low-frequency genes will be lost (Lindgren et

al 1996, 1997) The loss of gene diversity assessed by GD is approximately linear, reflecting the proportional decay in genic variance (Verrier et al 1989, 1991)

Genetic response and gain

Genetic response to one cycle of selection for a quantitative character (R) is a function

of additive genetic variance in the population (V A ), selection intensity (i), and accuracy (r TI ) r TI is the correlation between the predicted selection criterion I and the true, but unknown, breeding values of individuals T (Falconer and Mackay 1996)

Long-is also a function of the effects and frequencies of alleles at individual loci (Hill and Rasbach 1986) While such information is not available, the infinitesimal genetic model assumes an infinite number of unlinked loci, each with a small additive effect (Bulmer 1980)

Robertson (1960) developed the theory of selection limits under mass selection, but he did not consider the reduction in additive variance due to linkage disequilibrium (Bulmer 1971) Wray and Hill (1989) did this for index selection, and Dekkers (1992) and Villanueva et al (1993) for BLUP selection, but they did not consider the reduction in response due to finite population size This can be done by accounting for the effective size under selection (e.g., Robertson 1961; Caballero 1994; Wray et al 1994; Santiago and Caballero 1995) Villanueva and Woolliams (1997) further extended the theory of selection limit A theory incorporating all factors that affect short-, medium- and long-term response to predict cumulative response to selection was developed by Wei et al (1996)

Genetic variance

The additive genetic variance can be partitioned according to Bulmer (1976; see also

Verrier et al 1989; Jorjani et al 1997b, c)

hw l

a

where V a is the genic variance based on the gene frequencies, assuming perfect H-W

and linkage equilibrium; C hw is the covariance between alleles within loci due to H-W

disequilibrium; and C l is the covariance between loci due to gametic phase or linkage disequilibrium Genetic variance can also be partitioned into within- and between-

family components, V AW and V AB, respectively (Falconer and Mackay 1996)

infinite number of unlinked loci, selection will not affect V a, but will generate a

negative C l due to gametic phase disequilibrium, and thus a temporary reduction in V A

— the “Bulmer effect” (Bulmer 1971, 1976; 1980; Falconer and Mackay 1996) V of A

the population is reduced to V A′ in the selected group (Bulmer 1980)

A

A h k V

where h2 is the narrow-sense heritability; k = i(i−x); and i is the selection intensity and

x the corresponding deviation of the point of truncation from the population mean The

C l and decrease in variance is counteracted by free recombination at meiosis (Mendelian sampling), and a balance is reached after a few generations Therefore, the

recurrence equation for V A under random mating at any generation t +1 is

) 0 ( )

2 ) )

a net reduction of within-family variance as a result of negative C hw (Bulmer 1976; Verrier et al 1989; Wang 1996; see also Jorjani 1995b and Jorjani et al 1997b, c)

Positive assortative mating

When each tree is paired once with a random mate, the among-family additive variance is half the additive variance of the parents (variance of mid-parent values) (Falconer and Mackay 1996) PAM, i.e., mating “like with like”, causes a gametic-

phase disequilibrium among loci, similar to selection, and a correlation between loci in

the uniting gametes, resulting in a positive C l, enhancing among-family variance (Fisher 1918, Wright 1921; Falconer and Mackay 1996; see review by Jorjani 1995a) PAM also changes the genetic correlation of breeding values between relatives, and thus the partitioning of the initial random-mating variance components within and among families

PAM can also induce a positive C hw, increasing genetic variance (Bulmer 1976; see also Verrier et al 1989; Mueller and James 1983a; Jorjani et al 1997b, c) However, if the population size and number of loci are large, assortative mating will not result in a significant departure from H-W equilibrium (Bulmer 1980; Jorjani et al 1997b, c) Assuming a large number of loci, Bulmer (1980) gave the equilibrium additive variance

