This document contains the summary of a seminar on the importance of effective population size in plant breeding. The seminar covered various topics related to effective population size including its definition, factors affecting it, methods to estimate it, effects of genetic drift and selection, and implications for plant breeding and conservation. Case studies were presented on evaluating the impact of effective population size on genetic variation in maize breeding and on heterosis and inbreeding depression in a plant species with small isolated populations.

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Welcome
Anilkumar, C.
PALB 5062
PhD scholar

2. 5/6/2017 PG seminar 2
Seminar
on
Importance of effective population
size in plant breeding

3. Introduction
Methods estimate Ne
Factors affecting Ne
Ne effects on breeding
Case studies
In this hour----
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Population: It is the number of all the organisms of the same
group or species, which live in a particular geographical area,
and have the capability of producing off springs.
Census Population Size: The census population size (N) is
the number of individuals in the population
Effective population size: it is the corresponding population
size of a idealized (Fisherian) population that would function
in the same way with respect to genetic drift and inbreeding as
the focal population under interest.
Introduction

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An "ideal" population has the following characteristics,
Randomly mating population.
Consisting of N number of
diploid hermaphroditic individuals.
Sex ratio is 1:1.
All individuals are equally likely to produce offspring.
Constant number of breeding individuals from one
generation to the next.
There is no selection, mutation and migration.

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Genetic drift: it is the change in the frequency of allele
in a population due to random sampling of organisms.
Inbreeding coefficient (F): The probability that a
randomly chosen individual carries two allele of a gene
that are identical by descent from a recent ancestor or
The probability that an individual is autozygous.

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A Bottleneck Concept
 A population bottleneck is a sharp reduction in the size
of a population due to environmental events or human
activities.
 Inbreeding is the most common phenomena in cross-
pollinated crops, and in small outcross populations it has
resulted in deleterious effects and loss of fitness of the
population due to recombination between undesirable
genes (recessive identical alleles).
 Plant breeders have been advised to
maintain the optimum population
size

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Effective Population Size
 This concept was first given by Sewall Wright.
 In small closed population all the individuals eventually
become related by descent.
 How quickly they become related depends on the effective
population size.
 Effective population size is almost all the time smaller than
the real or census population size

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 Loss of heterozygosity in Fisherian population/idealized
population is mainly due to random genetic drift.
 Heterozygosity at a given point of time in the population is
given by,
Ht = H0*(1-(1/2N)t).
Where H0= heterozygosity at t=0
As t increases, Ht decreases.
As N decreases, Ht decreases

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 Random fluctuations of allele frequencies
 if population size reduced and drift acts more
intensively , it results in:
 At allelic level: random fixation of alleles (loss of
alleles)
 At genotype level: inbreeding and reduction of
heterozygosity ( because of fewer alleles)
Consequences of genetic drift

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Methods to estimate Ne
1. Heteorzygosity excess
2. Linkage disequilibrium
3. Temporal change in allele frequency
4. Relatedness and relationship
5. Multiple sources of drift/inbreeding informatation

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Heterozygosity excess
The smaller the value of Nm or Nf, the greater the difference
between paternal and maternal allele frequencies.
Simple functional relationship between the Ne of the parental
population and the amount of heterozygosity excess in the
offspring population
The negative value of D, indicating an excess of
heterozygosity and a corresponding deficit of homozygosity.

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measuring the heterozygosity excess, D, at a number of
loci in a population yields an estimate of the parental
population effective size.
The method is simple and is implemented in several
computer programs
The method has a low precision and accuracy,
frequently providing infinitely large estimates of Ne for
small populations
The estimator is also highly sensitive to non-random
mating and causes deviation from Hardy–Weinberg
equilibrium
Pros and cons….

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Linkage disequilibrium
LD would come exclusively from genetic drift and can be used to
estimate Ne

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 The LD estimator is simple to calculate and requires just a
single sample of multi-locus genotypes instead of two or
more samples
 It is especially suitable for species with a long generation
interval
 It is assumed that LD is produced solely from the finite
population size, and other confounding factors, such as non-
random mating and population structure, are absent.
 LD is highly dependent on the recombination rate between
loci

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Temporal changes in allele frequency
The allele frequencies never stay
constant and change systematically
owing to the forces of mutation,
selection and migration, stochastically
due to the random force of genetic
drift, or both
In the absence of the action of all of the systematic forces in a
population -----

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Relatedness and relationship
The pattern of genetic relatedness or relationship between
individuals in a population has a direct functional relationship
with the inbreeding, effective size of the population.
 Two individuals taken at random from a population with a
smaller Ne will have a higher probability of sharing the same
father, mother or both.
Also called sibship approach

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• Sibship can be inferred more accurately than other
quantities such as relatedness, which leads to more accurate
estimates of Ne.
• The approach applies to non-random mating populations
• It applies to diploid species, haplodiploid species,
dioecious as well as monoecious species with selfing.
• It provides not only an estimate of the summary parameter,
Ne, but also some information about the numbers of male
and female parents and variance in family sizes through the
sibship assignment analysis.

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Multiple sources of drift/inbreeding information
 Uses multiple sources of information
 combining multiple pieces of information may potentially
allow for a better delineation of the process and thus yield a
more accurate estimate of Ne
 approximate Bayesian
computation (ABC) to estimate
Ne from a sample of genotypes.

