SME
Ecology
Conservation biology
Use this for “A herd has 10 breeding males and 40 females. What is its effective size?”
Chart
10
40
This is an example. Type your own values to start a new problem.
Nₑ
=
4
×
×
+
N
Census size
calculated
s
Share effective
calculated · %
Formulas
N
=
Nₘ
+
Nf
50 = 10 + 40
Nₑ
=
4
×
Nₘ
×
Nf
Nₘ + Nf
32
=
4
×
10
×
40
10 + 40
s
=
100
×
Nₑ
N
64
=
100
×
32
50
Assumptions
•
Nₑ is the size of an ideal population that would lose genetic diversity as fast as this one.
•
Only breeding adults count, and each one of a sex is equally likely to parent each young.
•
The 50/500 rule: Nₑ of 50 avoids inbreeding for now; Nₑ of 500 keeps diversity for the long term.
•
Diversity lost each generation is 1 ÷ (2Nₑ) of what is left (Evolutionary Biology, Genetic drift).
Step-by-step
WE KNOW
Nₘ = 10, Nf = 40
FIND
census size (N), effective size (Nₑ), share effective (s)
Step 1 · Find census size (N)
Use N = Nₘ + Nf
The census counts every breeding adult.
N
=
10
+
40
N
=
50
Step 2 · Find effective size (Nₑ)
Use Nₑ = 4 × Nₘ × Nf ÷ (Nₘ + Nf)
Four times the product of the sexes over their sum: the rarer sex sets the size.
Nₑ
=
4
×
10
×
40
10 + 40
Nₑ
=
4
×
10
×
40
50
Nₑ
=
40
×
40
50
Nₑ
=
1,600
50
Nₑ = 32
Step 3 · Find share effective (s)
Use s = 100 × Nₑ ÷ N
The effective size as a percent of the census.
s
=
100
×
32
50
s
=
3,200
50
s
=
64%
Check
Put the numbers back in. Both sides should match.
50 = 10 + 40 ✓
32
=
4
×
10
×
40
10 + 40
✓
64
=
100
×
32
50
✓
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