Due to the counteracting effects of selection, PAM results in the greatest increase in variance at low selection intensity, as reviewed by Jorjani (1995a), where it also gives the greatest relative selection response (Baker 1973; Fernando and Gianola 1986; Smith and Hammond 1987; Tallis and Leppard 1987, 1988; Shepherd and Kinghorn 1994) Once selection pressure is removed or the population reverts to random mating,

C l is halved in each generation (assuming no physical linkage), while C hw is reduced immediately to zero (Bulmer 1971, 1976)

It is commonly accepted that, for practical purposes, one can assume that dominance variance is unchanged by assortative mating (e.g., Vetta 1976; Crow and Kimura 1970; Bulmer 1980; Falconer and Mackay 1996) However, Jorjani et al (1998) argued that with a small population size and large number of loci, the dominance variance would ultimately increase

Inbreeding

The initial genotypic variance V A(0) of a population is reduced as relatedness increases through a reduction of the Mendelian sampling variance, i.e., within-family variance The decline is proportional to the reduction in heterozygosity or increase in average

inbreeding coefficient F of the parents, caused by inbreeding and drift, The

relationship holds also under selection (Verrier et al 1989, 1990, 1991)

) 0 (

through departure from H-W equilibrium (Falconer and Mackay 1996) In this way inbreeding can double total variance at complete inbreeding

a variety of characters and species (Falconer and Mackay 1996; Lynch 1988)

For a range of distributions of mutant gene effects, the response to selection will be substantial after 20 or so generations, and there will be no limit to selection (Hill 1982) Assuming an infinitesimal model and accounting for all factors that affect variance, Wei et al (1996) found that under reasonable assumptions, mutational variance becomes important to selection response for time horizons above ten generations Caballero et al (1996b) found that fixation rate of genes with large effects increased proportionally with effective population size In general, the rate of selection response is greater with larger effective population sizes, favouring within-family selection (Hill 1982; Wei et al 1996; Caballero et al 1996b) The role of new mutants should be considered in designing long-term breeding programmes, in particular in using large populations (Hill 1982)

Inbreeding depression

Temperate forest trees typically have life-history traits that promote outcrossing, highly effective gene flow and high levels of heterozygosity (Ledig 1986; Williams and Savolinen 1996; Ritland 1998; Hamrick et al 1992) This allows them to carry a large genetic load of deleterious alleles that are expressed under inbreeding and result

in inbreeding depression, particularly when a population has experienced a large reduction in size In conifers, inbreeding depression has been observed at all life stages, and varies among species and traits, although vigour and fitness characters are most strongly affected (e.g., Koski 1973; Griffin and Lindgren 1985; Skrøppa 1996; Williams and Savolainen 1996; Durel et al 1996; Wu et al 1998a, b) Under selfing

(F=0.5), reports of reductions in height range from 9% for radiata pine up to 30−40 % for a variety of species In general, there is a linear relationship between overall inbreeding depression in a population and the inbreeding coefficient, but depression may vary considerably among equally inbred individuals (e.g., Falconer and Mackay

1996, Durel et al 1996; Wu et al 1998a, b)

Complete, partial and over-dominance have been proposed as genetic mechanisms for inbreeding depression, although most empirical data support that homozygosity for unfavourable recessive alleles is the major cause (Charlsworth and Charlsworth 1987; Williams and Savolinen 1996; Ritland 1998) Inbreeding depression affects non-target traits, as well as those under selection This allows purging of recessive deleterious

alleles by both artificial and natural selection (Lesica and Allendorf 1992; Hedrick 1994; Dudash et al 1997; Fu et al 1998), and a balance may finally be reached between decrease in performance from depression and increase from selection For reasonable assumptions, effective sizes between 30 and 250, corresponding to an

increase in F with 0.002−0.017 per generation will result in a balanced situation where fitness is maintained by natural selection (Meuwissen and Wolliams 1994) However over-dominant or weakly deleterious recessive alleles will remain in the population Latter and Robertson (1962) demonstrated that a slow increase in inbreeding results in less inbreeding depression when the increase is fast

