Gain and Diversity in Multi-Generation
Breeding Programs
Erik W. Andersson
Dept. of Forest Genetics and Plant Physiology
Swedish University of Agricultural Sciences, SE-901 83 Umeå
Doctoral Thesis
Swedish University of Agricultural Sciences
Umeå 1999
Acta Universitatis Agriculturae Sueciae
Silvestria 95
ISSN 1401-6230
ISBN 91-576-5629-0
 Erik W. Andersson, Sjoutnäs.
Printed by: SLU, Grafiska enheten, Umeå, Sweden, 1999
II
Abstract
Andersson E.W. 1999. Gain and diversity in multi-generation breeding programs.
Doctors Dissertation.
ISSN 1401-6230, ISBN 91-576-5629-0
Progress in tree improvement comes from utilizing the genetic diversity found in
unimproved forests. The balance between genetic gain and diversity is one of the
most important considerations for all breeders. The sustainability in gain extraction
over generations of the breeding program should be considered from its start. This
thesis examines various strategies for selection in breeding. Using coancestry and its
derivatives as a diversity measure, different methods are contrasted and compared
for their efficiency in giving response to selection, considering the subsequent
change in genetic diversity. It is concluded that restricted and unrestricted
phenotypic selection and restricted (individual and family) index-selection, using
data taking the performance of relatives into account, are fairly equal in terms of
selection efficiency. However, a genuine and substantial improvement in selection
response can be achieved by incorporating information on the population structure
into the selection criterion. A possible way to enhance the efficiency in realized gain
per unit decrease in diversity is to balance selection with relatedness. This can be
seen as maximizing the allele containing capacity of the breeding population with
regards to constraints on relatedness. Two ways to accomplish this, group merit
selection and a linear programming method optimizing gain with a restriction on
group coancestry are exemplified in this thesis. Benefits from coancestry-controlled
selection are far from negligible, and can have a role to play in tree improvement.
The breeding population should be seen as a dynamic entity regarding size and
family contributions over time. A decision-model for infusion of fresh unrelated
material is presented. The conclusion is that there often could be a place for
refreshing the breeding population with new selections the first cycles of breeding.
The diversity of regeneration material affects forests over the long term. It is
concluded that diversity of species undergoing domestication must be monitored,
with comparable measures throughout the whole breeding program, including seed
producing stages.
Key words:
breeding, coancestry, genetic diversity, selection, status number,
tree improvement.
Author’s address: Erik W. Andersson, Department of Forest Genetics and Plant
Physiology, SLU, SE-901 83, Umeå, Sweden.
III
To my family
IV
Contents
INTRODUCTION .................................................................................................... 7
GOALS OF TREE IMPROVEMENT ............................................................................... 8
PROBLEM ................................................................................................................ 9
OBJECTIVE OF THE THESIS ..................................................................................... 10
THEORETICAL CONSIDERATIONS AND APPLICATIONS ...................... 11
THE BREEDING POPULATION ................................................................................. 12
MEASURES OF DIVERSITY AND EFFECTIVE POPULATION SIZE ................................ 13
Coancestry-related diversity measures ............................................................ 15
Coancestry and its implications for selection ................................................... 16
EFFECTS OF SELECTION ......................................................................................... 17
Selection ........................................................................................................... 17
Genetic improvement of desired traits.............................................................. 18
Genetic variance .............................................................................................. 18
Inbreeding ........................................................................................................ 19
Drift occurs in small populations ..................................................................... 19
BREEDING EFFICIENCY .......................................................................................... 19
STOCHASTIC SIMULATION ..................................................................................... 20
MATING ................................................................................................................ 21
RESULTS AND DISCUSSION ............................................................................. 22
SUMMARY OF PUBLICATIONS ................................................................................ 22
Phenotypic versus Index selection .................................................................... 22
Coancestry-controlled selection ....................................................................... 23
Infusion of unrelated material .......................................................................... 24
GROUP COANCESTRY AS DIVERSITY MEASURE ...................................................... 24
Accumulation of inbreeding ............................................................................. 27
TIME FACTOR IS NOT REGARDED ........................................................................... 27
BREEDING UNDER TIGHT CONSTRAINTS ................................................................ 27
CONCLUSIONS..................................................................................................... 28
SUGGESTIONS FOR FUTURE RESEARCH ................................................... 29
LITERATURE CITED .......................................................................................... 30
ACKNOWLEDGEMENTS ................................................................................... 42
V
Appendix
In the thesis, publications are referred to by their roman numerals.
List of publications included
I.
E.W. Andersson, Spanos, K.A., Mullin, T.J., Lindgren, D. (1998)
Phenotypic selection compared to restricted combined index selection for
many generations. Silva Fennica 32(2): 111-120.
II.
O. Rosvall, Andersson, E.W. (1999) Group-merit selection compared to
conventional restricted selection for trade-offs between genetic gain and
diversity. Forest Genetics 6(1): 1-14.
III.
E.W. Andersson, Sánchez-Rodríguez, L., Andersson, B. (1999) Group
Coancestry controlled selection in a Pinus sylvestris L. breeding program.
Theoretical and Applied Genetics 00: 000-000.
IV.
Y.-Q. Zheng, Andersson, E.W., Lindgren, D. (1998) A model for infusion
of unrelated material into a breeding population.
Silvae Genetica 47(2-3): 96-101.
All publications are reproduced with the publisher’s kind permission.
VI
Introduction
A legitimate expectation of forest tree improvement is that erosion of genetic
variability should be assayed and controlled. An obvious purpose (or constraint) of
tree improvement is to prevent, or at least delay, the complications following
management of small populations (e.g., Namkoong 1982, 1984; Ledig 1992; Wei
1995a; Yanchuck and Lester 1996). The goal over time can be set to get more
progress in exchange for less diversity – sooner – without impairing the present
value of the breeding program. For the manager of a tree improvement program, it
would be the simplest thing to erode diversity for rapid genetic advancements, and
the chief difficulty lies in optimizing breeding and selection activities so that genetic
variation is maintained in the population (e.g., Kerr et al. 1998).
Tree breeding consists of several activities, of which selection for the next
generation is the most apparent. Selection is a vital part of plant and livestock
improvement, and has been the subject of many studies suggesting procedures to
enhance genetic gain (e.g., Bos and Caligari 1995). Testing procedures for
prediction of breeding values and estimating genetic variance are of great
importance for decisions in a breeding program (e.g., Williams and Matheson 1994).
A number of actions influence the rate of progress and the accuracy of decisions
made. In tree breeding, accurate breeding values are time consuming to obtain
because of the time required for trees to reach economic maturity and because of the
high cost of establishing and maintaining progeny in precise field tests. Differences
between testing environments and target environments for the improved
regeneration material continues to challenge breeders.
Genetic variation in the breeding population is the raw material for long-term
breeding progress (e.g., Kang and Namkoong 1988), and, at the same time, it can
provide superior genotypes to improve selection outcome (El-Kassaby 1992). The
high variability in the breeding population is crucial for the formation of superior
seed orchards with low relatedness among seed orchard trees (El-Kassaby 1995;
Rosvall et al. 1999).
