SME
Evolutionary Biology · Problem type
Chance a new mutation fixes
Use this for “What is the chance a new neutral mutation fixes in a population of 100?”
Chart
A log scale: each grid line up is 10 times the one below.
This is an example. Type your own values to start a new problem.
Pfix
=
1
2
×
Pₗₒₛₜ
Chance it is lost
worked out (not typed)
Tfix
Mean generations to fix
calculated
Formulas
Pfix
=
1
2 ×
N
0.005
=
1
2 × 100
Pₗₒₛₜ = 1 − Pfix
0.995 = 1 − 0.005
Tfix
=
4
×
N
400 = 4 × 100
Assumptions
•
A neutral new mutation: it starts as one copy among the 2N gene copies and does not change fitness.
•
An ideal population, so the effective size Nₑ equals N.
•
Each copy is equally likely to be the one every copy descends from, so the mutation fixes with chance 1 ÷ 2N.
•
The mean time to fix, 4N generations, counts only the mutations that do fix.
Step-by-step
WE KNOW
N = 100
FIND
chance it fixes (Pfix), chance it is lost (Pₗₒₛₜ), mean generations to fix (Tfix)
Step 1 · Find chance it fixes (Pfix)
Use Pfix = 1 ÷ (2 × N)
One
new
copy
among
2
N
:
each
copy
is
equally
likely
to
win.
Pfix
=
1
2 × 100
Pfix
=
1
200
Pfix = 0.005
Step 2 · Find chance it is lost (Pₗₒₛₜ)
Use Pₗₒₛₜ = 1 − Pfix
A new mutation either fixes or is lost.
Pₗₒₛₜ = 1 − 0.005
Pₗₒₛₜ = 0.995
Step 3 · Find mean generations to fix (Tfix)
Use Tfix = 4 × N
Drift
takes
about
4
N
generations
to
carry
a
neutral
copy
all
the
way.
Tfix = 4 × 100
Tfix = 400
Check
Put the numbers back in. Both sides should match.
0.005
=
1
2 × 100
✓
0.995 = 1 − 0.005 ✓
400 = 4 × 100 ✓
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