Inbreeding depression can be accounted for by reducing genetic response (R) by

inbreeding depression (e.g., Goddard and Smith 1990; de Boer and van Arendonk

1992, 1994; Wray and Goddard 1994) If inbreeding depression is directly proportional to inbreeding , the net genetic response is

Selection accuracy and intensity

The accuracy of selection can be improved in genetic testing by: (i) replicating measurements; (ii) including information from relatives, e.g., progeny, parents and sibs; and/or (iii) replicating the individuals vegetatively (Cotterill 1984; Libby 1969; Shelbourne 1991 Russell and Loo-Dinkins 1993) For simplicity, mass selection is used here to illustrate the effect of cloning on accuracy For selection on individual phenotypes, assuming an dominance model

E D

V V H

H

b

r

E D A

D A TI

++

There is generally a trade-off between selection accuracy and selected proportion for a limited total test size Increased accuracy by using more progeny or ramets per tree will decrease the number of candidates that can be tested and thus the selection intensity.

Selection for both genetic improvement and diversity

If information from relatives is used in genetic evaluation by classical selection indices (Lush 1947) or in BLUP (best linear unbiased prediction) (Henderson 1984), increased selection accuracy maximises response after a single generation However, advantages

in the short term may be offset in the long term (e.g., Quinton et al 1992; Verrier et al 1993) as described above, due to a higher reduction in variance from both the Bulmer effect and the increased rate of inbreeding (Wray et al 1994)

Different methods have been proposed to reduce inbreeding while keeping gains at the same level These methods use various selection and mating strategies, or both

simultaneously as reviewed in II The selection strategies have either direct or indirect

effects on restricting the magnitude of the variance in family size, or the expected relationship of long-term genetic contribution of ancestors with their breeding value (Wray and Thompson 1990; Toro and Pérez-Enciso 1990; Grundy et al 1994; Verrier

et al 1993: Lindgren et al 1993; Wray and Goddard 1994; Woolliams and Thompson 1994; Villanueva et al 1994; Brisbane and Gibson 1995; Meuwissen 1997; Meuwissen and Soneson 1998; Kerr et al 1998) These studies have not explicitly considered the optimum weight given to family information in the evaluation process

to minimise loss of response Villanueva and Wolliams (1997) investigated procedures that optimise both the index weights and the numbers selected Grundy et al (1998) developed indices that use weighted ancestral Mendelian sampling estimates Once the selection decisions have been made, the choice of the mating system can also affect the rate of genetic progress and inbreeding, as investigated by Santiago and Caballero (1994), Caballero et al (1996a), and Kerr et al (1998)

Consideration of both genetic response and diversity can be accomplished if a relevant measure of genetic diversity is incorporated into the breeding objective (Goddard and Smith 1990; Lindgren et al 1993; Wray and Goddard 1994; Brisbane and Gibson 1995) Lindgren and Mullin (1997) further generalised the breeding objective by considering group coancestry rather than inbreeding as the objective for diversity

ω

ω

This selection criterion (B ), which they termed ‘group merit’ (or ‘population merit’), ω

is the average of the breeding values (G ) of the selected individuals, minus their ω

group coancestry, (Θω) multiplied by a weighting factor, (c), converting response and

diversity to the same scale

The long-term consequences of various mating and selection strategies on BP diversity and PP gain were examined by Monte Carlo simulation The simulated breeding strategies were adjusted to exploit initial gene diversity at different rates, resulting in a

range of BP effective sizes N s The strategies were compared at the same level of

population N s or F for a time horizon up to ten generations Economics were not

specifically addressed, but by keeping the total number of field-tested progeny equal, alternative scenarios were evaluated at comparable levels of resources