Since generation turnover is exceptionally long in conifers, a successful approach to
effective tree improvement requires effective utilization of the genetic variability at
hand (El-Kassaby 1992) and the creation of new variation by recombination. In the
search for an adequate selection criterion, the realized genetic gain per unit diversity
sacrificed is indeed an important target. This target deserves to be given more
attention in the optimization of selection procedures (e.g., Toro and Pérez-Enciso
1990; Verrier et al. 1993; Wei and Lindgren 1994; Wray and Goddard 1994;
Villanueva and Woolliams 1997; Lindgren and Mullin 1997). In order to accomplish
this, all breeding activities must be considered, from selection and testing of plus
trees, which basically is sampling genes for recombination (Cornelius 1994; III;
IV), to the survival improved seedlings in the field (Ackzell and Lindgren 1994), as
must time (Cotterill et al 1989) and cost (Lindgren et al. 1997a).
7
Most often it is assumed that there is no more refined information, such as
information from genetic markers, on specific genotypic constitution available for
breeding decisions apart from the breeding values or the phenotypic values and the
relatedness between individuals subject to selection (Wei 1995a, and references
therein). Other information affecting selection decisions is thinkable, but is generally
incorporated as breeding population size, etc. For some time now, information
derived from molecular data has had promising prospects (O’Malley and McKeand
1994; Williams and Hamrick 1995), but there are few examples of successful
implementations in forest tree breeding, at least for quantitative traits, and there are
reasons to believe that practical obstacles are not easily overcome (Strauss et al.
1992; Szmidt and Wang 1998).
Goals of tree improvement
We could categorize the purposes of forest tree improvement into four major goals:
1.
2.
3.
4.
Provide seed with a suitable physiology. Seed should be mature, have high
germination percentage, and superior growth energy (El-Kassaby 1995). While
seed orchard design and management are important factors in this respect,
fertilization and horticultural practices can improve results. Selection criteria
can include the ability to produce seed of acceptable quality.
Ensure adaptability of regeneration material. In many planting projects, fieldsurvival is a key-trait of regeneration material (Fries and Lindgren 1986). The
ability to survive critical abiotic factors is a variable character that shows a
geographic pattern (e.g., Sorensen 1992; Xie and Ying 1993; Persson 1994).
The rules of provenance transfer constructed for Sweden are of help when
regional breeding populations are assembled.
Improve the genetics of commercial traits (e.g., White et al 1993, Wei 1995a).
Progress in breeding is dependent on how well the material is known and how
well this knowledge is incorporated into decisions made in the breeding
program. Estimates of genetic variance, and thus the potential for progress, are
improved by proper design of experiments (Williams and Matheson 1994).
Conserve genetic diversity in wild and improved forests (Namkoong 1984;
Eriksson et al. 1993, 1995). The inevitable loss of genetic diversity following
domestication must not be so severe as to reduce the adaptive potential of the
improved material (White et al. 1993; Namkoong et al. 1988). Along with
genetic improvement, there is a risk that genetic destitution will be the
consequence following rather quickly from radical or shortsighted selection
(Wei 1995a; Andersson et al. 1998a).
8
The two first objectives are well foreseen in sub-arctic and temperate areas by
contemporary tree improvement. Tree improvement activities are directed by
immediate needs, and today’s improved seeds posses the required ecological
competence in areas where the climate is harsh and forest operations depend on a
reliable regeneration. This is the case, at least regarding conifers in boreal and
temperate areas (e.g., Savolainen 1996). Where not available, current methods
appear to be reassuring to work out transfer rules.
Although large efforts have been invested in research, documentation and analysis,
much remains to be done to fill the most immediate knowledge gaps in the
aforementioned third and fourth breeding goals. These two objectives are the focus
of much of today’s research and applied breeding. The third objective is complicated
by the fact that desirable traits are often conflicting (i.e., wood density and growth
rate) and by the fact that the biological mechanisms behind many traits are not
readily understood. Objective number four has been brought into greater focus
lately, promoted by development of new techniques and by a growing public
concern (Ledig 1992, Szmidt and Wang 1998).
The impact on the potential adaptability of domesticated reforestation material,
compared to unimproved material, has become the scope of investigation (Yang and
Yeh 1992, Yanchuck and Lester 1996). Breeding programs are designed to assure
inclusion of even rare alleles, and to maintain levels of heterozygosity (El-Kassaby
and Ritland 1996). The results are not convincing that reforestation with improved
material is accompanied by detrimental effects on forests and forest ecosystems
(Stoehr and El-Kassaby 1997). On the contrary, improved survival rates, vigor and
growth characterize many forests planted with improved material (e.g., Savolainen
1996) due to the increased diversity in early generation seed orchard seed (Szmidt
and Muona 1985).
The diversity of many commercially interesting species have been described by a
wealth of molecular techniques (e.g., Hamrick and Godt 1990; Williams and
Hamrick 1995; Szmidt and Wang 1998, and references therein). Development of
molecular markers and population genetics theory enables advances in this field, but
much development of theory and tools remains to be done (Szmidt and Wang 1998).
Other drawbacks are that molecular methods are too imprecise for application to
most specific breeding management problems (Strauss et al 1992).
Problem
Work optimizing gain and diversity has made clear that the tradeoff between the two
is the most important focus of breeding (e.g., Dempfle 1975; Wei 1995a,b; Brisbane
and Gibson 1995; Zheng et al 1997; I-III). It is substantially easier to select for a
single objective or an index criterion (e.g., Namkoong1970; Baker 1986; Kang and
Namkoong 1988; Bos and Caligari 1995), than to optimize selection for
contradictory goals (e.g., Quinton et al 1992; Namkoong 1982). To select
9
simultaneously for both gain and diversity is a good example of such a dilemma. It
becomes even more complex when a compromise between long-term goals and
short-term goals is sought (Wei 1995a). Breeding programs, and consequently
breeding populations, are dynamic entities where the qualities of the resulting
regeneration material are the product of many decisions over a long period. A
dynamic decision system in the breeding program, gradually incorporating new
knowledge, will be even more important in advanced generations (Wray and
Goddard 1994a; Kerr et al. 1998).
The main focus of this thesis is the complex issue of breeding efficiency in tree
improvement and possible means towards its enhancement. The question arising is
how an efficient breeding, accounting for all steps in a breeding program such as
selection of plus trees, mating and selection should be defined. By efficiency is
meant the level of realized gain compared to the amount of genetic variability lost in
the process. Diversity Use Efficiency (DUE) used in II will be synonymous to
breeding efficiency in most cases, but herein breeding efficiency is used to indicate
that all steps in the breeding process should be included when evaluating strategy
options in forest tree improvement.
Objective of the thesis
The objectives of this thesis were: (a) to construct a model describing the
compromise between gain and diversity in multi-generation breeding, and (b) to
develop methods of combining these goals in forest tree improvement.
10
Theoretical considerations and applications
Studies presented in this thesis share a common approach to some central issues in
forest tree improvement. An attempt is made to discuss the meaning of some key
concepts and their use throughout this work. The genetic status of a breeding
program is influenced by many factors such as phenotypic and genotypic variability,
allelic diversity and heterozygosity (e.g., Kitzmiller 1990; El-Kassaby 1992). These
factors can be summarized as genetic diversity in a broad sense and the focus can
vary depending on the viewpoint of the observer.
