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Effective population size and inbreeding

How quickly is inbreeding increasing in my breeding group?

Answer: In a small breeding group, inbreeding increases each generation, even if you never breed siblings. How quickly mainly depends on the sex with the fewest individuals. The effective population size (Ne) says what size an ideal population with equal sex distribution your group corresponds to. Inbreeding increase per generation is 1 ÷ (2 × Ne). FAO uses 1% per generation (Ne of at least 50) as an upper limit in the conservation of livestock breeds, and the same figure is often used in zoo and laboratory animal breeding.

Formula

Ne = 4 × hanner × hunner ÷ (hanner + hunner)

ΔF pr. generation = 1 ÷ (2 × Ne)

Indavl efter t generationer = 1 − (1 − ΔF)^t (startindavl sat til 0)

Only animals that actually have offspring count

Symbols and units in the formula
SymbolMeaningUnit
hannerBreeding males (that actually get offspring)stk
hunnerBreeding females (that actually get offspring)stk
generationerNumber of generations forwardgenerationer
=Effective population size (Ne)dyr
=Inbreeding increase per generation (ΔF)%
=Inbreeding after the chosen generations%
=Ne if the same animals were evenly distributed by sexdyr

Validity and source

Source
Falconer & Mackay 1996 (Ne = 4·Nm·Nf ÷ (Nm + Nf), ΔF = 1 ÷ 2Ne); FAO: ΔF højst 1 % pr. generation

Does not apply when

  • The formula assumes random mating equal numbers of offspring per animal and non-overlapping generations. Uneven distribution of offspring (one male getting most) gives a lower Ne than calculated. Use the stud book or breeding programme for the actual matings.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Breeding males (that actually get offspring)5 stk
  • Breeding females (that actually get offspring)20 stk
  • Number of generations forward10 generationer

Giver

  • Effective population size (Ne)16.0 dyr
  • Inbreeding increase per generation (ΔF)3.13 %
  • Inbreeding after the chosen generations27.2 %
  • Ne if the same animals were evenly distributed by sex25 dyr

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Sådan bruger du den

Du bruger den, når du arbejder med avl af forsøgsdyr eller af dyr i en zoologisk have, og skal vurdere, hvor hurtigt indavlen stiger. Den viser især, hvor meget det betyder, at der er få hanner i avlen.

Step by step

  1. Tæl de hanner og hunner, der faktisk får afkom i en generation.
  2. Regn Ne = 4 × hanner × hunner ÷ (hanner + hunner).
  3. Regn indavlstilvæksten: 1 ÷ (2 × Ne).
  4. Sammenlign med målet: højst ca. 1 % pr. generation svarer til Ne på mindst 50.
  5. Er tilvæksten for høj, så brug flere hanner, eller byt dyr med et andet anlæg.

Typical errors

  • At tælle dyr, der ikke får afkom.
  • At tro at mange hunner kan opveje få hanner.
  • At glemme at ujævnt antal afkom pr. dyr sænker Ne yderligere.

Examples from everyday life

Gruppe af surikater i zooen

Zooens surikatgruppe har 2 avlshanner og 10 hunner, der får unger. Du vil se 10 generationer frem.

Breeding males (that actually get offspring)
2 pcs
Breeding females (that actually get offspring)
10 pcs
Number of generations forward
10 generationer

It means: Gruppens Ne er kun 6.7 dyr, og indavlen stiger 7.5 % pr. generation. Efter 10 generationer er indavlen 54.1 %, så gruppen skal have nyt blod fra et avlsprogram.

Forsøgsdyrkoloni

En koloni af outbred rotter har 20 hanner og 20 hunner i avl.

Breeding males (that actually get offspring)
20 pcs
Breeding females (that actually get offspring)
20 pcs
Number of generations forward
10 generationer

It means: Ne er 40 dyr, og indavlen stiger 1.25 % pr. generation. Det er lidt over målet på 1 %, så flere avlspar ville hjælpe.

Én han til hele gruppen

Et lille dyreanlæg har 1 han og 25 hunner.

Breeding males (that actually get offspring)
1 pcs
Breeding females (that actually get offspring)
25 pcs
Number of generations forward
10 generationer

It means: Ne er kun 3.8 dyr, selvom der er 26 dyr. Var dyrene fordelt ligeligt på køn, var Ne 26 dyr. Indavlen stiger 13 % pr. generation.

Rule of thumb

Ne er aldrig mere end fire gange antallet af det køn, der er færrest af.

How to check the answer

Sammenlign med stambogens indavlskoefficienter. De rigtige tal fra stamtavlen går forud for overslaget.