Baseline breeding strategy

The Swedish breeding program for Norway spruce was chosen as the baseline for the analysis Following a multiple breeding population strategy (Burdon and Namkoong, 1983), a large meta-population is subdivided into many independent BPs with the objectives of: (1) adequate conservation of alleles; (2) long-term adaptation; and (3) improvement of general-purpose goals (Danell 1991a, 1993a) The questions addressed in this study dealt primarily with the development of one such BP (BP).According to the current management plan for Norway spruce, each BP of 50 founders

is managed by double-pair mating, clonal testing, and predominantly balanced family selection to maintain a constant BP census size of 50 (Karlsson and Rosvall, 1993) In the simulations, a census size of 48 was used, which facilitated adjustments

within-to mating and testing designs in alternative scenarios while keeping the level of effort constant In the baseline scenarios,10-14 ramets per genotype were used to estimate breeding values for 40-50 progeny per parent Within each study, the same combined total of genotypes was generated and tested

Alternative breeding strategies

Two alternative strategies were designed to increase the contributions from better parents:

1 Balanced mating designs producing equal numbers of crosses per parent, combined with unbalanced selection of more progeny from better parents (US); and

2 Unbalanced mating to produce more crosses from better parents and fewer from poorer, followed by balanced within-family selection of equal numbers from each cross (UM)

In each approach, the intensity of imbalance could be adjusted from very mild, so that parent contributions were very nearly equal, to very aggressive, where parent contributions varied greatly

Mating design

In the baseline strategy, single-pair and double-pair mating (SPM and DPM, respectively) were assessed as mating designs giving balanced representation from each BP member Under SPM, the mating of the 48 BP members, each in one cross,

generated 24 families; while under DPM, each BP member was used in two crosses, for a total of 48 families When SPM or DPM was used in the baseline strategy, the pairing of mates was done randomly but with selfing excluded, so-called random assortment of mates (RAM) In other strategies, the mates were paired in rank order by phenotypic clone means, positive-assortative mating (PAM) PAM was applied to both US and UM strategies.

Selection to the breeding and production populations

To advance the BP in the baseline scenario, within-family selection generated balanced selection and equal contributions from each parent For unbalanced selection alternatives, selection was restricted either by limiting the maximum number of progeny selected per family or by group-merit selection (Lindgren and Mullin 1997)

By increasing the number of selections allowed per family or decreasing the weight given to group coancestry, a range of family selection intensities was achieved, resulting in varied parental contributions and BP effective sizes

Clonal selection was used to advance the BP and to select six clones for operational deployment, either as seed parents in a grafted seed orchard or for control pollination (seed PP) or for mass vegetative propagation (clone PP) The seed PP was the highest-ranking subset of the current BP Selection to the BP and seed PP was based on a combined-index value (CI), where full-sib family and individual clone mean values were weighted by their respective heritabilities (as reviewed by Baker 1986) The mix

of genotypes for clonal deployment was selected on clone means and came from the tested progeny of the current BP, and belonged to the same generation as the progeny

of the seed orchard

The PPs were selected without considering genetic diversity or inbreeding For the seed PPs, this implies that no additional restrictions on parental contributions were applied, beyond those for selection of the BP itself The intention was to study the performance and structure of the elite part of the BP, rather than to compose a complete PP In the actual Swedish program, PPs are to be assembled with the elite members of 3 or more such BPs to give the desired diversity in the regeneration material

Simulation model

A stochastic simulation tool, POPSIM (Mullin and Park, 1995), based on a quantitative infinitesimal model, was modified to allow for group-merit selection (Lindgren and Mullin, 1997) In the simulation model, each genotype is considered to

be the sum of independent genetic (additive, dominance and epistasis) and environmental effects, and the total phenotypic variation in a population is described

as the sum of independent variances for each of these effects

The additive breeding value for the ith individual in the founder population was

sampled from a normal distributionN(µ ,σ2) The initial population mean and σ2

were each set to 100; if related to this mean, the changes in genetic effects could be interpreted directly as a percent change The additive value of each offspring was

obtained as the average of the parents A f and A m plus a random Mendelian deviation sampled from (0 ,0.5 2 (1 ))