The genetic model frequently used in tree breeding is the infinitesimal genetic
model.The basic idea is that the genotype is formed by an infinite number of
individually inseparable genes, each with an infinitesimally small genotypic effect,
and each contributing only a very small fraction of the genetic variance by the
random, or random-like, transmission of alleles from generation to generation
(Fisher 1918; Wright 1921). In breeding of commercial species, the infinitesimal
genetic model has been, and still is, the prevailing concept dominating the theory of
selection (Wricke and Weber 1986; Falconer and MacKay 1996; Lynch and Walsh
1998). Traits of commercial interest are generally considered to show a quantitative
inheritance (e.g., Lynch and Walsh 1998). The use of allelic models is rare in
practical breeding, and in this thesis, no direct consideration is given to allelic
inheritance. Indirectly, group coancestry-derived diversity estimates presented
herein are convertible and equally applicable as probabilities for transmission of
alleles neutral to selection.
The model [1] used in publications I-IV is the quantitative genetic model of
composite gene action with no regard to interactions among genes, where: P is a
population mean; xi is the deviation of a family from the mean of the population; and
xi,j is the deviation of an individual from the mean of its family. The sum of these
three terms represent the genetic value of an individual, Gi,j:
Gi , j   P  xi  xi , j
[1]
The phenotypic variance observed for the population is constituted by the withinand among-family variances
VP  VF  Vw
[2]
The genetic variance is simplified, consisting only of variation in additive gene
effects; dominance effects and epistatic effects are considered to be absent. The
values chosen for different variance components in I-IV reflect plausible
heritabilities commonly reported from tree improvement programs.
11
In unrestricted phenotypic selection (PS, selection for phenotypic value), individuals
are ranked on the basis of their phenotypic value, and the best are chosen
irrespective of their relationship to other selected individuals. In restricted
combined-index selection (CIS, selection for breeding value), estimates of individual
breeding values are made more accurate by taking into account the performance of
relatives, while the numbers of selected relatives is limited to some preset number.
In the genetic model used in publications I-IV, family means are given by the mean
value of their progeny (Falconer and MacKay 1996). Mortality in the field, pests or
similar catastrophic events are not specifically considered. Evaluations are generally
conducted on predictions for a single quantitative trait, which can itself be a
weighted index composed of several quantitative traits (e.g., a tree’s volume,
straightness and health can be combined in a single breeding value).
In real-life breeding, individuals are not selected or rejected on the basis of their
superiority or inferiority for height or growth. The basis for selection is sometimes
modified by categorical assessments, so that individuals or families with inferior
qualitative attributes, or prone to damage from pest or disease, are rejected. This
negative selection is generally conducted without being specifically incorporated
into selection indexes (Zobel and Talbert 1984).
The breeding population
By ”breeding population” is generally meant the individuals that contribute as
parents to the next generation (e.g., Zobel and Talbert 1984), though it may be
confused with the set of potential parents that still have chance to contribute with
their genes. When breeders talk in general terms about the breeding population, they
may also be referring to potential candidates for the next generation, prior to
selection (e.g., Cotterill 1986).
A breeding population may or may not be structured. In some programs, individuals
may form a single group of inter-mating parents (Zobel and Talbert 1984; Cotterill
1986). Alternatively, the population may be divided into sub-populations, or
sublines (Burdon and Namkoong 1983; McKeand and Beineke 1980). Subdivision
may be random, or on the basis of geographic origin or breeding value, for the
purpose of managing genetic diversity (Williams et al 1995; Eriksson et al. 1993,
1995). The sub-lines may be bred to serve a specific purpose (e.g., Namkoong 1984;
Namkoong et al. 1988; Burley 1994), or they may be randomly assigned replicates
for the purpose of managing inbreeding in seed orchards (Lowe and van Buijtenen
1986; van Buijtenen and Lowe 1979). Other concepts for structured breeding
populations include ”nucleus” breeding (Namkoong et al. 1988), and ”elite-line”
breeding (Cotterill et al. 1989). The objective may be to retrieve genetically superior
individuals from the elite (Namkoong 1982), while maintaining the necessary
diversity in the main population.
12
The size of the breeding population is generally limited by budget constraints
(Lindgren 1997a). The idea of a larger breeding population in the initial phase has
been suggested in tree improvement by Lindgren et al (1997a) and for animal
breeding by Verrier et al. (1993), among others. This concept is investigated further
for a specific target level of group coancestry in publication III, where the concept
of a variable breeding population size is discussed. The idea is to determine the level
of group coancestry acceptable over the long term (Kerr et al 1998; Rosvall et al.
1999), and then to optimize the breeding population size accordingly.
Measures of diversity and effective population size
The reasons for monitoring diversity in forest tree improvement are many.
Arguments listed are, among others: that vulnerability to pests and other stresses
increases as genetic diversity is diminished; that a potential for altered breeding
goals in the future requires an inherent diversity in the breeding population; and that
the stability of future ecosystems can be threatened by the loss of diversity within a
species, that might lead to a loss of species in certain systems. In principle, there are
two approaches to maintain the necessary diversity for tomorrow’s forests: in situ
and ex situ conservation (Frankel and Soulé 1981). Yang and Yeh (1992) argue that,
while ex situ conservation is convenient for breeders in the short-term, in situ
conservation, within breeding programs, will provide greater potential to meet needs
of an uncertain future. Forest tree breeding is still in its infancy and as yet has
contributed little to the erosion of genetic resources, at least compared to other crop
and animal breeding programs, which reduces the risk in the foreseeable future in
many respects.
Differences in genetic constitution among individuals constitute the raw material
exploited by selection (Wright 1931). Knowledge about the level of diversity present
and its changes are of crucial importance for breeding (Caballero 1994). A useful
diversity measure should posses several desired properties, including:






simplicity;
ability to make comparisons between generations;
ability to handle overlapping generations;
ability to handle merged and split populations;
ability to handle breeding populations of variable size; and
ability to handle variations in the number of gametes and progeny transmitted
by different parents.
Most of the previous characteristics could be expressed as ”sensitivity” to variation
in demographic structure, mating system and gene migration. While a number of
diversity measures have been suggested, only a few remain in use in practical
breeding. Wright (1931, 1938) first defined the concept of ”effective population
size”, based on the magnitude of random genetic drift in an idealized population.
Wright worked with small populations, and the concept has been widely applied
(e.g., Lynch and Walsh 1998). Traditionally, the effective population size has been
13
defined as the ”number of individuals that would give rise to the sampling variance
or the rate of inbreeding appropriate to the conditions under consideration if they
bred in the manner of an idealized population” (Falconer and MacKay 1996).
Examples of such measures of effective population size have been: the inbreeding
effective number, measuring the change in average inbreeding (Kimura and Crow
1963a); the variance effective number, describing the change in variance in allele
frequency (Kimura and Crow 1963b); and the eigenvalue effective number,
measuring the rate of loss of heterozygosity (Ewens 1982). Recently, Wang (1996)
added a coancestry effective number. Modifications of the effective population size
concept have been presented and proven useful in quantitative genetics, population
genetics and in breeding of species with different reproductive systems (e.g.,
Robertson 1961; Ugarte et al. 1990; Caballero 1994; Ebbersten 1996).
The effective population size, in the conventional sense, is a rate of change, which is
averaged over generations. It does not refer to a single generation, but rather the
connection between generations. The traditional use of effective population size is
thus not a description of the ”state” of a population (Lindgren et al. 1996).
