SME
Physical Geography
Biogeography
Use this for “With S = 20A0.25, how many species should an island of 10,000 km² hold?”
Chart
S(A) = 20A0.25
Log–log axes: a power law draws as a straight line.
This is an example. Type your own values to start a new problem.
S
=
c
×
A
Formulas
S
=
c
×
A
z
200
=
20
×
10,
000
0.25
Assumptions
•
c and z are fitted for one group of species in one region; c is the count on 1 km².
•
Islands give z near 0.25–0.35; with z ≈ 0.3, ten times the area about doubles the species.
•
S is the number expected on average; a real island can hold a few more or fewer.
Step-by-step
WE KNOW
A = 10,000 km², c = 20, z = 0.25
FIND
species (S)
Step 1 · Find species (S)
Use S = c × Aᶻ
Raise
the
area
to
the
power
z
,
then
multiply
by
c
.
S
=
20
×
10,
000
0.25
10,
000
0.25
=
10
20 × 10 = 200
S
=
200
Check
Put the numbers back in. Both sides should match.
200
=
20
×
10,
000
0.25
✓
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Landforms from their shape and process
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Species lost when habitat shrinks
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