N σ − , where F fm is the average of F f and F m, which are the inbreeding coefficients of the female parent and male parent obtained from pedigree The dominance effect for an individual (D i′) was sampled from a normal family distribution with variance equal to (0 ,0.75 2(1 ))

fm

N σ − (the within-family portion of dominance variance) and with a family mean dominance effect sampled from (0 ,0.25 2)

members (F fm ), where the regression coefficient (b) expresses the reduction in

phenotypic value in units of phenotypic standard deviation (σP) for the trait in the

unselected base population Various b were chosen to generate 0.5 and 1.0 % inbreeding depression per 0.01 units increase in F at additive variance coefficient 0.1 The net gain in the progeny of n seed orchard parent trees in generation five was

obtained assuming no self pollination by adjusting the average additive effect of the parents with −bθnσP, where θn.is the mean par-wise coancestry of the parents By excluding self-pollination, the result became independent of the number of selected parent clones

Selection was applied to a single trait, which could be regarded as an index of

component traits if there is no change in genetic correlations due to selection (i.e., infinitesimal model) Testing was assumed to use single-tree plots (i.e., no

environmental covariances), in a single environment (i.e., no G×E interaction), with no

variances associated with cloning (i.e., no C-effects) By repeating the simulation of a

given scenario 100 to 500 times, the stochastic variation in expected genetic effects and variances of a single scenario was analysed by the coefficient of variation (CV %)

and the average outcome of repeated scenarios by the standard error (sd/n 1/2)

SUMMARY OF THE PUBLICATIONS INCLUDED

I

In the first study, a BP was managed for 10 generations, and the importance of a series

of genetic parameters and management alternatives were studied The BP was

modelled after a typical sub-population used in Sweden’s multi-population breeding strategy Parents were paired randomly and selection was applied only within families, i.e., each initial founder contributed equally to each new generation In this way, loss

of gene diversity came about only by genetic drift, and resulted in the greatest possible conservation of gene diversity

Provided that the population had no fewer than 24 members, which is half the current sub-population size in Sweden, increases in group coancestry, inbreeding and inbreeding depression over ten generations were not substantial For the baseline

alternative with N = 48, the GD, N s and F were 0.94 8.1 and 0.047, respectively

Departure from a linear increase in additive response per generation (1.1σA) was negligible Six trees could be selected as seed orchard parents with a status number of 3.9, with inbreeding in the seed crop of less than 5%, resulting in a total gain including inbreeding depression of 11.7σA Meanwhile, gain available from a clone mix of 6 genotypes with similar inbreeding was 13.1σA, mainly as a result of one more cycle of testing

Clonal testing continued to be efficient through ten generations at population sizes down to 24 This suggests an opportunity to further subdivide the Swedish BP to facilitate out-crossing in seed orchards However, with more sublines, response was reduced by inbreeding and inbreeding depression, lower additive variance, and reduced test accuracy Non-additive variance reduced the rate of increase of the additive mean A continuous accumulation of additive effects was more important than exploitation of non-additive variation, even when cloned planting stock is deployed Clonal testing was highly effective and robust, even with few ramets and low heritability Low stochastic variation among replicate runs indicated high precision, thus predictions of the breeding programme outcome are reliable within the limits of the model It was shown that the Swedish Norway spruce breeding strategy is sustainable

The increased contribution from better parents improved genetic response, but reduced

effective size Effective size at which maximum genetic response was achieved

increased over generations and was higher at high heritability (used to simulate high selection accuracy) than at low heritability Further, the increase in response by

varying parent contribution, i.e., reduced gene diversity, was much less at high heritability (accuracy) The greatest additional increase in gain per unit loss of gene diversity came from increasing the contributions from the very best parents This was achieved by a slight reduction of the weight on group coancestry in GMS, a mild level

of imbalance that could not be achieved by simple CRS

By comparing CRS and GMS at the same gene diversity, GMS proved to be beneficial for any weight on group coancestry other than the extreme weights of zero and infinity where the methods are effectively identical The largest improvement by GMS was for low heritabilities, while the importance of population size and selected proportion (family size) was small The benefit of GMS accumulated over generations