Tree breeding is not restricted to discrete generations due to the longevity of trees.
The option to deploy a breeding strategy including overlapping generations is
plausible, should the incentive occur. The theory concerning estimates of effective
population size of breeding situations involving overlapping generations becomes
quite different (Ebbersten 1996), although theoretical problems in estimating the
effective population size under such situations have been solved for simple cases.
The need for a measure describing the state of the breeding population is mostly due
to the fact that, apart from different selection alternatives, different mating systems
often are options in breeding (e.g., Toro and Peréz-Enzisco 1990; Caballero et al.
1996), and that the composition of the gamete pool can be affected by different
mating systems in subsequent generations (Lindgren and Mullin, 1998). The
traditional measures for effective population size measure deviations from an
idealized reference population with assumptions of specific patterns of gene flow
(Wright 1969). This is a complication in breeding where crosses often are controlled
and seen as a means to control genetic parameters (e.g., De Roo 1988; Villanueva et
al. 1994; Santiago and Caballero 1995). Furthermore, the gene-flow assumptions for
an idealized population are virtually never fulfilled in breeding populations
(Lindgren et al. 1996), nor in seed orchards (Eriksson et al. 1973), nor in the wild
(Wright, 1969). The complication caused by failure to satisfy these assumptions can
be circumvented by using the pedigree as a source for information about crosses
performed and for the estimates of overall genetic diversity (Lindgren et al 1996).
14
Coancestry-related diversity measures
By coancestry is meant the likelihood that two randomly chosen genes (chromosome
fragments) are identical due to common ancestry (Cockerham 1967). If this sampled
is performed in a population, Cockerham’s group coancestry [3], which is the mean
of all entries in the coancestry matrix, will estimate this probability correctly. It is
worth noting that Cockerham’s group coancestry is not dependent on how gametes
actually unite in the next generation.
For most situations in breeding, group coancestry-derived diversity measures are
directly comparable and the measures themselves are tightly linked to variance
effective population size (Lindgren and Mullin 1998). The status effective number
(Lindgren et al. 1996) is half the inverse of Cockerham’s group coancestry [4]
(Cockerham 1967). In all publications (I-V), group coancestry is used as the
measure of overall genetic diversity, and is the average of all entries in the
coancestry matrix, including the self coancestry of the individual, as well as that of
reciprocals (Cockerham 1967, 1969):

1
n2

i
[3]
i, j
j
Expressed as a function of Cockerham’s group coancestry, the effective population
size, or status number (Lindgren et al. 1995) is
Ns 
0 .5
,

[4]
where Ns is the status number. This seems intuitively appealing for conifers and for
most out-crossing hardwoods, and reflects the possible zygotic combinations
(Lindgren et al 1996). Breeders have the possibility to delay inbreeding by focusing
on the mating structure of the breeding population (Sánchez-Rodríguez et al. 1999),
and of the seed orchard (El-Kassaby and Reynolds 1990), thereby affecting
inbreeding in the regeneration material (Xie and Knowles 1994; Rosvall et al. 1999).
The most obvious way of accomplishing such a delay of inbreeding is, apart from
restrictions on selection within and among families, a strict control of the crosses
performed, thereby affecting to some extent the accumulation of relatedness in the
breeding population (Caballero et al. 1996; Villanueva et al. 1996; SánchezRodríguez et al. 1999). Estimates of coancestry-derived diversity measures are
straight forward, and only slightly more complicated when individuals from
previous generations are included in the breeding population or seed orchard,
(Lindgren et al. 1996), which supports the choice of the coancestry-based methods
used in this thesis. In a way, a seed orchard, where new clones are infused through
its operational life from the next generation in the breeding program, can be seen as
constituted of overlapping generations.
15
Coancestry and its implications for selection
In terms of diversity following selection, the status number indicates the quantity of
genetic information (or more precisely the potential to contain alleles within a
population), originally represented by the founders, that likely remains in the
(selected) progeny/population. For two unrelated parents, the status number (Ns) of
their first full-sib progeny will be 1, for their first two the Ns will be 1.33, and so on,
asymptotically approaching Ns = 2 for a full-sib family of infinite size. This is due to
the effect of sampling random genes by a limited number of offspring. The pair-wise
coancestries, as well as the group coancestry of the breeding population, are both
informative parameters describing the accumulation of relatedness in a population,
and hence the potential inbreeding indicated by ‘real’ random mating (e.g.,
Cockerham 1967; Ballou and Lacy 1995). It can also be phrased the other way: the
change in diversity is proportional to the increase in group coancestry. It reflects
how the allele-containing capacity of a population is affected by selection and
mating. The ability to carry allelic variants is the inverse of group coancestry, or two
times the status number of an individual or population. The group coancestry
approaches 1 asymptotically after an infinite number of generations of mating and
selection in a closed population due to final fixation of one allele per locus. Parallel
to this, the status number is reduced to 0.5, indicating that all genetic variability is
exhausted and that the population in genetic terms can be seen as equivalent to a
single gamete (Lindgren et al. 1996). When selection strategies are compared, the
strategy that maintains the status number at a higher level is the one that preserves
more of the original genetic variation (Askew and Burrows 1983; Ballou and Lacy
1995; Lindgren et al. 1996).
In Figure 1, we see that when a pedigree is initiated, the decline in the allelecontaining capacity is rapid, but that it levels out quickly. This rapid decline given
by the model probably leads us to the conclusion that it reflects a factual event. In a
way it does, since it illustrates the reduction in the capacity to contain alleles in a
closed population if the pedigree is known. In this particular case, the characteristics
of the breeding population are: size = 50, h2 = 0.2, non-assortative mating is
employed and within-family selection is carried out to sustain the breeding
population size. The event illustrated in Figure 1 is not readily interpreted in a
biological sense, and will be different for different species and populations since the
actual number of gene varieties in a population is much smaller than the census
number. Inbreeding and coancestry values are frequently used to describe the level
of relatedness in a population. A population’s group coancestry is relative to some
reference population, which by definition is non-inbred and non-related. This is the
definition of point zero on a relative scale (leftmost point in Figure 1). The genetic
erosion indicated by the increase in group coancestry is thus relative to our
assumption of unrelatedness in the "wild" forest. This is useful for comparisons
among different options considered in the management of the breeding population,
although the concept has its limitations and may be less useful for other applications.
16
Allele-containing capacity and gene diversity
Fraction of ACC and GD present
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0
1
2
3
4
5
6
Generation
Figure 1. Breeding gradually reduces the maximum allele-containing capacity
(ACC = ♦) and the maximum gene diversity (GD = ■) of a breeding population.
