Inbreeding and Inbreeding Depression

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Inbreeding and Inbreeding Depression
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Przewalskis horse
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Ralls Ballou (1983)
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Back to inbreeding
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Chondrodystrophy in California condors (q 0.17)
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Power of inbreeding

• 35,000 loci in mammals
• 5,000 can mutate to produce lethals (mice)
• Mutation-selection equilibrium for a partially
  recessive lethal is 5 x 10-4
• What is probability of an individual being
  homozygous for at least one lethal recessive
  under random mating?
• Pr(not a lethal homozygote) 1 q2
• Over all loci (1 q2)5000
• 1 (5 x 10-4)25000 0.99875
• Pr(lethal homozygote) 1 0.99875 0.00125
• What happens if all matings are full-sib?
• (1 q2) becomes (1 q2 Fpq) with F 0.25
• 1 (5 x 10-4)2 (0.25 x (5 x 10-4) x
  0.9995)5000 0.53
• Pr(lethal homozygote) 0.47

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Accumulation of inbreeding
Ft 1 1 1/2N)t(1 F0) Where t
generations and F0 initial inbreeding
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Accumulation of inbreeding in a small, captive
population (N 4)

• Generation 0, assume F0 0
• Generation 1, F 1 (1 1/2N)1 1 (1
  1/8)1 0.125
• Generation 2, F 1 (1 1/2N)2 1 (1
  1/8)2 0.234
• Generation 3, F 1 (1 1/2N)3 1 (1
  1/8)3 0.33
• Generation 4, F 1 (1 1/2N)4 1 (1
  1/8)4 0.41
• . . .
• Generation 10, F 1 (1 1/2N)10 1 (1
  1/8)10 0.74

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Estimating inbreeding with pedigrees

• What is inbreeding coefficient of individual X?
• Pr(A1 transmitted to offspring) ½
• Pr(X is A1A1) (½)4 1/16 0.0625
• Pr(X is A2A2) (½)4 1/16 0.0625
• Pr(X is A1A1 or A2A2) (½)4 (½)4 (½)3 1/8
  0.125

A1A2
B
C
A
½
½
D
E
½
½
X
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What if A is already inbred?

• A1 and A2 have Pr(identity by descent) FA
• Pr(X is IBD due to past inbreeding)
• Remember, due to past inbreeding, A has
  probability FA that A1A2 are IBD
• Pr(A1 from mother and A2 from father) (½)4
• Pr(A1 from father and A2 from mother) (½)4
• Pr(either) (½)3
• Pr(X inbred due to past inbreeding) (½)3 FA
• Overall inbreeding of X is sum of (½)3 (½)3 FA

A1A2
B
C
A
½
½
D
E
½
½
X
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More complex pedigrees

• F S(½)n(1 Fca)
• Where n is of individuals in path to common
  ancestor and back
• And Fca is inbreeding coefficient of common
  ancestor
• Summed over each common ancestor

B
C
D
E
F
G
X
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F S(½)n(1 Fca)
FE (½)2 ¼ 1 ¼ 5/4
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Repeated backcrosses
Ft ¼(1 2Ft-1 Ft-2)
Ft ¼(1 FA 2Ft-1)
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Indices of Inbreeding

• FIS
• Kinship
• Index of coancestry measured between 2
  individuals
• Equal to inbreeding coefficient of their
  offspring
• Mean kinship
• Kinship of all possible pairs averaged

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Terms

• Autozygous
• 2 alleles in an individual are identical by
  descent
• Individual is homozygous
• Allozygous
• 2 alleles in an individual are derived from
  different ancestral alleles
• Homozygous or heterozygous

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Estimating loss of genetic diversity through
pedigrees

• Gene drop analysis
• Simulation of the fates of specific alleles in a
  specific pedigree
• Each founder is assigned 2 unique alleles
• Alleles are transmitted to offspring randomly and
  are tracked through pedigree
• Monte Carlo simulation for replicates

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Inbreeding depression

• Decrease in fitness due to increase in
  homozygosity or decrease in heterozygosity
• Increase in homozygosity increases expression of
  deleterious recessives
• Decrease in heterozygosity reduces fitness
  (heterozygosity-fitness correlation)

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Heterozygosity-fitness correlations

• Meta-analysis (Reed and Frankham 2003)
• Analyzed 34 studies, each based on gt2 populations
• 28 studies showed a relationship betwee
  heterozygosity and fitness overall r 0.44

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Heterozygosity-fitness correlations

• Red deer on Rhum (Slate et al. 2000)
• Lifetime reproductive success greater for more
  heterozygous females
• Granville fritillary butterfly (Saccheri et al.
  1998)
• Metapopulation structure in Finland
• 1600 meadows
• 200 extinctions and 114 colonizations annually
• Risk of extinction was related to heterozygosity
  in the population

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Impact of inbreeding depression

• A little quantitative genetics
• Assume the genotype at a single locus (2 alleles)
  yields a phenotypic trait that can be measured
• Assign values of trait to genotypes
• A1A1 a
• A2A2 -a
• A1A2 d (dominance deviation)

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• Inbreeding depression (ID) 2pqdF
• Heterozygote frequency x dominance deviation (for
  deleterious alleles) x F

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• Example 12.1 from Frankham
• Demonstrate that ID needs dominance

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ID linear to F
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Measuring ID

• Ratio of inbredoutbred fitness
• ? 1 (fitness of inbred offspring/fitness of
  outbred offspring)
• Equivalent to ID/M0
• Example (Ralls and Ballou 1983)
• Juvenile survival of dorcas gazelles
• Survival of inbred gazelles 40.5
• Survival of outbred gazelles 72.0
• ? 1 0.405/0.720 0.44
• Value of ? depends on F, which must be specified
• Most often applied to plants by comparing fitness
  of selfed plants (F 0.5) to outbred individuals

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Measuring ID

• Lethal equivalents
• LE set of deleterious alleles that would cause
  death if expressed
• Always recessive so LE refers to homozygous
  recessive genotype
• If homozygous recessive at one locus causes
  death, LE 1 for that locus
• If combination of 2 loci homozygous recessive
  causes death, LE 0.5 for each
• If 4 loci, LE 0.25 for each, etc.

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• S is survival rate
• S e-(ABF)
• ln S A BF
• A measure of death due to environmental causes
  and genetic damage in a randomly breeding
  population
• F inbreeding coefficient
• B reduction in survival in homozygotes
• of LEs per gamete
• 2B of LEs per individual

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LEs in the real world

• Ralls et al. (1988) Estimates of lethal
  equivalents and cost of inbreeding in mammals,
  Conservation Biology
• LE per individual ranged from -1.430.3
• Mean 4.6 median 3.1
• Average cost of full-sib or parent-offspring
  mating (F 0.25) was 0.33 (33 higher mortality
  than outbred offspring)
• Source of founders (wild, captive, unknown) did
  not make a difference on survival of offspring
• Likely an underestimate because they only
  considered the effect of juvenile survival

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Inbreeding and population viability
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Correcting inbreeding depression

• Genetic rescue