The optimal weight given to group coancestry depends on the breeding objective Diversity-use efficiency (DUE), i.e., unit increase in response per unit loss of gene diversity, was therefore best analysed by comparing gain at the same gene diversity A general strategy for efficiency in the use of diversity seems to be to successively increase the weight on group coancestry as the among-family variance component decreases

III.

In the third study, an investigation was made of how PAM and selection by GMS, by which parent contribution was varied, can combine sustainable breeding and enhanced genetic gain in intensively selected PPs

PAM substantially improved genetic gain in PPs, by increasing the additive variance

of the BP This effect was greater the more balanced were the parent contributions, i.e., the more genetic diversity was conserved in the BP If variation in parent contributions was large and effective size low, the enhanced variance by PAM was converted to a small improvement of the BP, leaving little extra gain potential when selecting PPs The highest PP total gain was achieved at a higher effective size, i.e., gene diversity, than was the highest BP response, and the PP gain obtained at the highest level of BP diversity was not much lower than the highest possible This effect was amplified in the presence of inbreeding depression

Varying parent contributions affects both group coancestry and inbreeding PAM itself does not affect group coancestry, but does increase inbreeding, through departure from H–W equilibrium: In this way, PAM generated a population structure where relatedness was more represented by inbreeding than by pair-wise coancestry The effect is similar to that observed for sublining, and results in less inbreeding of seed orchard progeny For a given level of inbreeding in the seed orchard progeny or in a genotype mix for clonal deployment, gain was higher for PAM than after random mating When inbreeding depression was included in the simulation, inbreeding was counteracted by selection, and the enhancement of PAM on PP gain was slightly reduced

The fourth study continued the investigation on genetic gain and diversity when applying PAM to various mating and selection strategies, while allowing greater contributions from the better parents to the next-generation BP This was accomplished by

(1) balanced mating designs producing equal numbers of crosses per parent combined

with unbalanced selection of more progeny from better parents by GMS (US

strategy, as in paper III), and

(2) unbalanced mating, where the contributions of the best parents were increased by

making more crosses in exchange for fewer crosses among the low-ranking parents, followed by balanced within-family selection of equal numbers from each cross (UM strategy)

In this way, balanced SPM was modified to generate “unbalanced 2:1:0 designs”, with the parents used in 2, 1 or 0 crosses, and DPM in correspondence to “unbalanced 3:2:1 designs” An increasing degree of imbalance was reached by increasing the number of crosses exchanged

Over 5 generations, PAM inflated the additive variance more for the UM strategies than for those using US This higher variance in the BP also led to greater gain in selected sub-populations used for seed production or clonal deployment, which compensated for the lower BP response in the UM compared to US strategies

Particularly under UM, PAM generated a population structure resembling an “open elite nucleus” PPs derived from the nucleus had not larger coancestry and inbreeding

as more high-ranking parents were involved in extra crosses, in spite of lower BP effective size PAM under US generated more relatedness and inbreeding in the nucleus as parental contributions from selection became more unbalanced These differences in population structure affected the net gain in the presence of inbreeding depression For the progeny of a seed orchard from the UM strategies, net gain

increased with decreasing status effective number, N s, in the BP, while group coancestry among the orchard trees was stable In contrast, the net gain from orchard

progeny decreased as the BP N s decreased for US strategies For both strategies, the

net gain from a clone mix was generally higher at lower levels of N s in the BP, although inbreeding increased

