inbreeding - jvanderw.une.edu.au
Post on 01-Mar-2022
3 Views
Preview:
TRANSCRIPT
Overview
• Relatonships between individuals! Inbreeding (F)! Coancestry (f)
• Effective population size (Ne) &F rate• Consequences of inbreeding• Balancing F and genetic merit
Coefficient of inbreeding (F)
Inbreeding is due to the mating of relatives
The coefficient of inbreeding (F) is the probability that two alleles at a randomly chosen locus are identical by descent (IBD)IBD = copies of same alleles from common ancestor
F ranges from 0 to 1
What is F of individual X?Recall: The coefficient of inbreeding (F) is the probability of the 2 alleles at a randomly chosen locus being identical by descent
Shortcut: n = 3 descendents (D, A, E) in the closed loop -FX = (½ )3 = 1/8
161
21
21
21
21
11 ====
==== xxxp AA
161
21
21
21
21
22 ====
==== xxxp AA
81====xF
AB C
D E
X1 2XX
A A1 2
What is F of individual X?Recall: The coefficient of inbreeding (F) is the probability of the 2 alleles at a randomly chosen locus being identical by descent
161
21
21
21
21
11 ====
==== xxxp AA
161
21
21
21
21
22 ====
==== xxxp AA
41====xF
A B
C D
X
A1A2 B1B2
X1X2 161
21
21
21
21
11 ====
==== xxxp BB
161
21
21
21
21
22 ====
==== xxxp BB
Shortcut: 2 closed loops (C,A,D n=3 & C,B,D n=3)FX = (½ )3+(½ ) = 1/43
Common ancestor X is inbred (F=0.25)
X Y
P Q
R
C DLoops are
P,X,Q (1/2)3 x (1+0.25) = 0.156
P,Y,Q (1/2)3 x (1+0) = 0.125
FR = 0.281
What is F of individual R?A B
Common ancestor is not inbred! sum over loops, where n is number of animals in
each loop excluding x itself
Common ancestor is inbred! sum over loops, but multiply by F of the common
ancestor (FA)
nXF )2
1(ΣΣΣΣ====
(((( ))))(((( ))))An
X FF ++++××××ΣΣΣΣ==== 1)21(
Question
Which alleles are IBD (identical by descent) and which are IBS (identical by state)?
A1A2 B1B2 B1B2 C1C2
A1B1 A1B2 B2C1
A1A1 B2B2
Another measure of relatedness
The coancestry (fij) is the probability that two gametes taken at random from two individuals (i & j) carry alleles that are IBD
f ranges from 0 to 1
What is f of individuals D,E?
The coancestry of i & j (fi,j) is equivalent to the F of their progeny
AB C
D E
Pick an allele in D and an allele in E. Chances of being IBD are 2/8 if an paternal allele was picked, and 0 otherwise.
Recall: The coancestry (f) is the probability of that 2 gamettes taken at random from 2 individuals carry alleles identical by descent
A1A2 C1C2B1B2
A1B1A1B2A2B1A2B2
A1C1A1C2A2C1A2C2
81====f
sire
Another measure of relatedness
Addditive genetic relationship (a) between 2 individuals reflects their proportion of genes in common
! e.g. between parent and offspring a=0.5! e.g. between two full-sibs a=0.5! e.g. between two half-sibs a = 0.25
Ne
The size of the idealized population with the same inbreeding rate as the actual population
The idealized population has ‘simplified’ properties:! Closed! Random mating! Discrete generations! Constant population size! Equal sex ratios! Poisson distribution of family size
Calculating Ne
Accounting for unequal sex ratio! Ne = 4 Nm Nf / (Nm + Nf)! Effective pop’n size reduces towards sex with
fewer breeding individuals
472.719.57.97.34Ne100,000220205202224N99999200200200202Females / generation
1205222Males / generation
The rate of inbreeding
F can be calculated directly for progeny. This is useful when designing specific matings
For populations it is more relevant to calculate the inbreeding rate
t
t NeF
−−=
2111 where t is number
of generations
Note - this only holds for no selection and random mating
F rate
t
t NeF
−−−−−−−−====
2111
Generation 0
A1A2 A3A4 A5A6
Gene pool: 2N alleles
Generation 1
Sample with replacement. The probability of sampling 2 copies of the same allele is 1/(2N). The probability of sampling 2 different alleles is 1-1/(2N) (in later gen’s x by F as some alleles will be IBD)
N21
N211 −−−−
A4A1A1 A3 A5 A3 A4A6
A2A2 A5
A2A2 A6A3
1211
21
−−−−
−−−−++++==== tt F
NNF
A6
Example calculation! F after 20 years when breeding with age structure
• Lm=2.5 years, Lf = 4 years, L=3.25 years
• Number of animals entering flock per generation
Nm=1 male / year x 3.25 years / gen = 3.25 male / gen
Nf=20 fem. / year x 3.25 years / gen = 65 fem. / gen
• Ne = (4NmNf)/ (Nm+Nf) = (4x3.25x65)/(3.25+65)=12.38
Age 2 3 4 5 6
Males 1 1
Females 20 20 20 20 20
23.038.122
11125.3/20
25.3/20 ====
−−−−−−−−====
xF
t
t NeF
−−=
2111
f rate
At equilibrium,under consistent selection and with random mating, ∆F is equal to ∆f
Constraining ∆f is likely the most effective way to constrain ∆F! i.e. select parents such that the mean f (of all
mating pairs) is restricted to an acceptable level
Questions
! In breeding programs recording pedigree are absolute values of F usually known?