This is an example of within-family selection for five generations
Effects of selection
Selection
Artificial selection affects the genetic variability and the relative size of variance
components of a breeding population (e.g., Bulmer 1971; Harris 1982; Namkoong
and Roberds 1982). Repeated recurrent selection can give a sustainable response
under certain limitations (Gomez-Raya and Burnside 1990; Dudley and Lambert
1992). The limits to selection are predictable if a species is responding according to
the infinitesimal genetic model (Robertson 1960; Crow and Kimura 1979). After a
number of generations, other factors that are not included in the model will become
increasingly important, e.g., escalating inbreeding depression (Burrows 1984a,b;
Kang 1989; Leitch et al 1992; Williams and Savolainen 1995), or altered adaptivity
(Kang and Nienstaedt 1987; Kitzmiller 1990). Selection means that deleterious or
yield-reducing alleles are gradually removed. It can also be that relatively rare
alleles in the breeding population are favored, and that their increasing abundance in
the population at different stages will give a selection response that was not foreseen
17
from initial estimates of the genetic variance. This phenomenon is sometimes
referred to as the ”breeding window". The breeding window describes the
phenomenon whereby genes that are rare or abundant in a population do not
contribute much to the genetic variance in that population.
Genetic improvement of desired traits
Selection alters the performance of individuals and populations by changing gene
frequencies (e.g., Wright 1969; Crow and Kimura 1970). Selection can be effective
in altering gene frequencies if there is a strong correlation between the phenotype
and the genotype, and more so if the character is affected by a small number of
genes (Falconer and MacKay 1996). Most characters of commercial interest are,
however, thought to be affected by a large number of genes (e.g., Zobel and Talbert
1984; Namkoong et al 1988; Lynch and Walsh 1998). Along with the additive
genetic effect, there are also other variance components emanating from composite
gene action. Dominance effects, epistatic effects and pleiotropic effects may all
affect phenotypic expression and hence the relevance of the simplified quantitative
model assumed in I-IV.
The target to be maximized is generally a quantitative trait or index of traits (e.g.,
Bulmer 1980; Baker 1986; Wricke and Weber 1986). The index is likely to follow
what can be expected from the quantitative model, even if an included trait deviates
from the assumed quantitative model. Estimation of breeding values is a vital part of
breeding, but there is a substantial risk of overestimating genetic differences among
individuals and families as well as the response to selection if the phenotypic values
are used as-measured (Henderson 1963), both for unrelated families and individuals
and when families and individuals are related (Henderson 1975).
Genetic variance
Low heritability and large population size are factors that generally help to preserve
genetic variance (e.g., Spanos et al. 1996; I; II). Different selection methods, such as
PS or CIS, have little impact on the retained genetic variance when compared at the
same diversity (I; II), but in combination with for example assortative mating, the
effects are significant (Bulmer 1971; Baker 1973). Estimates of genetic variance are
important for estimates of heritability as well as predictions of future gain potential
(Harris 1982; Gomez-Raya and Burnside 1990). Genetic variance is a moving target
in the long-term perspective. Nevertheless, there are examples that show that the
production limit may not be well described by estimates of the genetic variance in
early generations, and Dudley and Lambert (1992) used historical data to
demonstrate seemingly inexhaustible response to selection in maize after 90
generations .
18
Inbreeding
Inbreeding is generally not desired in reforestation material (Kang and Namkoong
1988; El-Kassaby 1995; Harju 1995). It is, however, important to point out the
difference between inbreeding in the breeding population (Williams and Savolainen
1996) and in the production population (Lindgren and Mullin 1998). With proper
design in orchard composition and spatial arrangement, inbreeding can be delayed in
the seed crop, even if inbreeding is substantial in the parent population (Eriksson et
al 1973; Lindgren and El-Kassaby 1989; Xie and Knowles 1994). It may be further
reduced by supplemental pollination (El-Kassaby and Reynolds 1990) and pollen
contamination (Rudin and Lindgren 1977; El-Kassaby 1995; Xie and Knowles 1994;
Harju 1995; Lindgren et al. 1995). Inbreeding within the breeding population can
also be controlled by mate allocation (Toro and Perez-Encisco 1990; Caballero et al.
1996; Meuwissen 1997; Kerr et al 1998).
Drift occurs in small populations
The potential to carry alleles is proportional to the size of the population (e.g.,
Kimura and Crow 1964), and the potential allele-containing capacity decreases even
more if the population becomes so small that stochastic events play a significant role
(e.g., Haldane and Waddlington 1931; Boichard et al. 1997). Genetic drift can be
described as the random deviation in allele frequencies observed in small
populations from what would be expected in a population of infinite size (Crow and
Kimura 1979). This means that there is an increased chance of extinction and
fixation of alleles in small populations for stochastic reasons (e.g., Chevalet and de
Rochambeau 1985; Allendorf 1986), a phenomenon which is more serious in
breeding where maintaining genetic variability is the key to sustainable progress
(Caballero et al. 1991). Another side of the same stochastic phenomenon is that the
frequency of relatively rare alleles may be elevated to a higher frequency and even
fixed by chance. Drift has a greater impact on those alleles that are either very rare
or very common, and less impact on those alleles found at more intermediate
frequencies. Tree breeding population sizes are generally on the edge where
stochastic events could or could not be subject to considerable stochastic shifts in
gene frequencies (Namkoong et al. 1988; Aggrey et al. 1995).
Breeding efficiency
The wide use and indisputable success of mass selection on phenotype is familiar
from centuries of domestication of animals and agricultural crops (e.g., Burton
1974a, b; Dudley and Lambert 1992). Examples from early breeding illustrate that
breeding can be successful without necessarily being efficient, at least for species
with a short generation cycle and a high variability. When evaluating the relative
efficiency of alternatives in tree improvement, where generation turn-over time is
typically long, it seems important to have a model for diversity that enables precise
estimates, not only for the realized genetic gain, but more so for the diversity
19
consumed by one or more steps considered simultaneously in the breeding process
(e.g., Lindgren et al. 1996; Kerr et al. 1998).
Breeding efficiency is a concept in need of a concise definition, something that is
not easily accomplished. By breeding efficiency is meant the progress in additive
genetic gain per unit of diversity lost. It is a measure of conversion efficiency of
variation to gain (DUE in II). For the purpose of comparison, efficiency of selection
(E) can be defined as:
E
G

[5]
where G is the progress, and is the group coancestry. The increase in  is a
consequence of selection and mating, and reflects the overall effect from the
build-up of relatedness of artificial breeding. The benefits of this efficiency measure
are mainly that it is consistent for different population sizes, and that it enables
comparisons across generations.
A method suggested by Lindgren and Mullin (1997), called ‘population merit
selection’ and later referred to as ‘group merit selection’ (GMS) (Zheng et al, 1997;
II; IV) incorporates a penalty factor, or weight, on group coancestry during
selection. The penalty factor could be chosen to attain a desired diversity. The
optimal tradeoff between gain and diversity cannot be given generally, but for any
penalty factor, c, the efficiency of selection will be maximized. Arguments can be
raised that the algorithm used for demonstration purposes by Lindgren and Mullin
(1997) is giving no insight to the relationship of gain relative to coancestry, or that
considerable trial-and-error is required to target a desired . Nevertheless, the
method has been shown to give at least as much gain as any other heuristic method
(Lindgren and Mullin, 1997).
In III, we suggest the use of integer linear programming (ILP), as an alternative
procedure to optimize group merit. ILP is a versatile method, despite requiring
considerable time while searching for the optimum. It appears likely that both
optimization methods would render the same set of selections, given the same
restrictions.