DISCUSSION

High net gain at high genetic diversity

These studies demonstrated that there is not necessarily a trade-off between genetic gain and gene diversity, when the net gain in the final production forest is considered, rather than the mean of the BP Under PAM and group-merit selection (US-strategy), the greatest seed orchard progeny gain was achieved at the very highest BP effective size, which was reached under the most conservative breeding and selection, i.e.,

within-family selection and equal parent contributions (IV) (Figure 2) For other

strategies (UM-strategies), the increase in gain from unbalanced parent contributions was positive, but low Since within-family selection makes use of only half of the initial additive variance, it is generally regarded as inefficient in short-term breeding, compared to more aggressive selection programmes, except for very long time-horizons (Dempfle 1975)

1 2 3 12…

Figure 2 Net gain (assuming no self-pollination) in progeny of seed orchards from BPs of

and unbalanced selection strategy by GMS (US); and in the 3:2:1 unbalanced mating and balanced selection strategy by varying the number of crosses exchanged from low to high

100 clones per parent and 10 ramets per clone (From Figure 5 in IV).

The explanation to these findings is the combined effects of:

(i) high selection accuracy (heritability) due to clonal testing;

(ii) high selection intensity;

(iii) decrease in family variance due to selection;

(iv) increase in family variance by PAM; and

(v) population size and inbreeding depression

Improved accuracy from clonal replication and high selection intensity from a large

total test size substantially increases selection response within families (I), and decreases family variance when family selection is also allowed (II) Consequently,

the highest family (and total) variance is retained under within-family selection, maintaining the highest potential for additional gain in PPs In addition, the greatest

enhancement of variance by PAM is reached under within-family selection (III)

Finally, reduction in selection response in the BP, and reduced performance in production forests by inbreeding and inbreeding depression, can be kept lower the

higher is the BP effective size (IV) Consequently, when family variance is greatly

reduced by accurate, intensive selection, the loss in gain expressed by progeny of an elite seed orchard can be larger than the additional gain achieved through higher

contributions from better parent trees (IV) This seed orchard example is an extreme case, and the result will vary depending on population size and strategy (Figure 2) and

type of PP, but the mechanisms are general The conditions, assumptions and implications will be discussed further

Accuracy

Cloning is a useful way to improve precision in forward selection (e.g., Libby 1969; Burdon and Shelbourne 1974; Burdon 1986; Shaw and Hood 1985; Shelbourne 1991; Russell and Loo-Dinkins; Mullin and Park 1992; Foster 1986, 1993), while it has less impact on the accuracy of conventional genetic parameters and backward selection (Araújo et al 1996) Cloning can also resolve additional covariances among relatives, making possible the partitioning of non-additive genetic variance into dominance and epistasis components (e.g., Mullin et al 1992) The optimal distribution of clones and ramet numbers for a given overall test size will depend on genetic parameters and whether the selection objective is the total genetic gain for clonal deployment or the additive response for advancing the BP, as was considered here (e.g., de Boer et al 1994) The current studies demonstrate that clonal testing is highly effective for selection among sibs under a variety of conditions, including high levels of non-

additive variance and under inbreeding depression (I) The response compared to

phenotypic within-family selection is improved by increased selection intensity

(Figure 3) and decreased heritability Paul et al (1997) reviewed inconsistent levels,

ratios, and time trends in genetic variance components, but it seems reasonable to assume that non-additive variance for growth traits is a quarter to half of the additive variance (Wellendorf 1983; Yeh and Heaman 1987; Yanchuk 1996; Li et al 1996; Skrøppa 1996) Epistatic variance of similar magnitude was reported by Mullin and Park (1994), so the real proportions of non-additive variances were well within the ratios of non-additive to additive variance considered here

Figure 3 Ten generations accumulated additive response of within-family selection based on

clonal testing or individual phenotype, at various total test sizes per family (selection intensity)

The optimal distribution of clone and ramet number was used for each total test size N = 48;

strategy is 560 trees per parent (From Figure 9 in I).