! How can F within a population be reduced within the short-term?
! Should a desired long-term rate of inbreeding be included in the breeding objective?
Consequences of inbreeding
Inbreeding can result in:! Increased expression of recessive genes! Loss of performance & viability termed inbreeding
depression! Loss of genetic variation within the inbred population
Inbreeding increases expression of recessive alleles
Genotype frequencies! Non-inbred: q2 2pq p2
! Inbred: q2+pqF 2pq-2pqF p2+pqF
Example, q=0.02 (2%)
10.2 in 1000
0.50
5.3 in 10002.9 in 10000.4 in 1000Prob. aa
0.250.1250F
Change in genotype frequenciesin response to inbreeding
For example, p=q=0.5
Note that allele frequencies do not change
0.500.5At F=1.0
0.3750.250.375At F=0.5
0.250.500.25At F=0
p2+pqF2pq-2pqFq2+pqFFrequency
AAAaaaGenotype
Inbreeding depression reduces productivity & viability
Inbreeding depression! Due to increased homozygosity, in relation to traits
that show dominance! Most notable effect is on reproductive fitness
Inbreeding depression is typically greater in the wild than in captivity! Trait depression variable, often 2-20% per 10% F
Inbreeding depression
For example Zebra fish, survival to 30 days was depressed by 43% per 25% F
020406080
100
0 0.1 0.2 0.3
F
% S
urvi
val
Inbreeding reduces genetic variance
As individuals become more alike, the withinpopulation genetic variance decreases
VA is additive genetic variance
VA (with inbreeding) = (1-F) VA (without inbreeding)
Questions
! A recessive allele (called non-Agouti) causes uniformly black sheep. Would this be more of a problem in a lowly or highly inbred population?
! If a trait is controlled by purely additive genes (i.e. no dominance) will expression of the trait be effected by inbreeding depression?
! Why is it a concern that inbreeding reduces genetic variance?
Genetic gain and inbreeding
Select few individuals
high genetic gainbut
low Ne and high F
Need to balance rates of F and genetic gain
Select many individuals
low genetic gainbut
high Ne and low F
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
mea
n EB
V
coancestry
The relationship between merit and relatedness
Unlimited reproductivity
Restricted reproductivity
Mean coancestry of selected parents
Mer
it
Optimal contribution theory
Aimed at maximising long-term response by weighting genetic response against future contributions to inbreeding
Maximise an objective function of:
where G is genetic merit, b is a weight, and f is coancestry
fbG ∆∆∆∆−−−−∆∆∆∆
Balancing merit and diversity
‘Total Genetic Resource Management’ (TGRM)! a software program (Brian Kinghorn)! determines which animals to select for breeding,
and how these animals should be mated to each other ‘mate selection’
! balances genetic merit & f, but also handles logistical and other constraints
! driven by an evolutionary algorithm
Possible outcomes
Judgement
Data construction:Pedigree
Trait records
TGRM Control CenterInternet driven
Action : A mating list
Opportunities ConstraintsAttitudesIssuesCosts
TGRM Server
Summary and useful concepts
• Inbreeding is due to mating of relatives, and may have undesirable consequences
• The inbreeding coefficient is relative to some base population, and thus it is more useful to consider the rate of F rather than the absolute value
• Theories exist to balance rates of F and genetic gain
top related