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How big is “big enough”?
50/500 rule (Franklin 1980)
 if Ne > 50 leads to short term survival (avoid inbreeding )
 if Ne > 500 needed for long term survival (ability to evolve in
changing environments)
 A genetically effective population size of at least 50
individuals is necessary for conservation of genetic diversity
in the short term and to avoid inbreeding depression
 A Ne of 500 is needed to avoid serious genetic drift in long
term

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Factors affecting Ne
Division into two sexes: a small number of individuals of
one sex can greatly reduce effective population size (Ne)
below the total number of breeding individuals (N).
Ne =
4NmNf
Nm+ Nf
Variation in offspring number: a larger variance in offspring
number than expected with purely random variation
reduces Ne below N.

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Inbreeding: Ne is reduced because inbreeding causes faster
coalescence of an individual’s maternal and paternal alleles
compared with random mating, Selfing causes Ne to be
multiplied by a factor derived from F (inbreeding coefficient)
Mode of inheritance: The mode of inheritance can also greatly
alter Ne, and hence expected levels of neutral diversity
The population size of sex chromosome
is smaller than the autosomes.
Ne for X-linked genes
Ne =
9NmNf
4Nm+2Nf
If Nm = Nf, then Ne = 3N/4

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 Age- and stage-structure: in age- and stage-structured
populations, Ne is much lower than N
 Changes in population size: low population size have
a disproportionate effect on the overall value of Ne
Natural and artificial populations

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Spatial structure: spatial isolation and small
population size appears to result in substantial fixation
of recessive to nearly recessive deleterious mutations.
Genetic structure: Directional selection causes a
reduction in Ne at linked sites due selection pressure or
frequency-dependent selection

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Selection and effective population size
In the absence of selection or when selection acts on a
non-inherited trait, the effective size is simply a function
of the variance of the number of offspring per parent
predictions of Ne is more complicated when selection acts
on an inherited trait
The product of Ne and the intensity of selection is
important
Selection efficiency depends on effective population size

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Selection at linked loci :
The real rates of inbreeding are expected to be larger than
those predictions when selection acts on a system of
linked genes.
Selection assuming unlinked genes :
assumes random association of genes and leads to
segregation and recombination. Therefore less inbreeding

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Effective population size in conservation practices:
 Effective population size (Ne) is an important concept in the
management of threatened species
 Minimising the loss of genetic variation is one of the main
objectives of captive breeding programmes.
 This is achieved through minimising genetic drift and, therefore,
maximising Ne.
 A classical strategy to follow is the equalisation of family sizes.
 This is known as minimal inbreeding and it is the recommended
procedure for applications in germplasm collection and
regeneration

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Effect on heterosis:
 Crosses between natural populations can result in heterosis if
recessive deleterious mutations have become fixed within
populations because of genetic drift
 Heterosis is high with intermediate mutation rates, intermediate
selection coe•ffecients, low migration rates and recessive alleles
 Cross breeding to other populations alleviates the effects of
inbreeding and genetic drift

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In case of clonal reproduction….
estimates of effective population size
rarely incorporate the contribution of
both asexual and sexual reproduction.
use a stage-structured demographic model
Ne is more sensitive to changes in the mean and variance of
asexual populations
Values more than 50 are required before drift causes the
loss of SI alleles, which are under balancing selection

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Case study: 1
Background:
 In recurrent selection number of lines selected for inter-
mating depends on the number of lines evaluated and
selection intensity
 Similarly, for a given selection intensity, an increase in the
number of lines selected requires an increase in the
number of lines evaluated.

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Little information is available concerning the effect of
effective population size on genetic variance in plants.
The objectives of study were to
(i) evaluate the performance of the BS11C0 and the BS11C5
populations
(ii) compare the magnitude of additive genetic variance and
its interaction with the environment, phenotypic variance,
heritability, and phenotypic and additive genetic
correlations within the C0 and C5 populations.

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 All the populations together divided into 10 sets
 All the entries replicated twice, and replications were
nested within sets
 evaluated at five environments

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Statistical Analysis
 Pooled analysis of variance over sets and environments
was done
 The sum of squares of genotypes, genotype × environment,
and pooled error were partitioned into different sources of
variance and they are translated to appropriate genetic
components of variance.
 Estimated additive variance, additive × environment
variance, phenotypic variance and heritability in all the
populations

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Output of the study:
 Use of smaller effective population size would not
compromise genetic progress in a short-term maize
breeding program
 Genetic drift always may not necessarily result in an
immediate and drastic decrease in genetic variance.
 However, there is little advantage to use large effective
population size to maintain genetic variability for short-
term recurrent selection.

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Case study: 2
Background:
In small isolated populations, genetic drift is expected to
increase chance fixation of partly recessive, mildly deleterious
mutations, reducing mean fitness and inbreeding depression
within populations and increasing heterosis in outcrosses
between populations.

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Material: Hypericum cumulicola
 selected 16 subpopulations separated by between 0.25 and
12.0 km in southern Highlands of Florida,
 DNA extracted by means of CTAB procedure
 Samples were screened for 10 unlinked microsatellite loci
for genetic variations
 Coalescent methods that explicitly account for migration
was used to predict more accurate estimates of relative
effective population sizes.

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To test the fitness and heterosis…
 Hand pollinated the individuals within populations and
also between populations
 seeds collected and raised as population families
 Data analyzed in a mixed-model ANOVA
 Population mean fitness, heterosis, and inbreeding
depression were calculated.

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Outcome
 Greater effect of genetic drift on the frequency of partly
recessive deleterious mutations in small populations.
Individual fitness was much lower in small populations
Heterosis was much greater and inbreeding depression was,
on average, lower in smaller populations.
Strong heterosis has been observed in crosses between widely
isolated natural populations

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