Stochastic simulation
Stochastic simulation has proven to be a useful tool in genetics (Levin 1969) and has
found a role in forest tree improvement (e.g., King and Johnson 1993; Mahalovich
1990). Real-life breeding programs are never repeated and resource limitations
prohibit trials with wild ideas. Stochastic simulation was the approach taken in
publications I and II, where the decision-support tool POPSIM (Mullin and Park
1995) was used. The simulator can be set for high resolution in the comparison, i.e.,
by starting with identical individuals in the populations, something that is virtually
20
impossible to achieve in field studies. This computer software tool incorporates
many features of real-life tree improvement programs, and the versatility of the
software goes far beyond the scope of I and II. In publications III and IV,
simulations were programmed by the authors
If there is reason to believe that the quantitative model describes the behavior of a
population under study, then the possibility to repeat many times the simulation of a
given breeding plan enables even minute differences between alternative strategies
to be identified. A number of such minor effects can easily add up and lead to
substantial losses in output from the breeding program. Despite its advantages,
simulation is insensitive to biological factors that are often not represented in simple
quantitative models, such as inbreeding depression, and its power to foresee the
future selection response should not be overemphasized (Clegg 1997).
Mating
Mating designs have an impact on selection response and thus on the diversity
following selection (e.g., Kimura and Crow 1963a; Kinghorn 1987; Caballero et al.
1996; Sánchez Rodríguez et al. 1999). The chance that a candidate for selection will
actually be selected is dependent on its phenotype, the breeding values of its parents
and its relationship to other selected individuals. In the first generation, when no
prior relationships are known, the group coancestry of the progeny population
eligible for selection to the next generation will be the same, irrespective of how
parents are mated (provided all parents contribute the same number of gametes).
Since the incentives for selecting an individual candidate will depend on how
parents with different breeding values are crossed, and on how family means are
distributed, the mate allocation will not be without importance. In principle, there
are two ways to allocate crosses: random and non-random (e.g., Baker 1973). The
mating design implemented will have an impact on the relative size of within- and
among-family variance components (e.g., Bulmer 1980; II; III)
The effects of different mating systems, such as assortative and non-assortative
mating, on selection responses and on the accumulation of relatedness have been
investigated (Nagilaki 1971; Tallis and Leppard 1992; Garcia and Sánchez
Rodríguez 1992). There are several ways to pursue non-random mating for specific
purposes in breeding, including minimum coancestry, compensatory, and factorial
mating (Wright 1921; De Roo 1988; Toro and Peréz-Encisco 1990; Villanueva et al.
1994; Santiago and Caballero 1995; Caballero et al. 1996). Different methods for
mating optimization are also available, e.g., integer linear programming (Jansen and
Wilton 1985; Toro et al. 1988), and simulated annealing (Kerr et al. 1998).
21
Results and discussion
Summary of publications
Phenotypic versus Index selection
The efficiency of combined-index selection compared to phenotypic selection was
investigated by simulation in I, covering genetic gain and diversity for five
generations. The tool for simulation used was POPSIM ver. 2.4 by Mullin and Park
(1995), enabling comprehensive comparisons of the two selection strategies.
Phenotypic selection proves to be a fail-safe method for artificial selection (Burton
1974a,b; Wei 1995b), and performs well in terms of selection efficiency, compared
with methods that take family data into account (Dempfle 1990), if comparisons are
made at a similar level of overall genetic diversity. This had been shown earlier for
the one-generation case finite case (Andersson et al 1998a,b), and for a finite-family
and multi-generation case (Belonsky and Kennedy 1988; Verrier et al. 1993). Wei
(1995a) drew similar conclusions in a series of publications, mostly under an
assumption of infinite numbers of families of infinite size. Tools employed in this
thesis (i.e., group coancestry) made it possible to verify these findings for the finite
case under circumstances that resemble more closely real-life tree breeding
programs.
Results in I show that, for moderate to high heritability, unrestricted phenotypic
selection is about as efficient as is combined-index selection, when compared at the
same level of diversity, a finding that is supported in Andersson et al. (1998a,b).
Combined-index selection, however, has an advantage in terms of selection
efficiency in cases where the heritability is low, especially for large family sizes
(Andersson et al. 1998b). Spanos et al. (1996) extended the comparisons to restricted
phenotypic selection for a wide variety of heritabilites, family sizes and breeding
population sizes, reporting both for gain and residual additive genetic variance.
Generally, there were no important differences in selection efficiency observed.
This is an encouraging result, not only for the extensive types of breeding program
suitable for developing countries (Cotterill 1986), but also for species where detailed
information on family structure is difficult to register (Burley 1994). Examples of
this are breeding programs with open pollination (Cotterill 1986; Bila and Lindgren
1998). It is also evident that nature itself, if such a generalization can be justified,
has been successful performing selection solely on the phenotype, and for apparent
reasons no species in nature can afford a misuse of its within-species diversity. In
this context it should be remembered that phenotypic selection under natural
circumstances gives moderate progress in large populations when conditions are
stable, and more rapid change in the phenotypic mean when population sizes are
small or when there is a directional selection pressure (Wright 1969; Ewens 1989).
22
Coancestry-controlled selection
II and III focus on various aspects of group coancestry-controlled selection. There
has been extensive research in this field, initiated by animal geneticists who have
presented a number of strategies for selection aimed at reducing either inbreeding or
average coancestry. Models presented for animal breeding have all been valuable
contributions to selection theory in tree improvement.
In II, a study is made of the properties of group-merit selection (GMS). GMS is a
superior method compared to conventional restrictions on relatives, for all levels of
resulting diversity, with the exception of the extreme maximum or minimum, where
the two methods give identical results (Lindgren and Mullin 1997). GMS thus
maximizes the rate of conversion of genetic diversity to breeding progress. One
conclusion in II is that a more conservative selection strategy (a higher weight on
group coancestry) is to be preferred the further into the future we aim to optimize the
breeding program. This is also supported by intuition – the longer the time
perspective, the more critical it would be to reject individuals early in the breeding
program.
One conclusion would be that GMS very well can be the method of choice for the
solicitous breeder, since it is virtually impossible to restart the breeding program due
to a too-early exhaustion of the genetic variability. The qualities of individuals
suitable for the seed orchards will remain practically unaffected by this small
modification of the selection strategy (II).
Another method of achieving identical results, but with more flexibility in terms of
selected individuals per family, is by imposing restrictions on group coancestry by
means of linear programming. A linear model was used in III for selection with a
constraint on coancestry. In III, we show how an optimal initiation of a breeding
program could be achieved, while taking advantage of a large testing effort from a
large number of wild plus trees. It is shown that gain can be maximized while
applying constraints on group coancestry, both for fixed and variable population
size. The optimal solution is a compromise between additional contributions from
the best families giving a substantial increase in gain, and contributions from the
families that would have been excluded by within-family selection. Earlier, linear
programming in breeding has been used by Jansen and Wilton (1985) for mate
allocation. Toro and Pérez-Encisco (1990) combined selection and mating for
simultaneous optimization by linear programming, and Sanchéz et al (1999) used the
method for mating and selection in Drosophila.
It appears beneficial to plan a breeding program based on the long-term benefit
desired (Wray and Goddard 1994; Lindgren and Mullin 1998; Kerr et al 1998; II).