Variation in inbreeding depression and some types of C-effects introduce error to the prediction of additive effects, but only some types of C-effects will bias the estimate of predicted breeding values from clonal tests (Libby and Jund 1962; Burdon and Shelbourne 1974; Frampton and Foster 1993; Mullin and Park 1992; Borralho and Kanowski 1995) The influence of C-effects was not investigated, but C-effects common to full- and half-sib families, and individuals within families, will bias the breeding values similarly to dominance and epistatic effects, respectively (see

Johansson et al 1993) In I, dominance effects (with 75% of the dominance variance

among and 25% within full-sib families) and epistatic effects (with all variance within families) were simulated at ratios to additive variance from 0:1 to 1:1, resulting in a reduction in the additive response of up to a 25 % Published estimates of variation due

to C-effects indicate a non-significant or small proportion of total variance, when juvenile material is propagated and traits analysed in later years (Cannell et al 1988; Farmer et al 1988; Paul et al 1993) Much can also be done to control the impact of common environment among groups of trees during propagation Thus, non-additive effects and C-effects can be present under clonal testing for additive response, but will not necessarily jeopardise its effectiveness

Polycross progeny testing of individual candidates gives unbiased estimates of breeding values and will provide a more accurate basis for selection than that on

individual phenotype While each individual progeny test tree includes only half of the additive effect, that of the tested female parent (the contribution from the polycross pollen parent will just add to the statistical error), tested ramets contain the full additive effect of the tested clone Therefore, progeny testing is less precise than clone testing at a given total test size, and an optimal distribution of tested parents and progeny per parent will result in less selection intensity and less response (Burdon and Shelbourne, 1974; Matheson and Lindgren, 1985; Danell 1991b, 1993b) For species that cannot be cloned, progeny testing of the new generation trees involves a time delay, which will reduce response per unit time Top-working scions from seedlings or young trees into mature trees can promote flowering at very early age (Bramlett and Burris 1998), and polycross pollination would then provide seed for progeny testing with minimum delay.

It should be emphasised that increased intensity and accuracy of within-family selection enhances gain without any loss of gene diversity, thus diversity use efficiency (DUE, i.e., increase in response per unit loss of gene diversity) is improved without compromising gene diversity Evaluation methods that use sib and parent information

in Index and BLUP selection to increase accuracy give higher family selection intensity and response (Henderson 1984), but co-selection of relatives also reduces

gene diversity (II, III, IV)

Effect of selection on variance – “the Bulmer effect”

The reduction of genetic response to selection, i.e., gametic phase disequilibrium, increases until an asymptote or equilibrium is approached after a few generations (Bulmer 1971) This principle is shown for random mating and the baseline settings in

Figure 4a, where the entire decline in additive variance in the first cycle is due to

selection, while in later generations inbreeding also contributed to the decline Asymptotic response is often reported to be about 25 % less than the first generation response (Wray and Hill 1989; Dekkers 1992; Villanueva et al 1993; Kerr 1998)

Generally, the reduction increases with selection accuracy (Figure 5a) and intensity

(Bulmer 1971; Mueller and James 1983b; Wray and Hill 1989; Gomez-Raya and Burnside 1990;), and is thus increased by clonal testing Further, if the decline is not considered, a higher-than-optimal weight would be given to family information in a selection index, and gene diversity would be depleted for nothing The decline in

variance due to linkage disequilibrium per se does not affect gene diversity.

0 4 8 12 16 20

Figure 4 (a) Decline in BP additive variance due to selection “the Bulmer effect” (including

decline due to inbreeding after the first cycle) under random mating (RAM) for unrestricted

CI-selection, and within-family CI-selection, and (b) the corresponding decline in response N = 48;

clone (From III)

0 20 40 60 80

Figure 5 The effect of accuracy (h 2 = 0.2 and 0.8) on (a) additive variance and (b) accumulated

Leftmost points correspond to unrestricted selection and rightmost points to within-family

selection SPM; N = 40; 50 progeny per parent, no clonal replicates (From Figure 1 in II).