The tendency is that the longer is the time perspective, the higher the weight that
should be given to maintaining genetic diversity in the breeding population
(Brisbane and Gibson 1995; II). When defining the long-term goal for the breeding
program, it seems a paradox that the selection that gives the highest selection
23
response in the long time horizon appears to be the most restricted in early
generations (Rosvall et al 1999). In real-world situations, where an interest rate often
is set on money invested in breeding, it is obvious that a compromise has to be made
between long- and short-term benefits (Lindgren 1995, III).
Infusion of unrelated material
Infusion of unrelated material into a breeding population is considered in publication
IV. In many breeding programs, inferior genotypes can be identified only after
screening, and at the same time there is an abundance of untested plus trees available
in the wild forest. Replacement with additional wild selections might be an option
(El-Kassaby and Ritland 1996), or exchange of material could be made between
breeding populations (Eriksson et al 1993). The principle is that by early
replacement, the infused individual gives not only an increased mean performance,
but also an increased potential for breeding advancement by adding new genes, and
reduces the accumulated inbreeding in the breeding population (El-Kassaby and
Ritland 1996). It should be kept in mind that the infused material has little effect on
the prospect of finding clones for a superior seed orchard, as it replaces the worstperforming quartile of the breeding population. In later generations, the incentives
for infusion will be enervated, due to the increasing differences between the
improved breeding population and the unimproved plus-trees. The example in IV is
for untested plus-trees, but the approach has, in principle, a potential for programs
with an abundance of tested candidates that were earlier rejected.
Conclusions drawn from IV are that replacement of individuals in a breeding
program is dependent on a number of factors such as initial number of individuals in
the breeding program versus the targeted number of individuals in later generations.
Heritability, genetic value and family size are other factors influencing the
incentives for replacement. Other factors affecting the optimal number of
replacements are relatedness in the breeding population, inbreeding and the
relationship between coancestry within and among full-sib families. One finding is
that a general recommendation on infusion of fresh material into a breeding
population is difficult to make from the specific example given, although it seems
likely that infusion is recommended to some extent in most situations. The need for
infusion is affected by testing procedures, and on the precision of testing.
Replacements are more likely to be beneficial in breeding programs involving
progeny testing. In publication IV, it is illustrated that the option to infuse new
material is not an option after some generations without purging much of the
realized genetic gain.
Group coancestry as diversity measure
One of the major advantages of using status number, and the corresponding diversity
measures derived from group coancestry, is that they give a precise comparison of
the reduction in genetic diversity between alternative breeding strategies for a
breeding population due to recent relatedness. The accumulation of coancestry is
accounted for, irrespective of initial relatedness in the population that has its origin
24
prior to the pedigree record. This is an important feature, since the assumption that
selected plus trees are unrelated and non-inbred rests on shaky ground (Lindgren et
al. 1996). Methods to address the problem with initial relatedness have been
proposed for maize by Bernardo (1993), for monkeyflowers by Ritland (1996), and
for a variety of other species (e.g., Isabel et al. 1995). In Scots pine, it is an
established fact that there is a family structure in forest stands (Szmidt 1984;
Yazdani 1985; Mouna and Harju 1989). These investigations have been performed
with various types of genetic markers, assuming a correlation between registered
characteristics, the nucleotide sequence and the genetic background. However, the
interpretation of marker-based estimates on relatedness is not obvious, but
development in this area is rapid and might shed light on possible ways to
incorporate marker data into coancestry estimates. The assumption that conifers are
unrelated when selected for a breeding program implies some conclusions, leading
to awkward insights, such as:




an additional tree introduced into the breeding population will give a constant
contribution to diversity. This follows from the definition;
diversity is infinite in the reference forest where trees are sampled, because the
allele-containing capacity is confused with actual diversity, even though the two
concepts are not comparable;
the decline of genetic diversity will depend on when we start the breeding
program, so that if the ‘cost’ of declining diversity is infinite, then the present
value of the breeding program would be maximized by postponing the initiation
indefinitely; and
generation shifts and the formation of a family structure in the wild forest do not
lead to a build-up of relatedness among trees and, thus, no decline in genetic
diversity.
By working with group coancestry and its derivatives, there is an opening for a
theory that would enable a comparison of the domesticated forest with a wild
reference. This could be expressed through an assumed base level of relatedness
among the trees in natural stands, rather than the assumption that trees are unrelated.
Such a reasoning would assume the existence of a functional similarity between
genes ‘identical by state’ and those ‘identical by descent’. The focus of such theory
would be to describe a plausible level of initial coancestry in the sample of founder
trees. Another way to view the effects of increasing group coancestry in breeding
populations is by proportion gene diversity (GD), given by:
GD  1    1 
1
2  NS
[6]
GD will be 1 for an unrelated population of infinite size. If, after a number of
generations a breeding program leads to a reduction of Ns by 90 %, the GD would
drop to
25
GD 1
1
 0.95
2  0.1  N S
[7]
This reduction may be perceived as much less drastic, and indicates perhaps more
accurately the actual decline of the genetic base in the breeding population. One
draw-back is that if Θ is the likelihood of sampling genes identical by descent, 1-Θ
will be the likelihood that they are not identical by descent, even if there only exists
a limited number of allelic varieties in the population. Beyond being less drastic,
gene diversity is devoid of information on the genetic constitution of the population,
saying no more than group coancestry or status number.
The level of initial coancestry appears to be less important than the consequences of
departing from the idea of ‘unrelatedness’ in the reference population, since even
very low levels of initial average coancestry will have drastic effects on estimates of
status number of a population (or species). If, for example, a base coancestry of 0.01
was assumed, the status number for an infinite population would be 50, while 50
selected candidate trees would have a status number of 25, rather than 50. Finally,
the status number would coincide with the (average) number of alleles per
polymorphic locus. After accepting this view, the consequences of breeding on
diversity would appear much less severe and more readily understood,
corresponding better with results from biochemical studies of allelic diversity (e.g.,
Hamrick and Godt 1990). The consequence would be, even for an assumption of
moderate relatedness among randomly chosen trees in the forest, that the focus
would shift from the diversity aspect as the prevailing restriction to a focus on
realized genetic gain and long-term productivity in the domesticated forest. A
similar remark has been made by Danell (1993a), asking the question if we are “too
concerned conservationists but too unproductive breeders.”
Regardless of the actual diversity in tree species undergoing domestication, the
general conclusion from I-IV is that the efficiency of tree breeding can be assessed
by benchmarking how the allele-containing capacity of the breeding population is
managed, for different breeding alternatives. For this, we appear to have a functional
model as used in publications I-IV, although there probably are conclusions that lie
hidden in the results which we at the moment are unable to draw. The concept of
coancestry-derived diversity measures, applied in publications I–IV, has the
appealing feature of economizing as conservatively as possible with the amount of
genetic information available for the breeding population at a certain stage of its
domestication. Irrespective of the actual number of functional alleles in the wild and
in the sampled population, this is seemingly an attractive way to deal with this
uncertainty.
26
Accumulation of inbreeding
One of the most crucial aspects in the long perspective is to avoid inbreeding (Toro
et al 1988; Meuvissen 1997). Rosvall et al (1999) simulated the Swedish breeding
program for ten generations and demonstrated that a group coancestry increasing
with 1.21% per generation, for each breeding zone in a multiple population breeding
program, can be accepted without severe inbreeding problems, neither in the
breeding population nor in the production population. That result was obtained by
applying GMS, and would be more efficient in terms of gain per diversity than, for
instance, within-family selection, which has been heretofore regarded as the main
alternative (Danell 1993b). This finding agrees with parallel work by animal
breeders working with predefined rates of inbreeding (e.g., Meuwissen 1997;
Sánchez Rodríguez et al. 1999).
Time factor is not regarded
This thesis makes comparisons between selection methods, something which is
complicated by the fact that the present value of the components in the target
function – gain and diversity – are thought to have the same time horizon. The profit
from increased growth will be realized within a relatively short time horizon, while
the cost of lost genetic diversity partly lies far into the future. One could imagine
phrasing an objective for present value, but the rotation and the following estimate
of benefits from an improved forest bring over-whelming uncertainties. It has not
been within the scope of this work to address this question, meaning that the drop in
status number, or allele-containing capacity, becomes visible without delay, while
the possible biological effects are likely to be delayed.
Breeding under tight constraints
In developing countries, where the continuity of resources are unpredictable,
phenotypic selection has its benefits. Even in the simplest breeding programs there
will be progress, and in terms of management of the genetic capital, the efficiency is
in most cases, just as high. In such cases, the process of extracting genetic gain will
be a little slower if we do not have complete pedigrees and thus are forced to select
on the phenotype, although use of family means offers a way to moderate the
accumulation of coancestry following selection (Lush 1947). There are some cases
where selection on the phenotype can be recommended as an efficient and robust
selection method:



when crosses are difficult to record and/or the pedigrees are incomplete;
when population or progeny sizes are small; or
when the heritabilities are moderate to high.
However, in cases where the pedigree is known, we generally do better with
coancestry-controlled selection (II-IV), and in such cases, restricted combined-index
selection will not appear as the most favourable alternative either.
27
Conclusions
With current knowledge about the efficiency of selection, as defined in this thesis
(e.g., I-IV; Andersson et al 1998a,b), breeding programs appear to be more-or-less
equally efficient, irrespective of the selection procedure chosen. GMS and similar
approaches (II–IV) do give an enhancement in selection efficiency, but at the same
time it appears difficult to optimize more than a very limited number of decisions at
the time in breeding. However, methods at hand give us good opportunities to
moderate the rate of progress to suit our purposes.
In terms of breeding efficiency in the broader sense, there are no evident shortcuts to
a higher effectiveness. Even in situations where information on pedigrees is not
readily available, the pursuit of genetic gain requires that selection be conducted.
The efficiency of selecting on individual phenotype is, in most cases, as efficient
(from a diversity-use point-of-view) as when information on relatives (i.e.,
progenies) is used to predict breeding values, even if progress is slower per unit
time. For low heritabilities and/or large family sizes, greater weight is placed on the
family mean, and in such cases (restricted) combined-index selection is the preferred
method for greatest efficiency, if group-coancestry guided selection cannot be
conducted.
In order to get a geniune enhancement of selection efficiency, more sophisticated
selection methods that regulate group coancestry, such as GMS, must be employed.
An better start to a breeding program can be achieved either by a larger breeding
population size in the first generation (III), or by replacements in later generations
(IV). Rules of thumb for the optimal size in the first generation, optimal number of
replacements, or how these individuals should be composed seem unattainable from
results presented in this thesis, except in a very general sense. Each breeding
population has a its own population-specific parameters, and the breeder employing
optimal management must be guided by the characteristics of his breeding
population.
Tree breeding takes considerable time and the necessity to restart a breeding
program which is inappropriately set up is something to be avoided. Tree
improvement programs must be designed to be efficient and sustainable from their
very beginning. For a landowner, the allowable cut will in the end be affected by
means of a reformed silviculture and outcome of investments in forest tree
improvement.
28
Suggestions for future research
It is difficult to combine long- and short-term goals that very often are in conflict
with each other. Much effort has been put into development of efficient testing and
selection procedures. Nevertheless, a procedure to optimize outcome from the
current breeding cycle, while at the same time optimizing several generations ahead,
would appear to be extremely time consuming if an exhaustive search is to be made.
Possible iterative approaches have been developed, such as “simulated annealing”
(Kerr et al, 1998) and “ant colony optimization” (Dorigo et al. 1996). The dynamics
of living plants, together with the technical aspects of such procedures, would also
make the validity of results questionable, independent of the elegance of the
operation. For some time to come, breeders will be compelled to use methods that
maximize a very limited number of decisions at any given time. For many
foreseeable errors, the only apparent losses are genetic gain, diversity and time.
Diversity can be replenished, but time lost is rather more difficult to recover.
Single-generation approximations for gain and diversity, and maximizing return
from a single selection cycle has its limits. Currently, there is no theory or algorithm
that can foresee consequences over more than one breeding cycle. A model for
breeding that comprises a number of steps is far more desirable and would constitute
a significant step forward. In order to accomplish this, specific search algorithms
must be developed and should be flexible and adaptable to changing goals of
breeding. Parameters of an optimal breeding strategy will probably prove to be
variable over time, and allocation of resources for testing would be skewed towards
the highest yielding families and individuals. Although initially closed, a breeding
population will not remain closed once the value of additional genes from the wild
becomes apparent.
29
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Acknowledgements
My first and strongest recognition goes to Professor Dag Lindgren, who with
emphasis and with a never-ending energy directed the evolution of this thesis. His
views on breeding theory have made a strong impression on me, as well as on my
work. My interest in genetics, combined with his devotion and experience, gave this
result after long days and nights, with dynamic talks on most aspects of tree
improvement, science and on life in general. Some of the ideas presented here are
my ideas, but had it not been for the discussions with Dag, sometimes at the most
unexpected times of the day, they would likely never have been formed, much less
been converted into research. Of my collaborators at the department, Dr Tim Mullin
has played a prominent role, not only as assistant supervisor and co-writer, but also
as a very constructive discussion partner. Dr Mullin has also been very patient in
helping out with my English. Others who have contributed with their time, thinking
and skills are: Drs. Bengt Andersson, Anders Ericsson, Tore Ericsson, Yousry ElKassaby, Estelle Lerceteau, Gene Namkoong, Kermit Ritland, Leopoldo Sánchez
Rodríguez, Ola Rosvall, Kostas Spanos, Run-Peng Wei, Francis Yeh, Yong-Qi
Zheng, Stefan Löfmark, and Gertrud Lestander. Providing great moral support, have
been visiting scientists at the department and in some cases fellow post-graduate
students: Dr Hannele Tuominen, Dr Dag Rudin, Dr Anders Fries, Adolfo Bila, KyuSuk Kang, Dr Katarina Lindgren, Maria Ribeiro, Laura Parducci, Robert Nygård,
Dimitris Athenassiadis, Dr Jan Erik Nilsson, Seppo Ruotsalainen, Dr Anni Harju,
Thuy Olsson, and Torgny Persson. The list must end somewhere.
A special gratitude goes to Tomas Andersson and Anna-Lena Axelsson for their
support and for letting me share their home during these years. Before beginning my
studies in genetics, I had a serious discussion with my family who gave me their
unconditional support. I want to express my deepest appreciation to my parents Elsa
and Widar Andersson, and my sister Solveig Widarsdotter; over the last four years,
their continuing support has been immeasurable. Finally, my thoughts go to my love
Margareta Lindhagen for her concern, support and advice.
42