SME
Grade 7 Science · Life Science
Natural selection
Use this for “Each generation has 4 more brown beetles than the last. How many are brown by generation 5?”
Diagram
Brown beetles: 2, 6, 10, 14, 18
In all: 20, 20, 20, 20, 20
Share of all: 10%, 30%, 50%, 70%, 90%
This is an example. Type your own values to start a new problem.
N
Beetles in each generation
example
b₁
Brown beetles in generation 1
example
d
More brown beetles each generation
example
b₂
Brown beetles in generation 2
worked out (not typed)
b₃
Brown beetles in generation 3
worked out (not typed)
b₄
Brown beetles in generation 4
worked out (not typed)
b₅
Brown beetles in generation 5
worked out (not typed)
Formulas
b₂
=
b₁
+
d
(brown
beetles
in
generation
2
=
brown
beetles
in
generation
1
+
more
brown
beetles
each
generation)
6 = 2 + 4
b₃
=
b₂
+
d
(brown
beetles
in
generation
3
=
brown
beetles
in
generation
2
+
more
brown
beetles
each
generation)
10 = 6 + 4
b₄
=
b₃
+
d
(brown
beetles
in
generation
4
=
brown
beetles
in
generation
3
+
more
brown
beetles
each
generation)
14 = 10 + 4
b₅
=
b₄
+
d
(brown
beetles
in
generation
5
=
brown
beetles
in
generation
4
+
more
brown
beetles
each
generation)
18 = 14 + 4
Assumptions
•
Beetles vary: some are brown, some green. Birds see green beetles on brown bark more easily and eat more of them.
•
Brown beetles survive and breed more, so each generation has more brown beetles than the one before.
•
The population stays the same size, and here it gains the same number of brown beetles each generation: a simple model of an average.
•
Nobody chooses to turn brown. The environment favors the beetles that already are.
Step-by-step
WE KNOW
N = 20 (beetles in each generation), b₁ = 2 (brown beetles in generation 1), d = 4 (more brown beetles each generation)
FIND
brown beetles in generation 2 (b₂), brown beetles in generation 3 (b₃), brown beetles in generation 4 (b₄), brown beetles in generation 5 (b₅)
Step 1 · Find brown beetles in generation 2 (b₂)
Use b₂ = b₁ + d (brown beetles in generation 2 = brown beetles in generation 1 + more brown beetles each generation)
The generation before, plus the brown beetles gained: more brown beetles survive to breed. A steady gain is a simplification: real gains depend on how many brown beetles there are.
b₂
=
2
+
4
b₂
=
6
Step 2 · Find brown beetles in generation 3 (b₃)
Use b₃ = b₂ + d (brown beetles in generation 3 = brown beetles in generation 2 + more brown beetles each generation)
The generation before, plus the brown beetles gained: more brown beetles survive to breed. A steady gain is a simplification: real gains depend on how many brown beetles there are.
b₃
=
6
+
4
b₃
=
10
Step 3 · Find brown beetles in generation 4 (b₄)
Use b₄ = b₃ + d (brown beetles in generation 4 = brown beetles in generation 3 + more brown beetles each generation)
The generation before, plus the brown beetles gained: more brown beetles survive to breed. A steady gain is a simplification: real gains depend on how many brown beetles there are.
b₄
=
10
+
4
b₄
=
14
Step 4 · Find brown beetles in generation 5 (b₅)
Use b₅ = b₄ + d (brown beetles in generation 5 = brown beetles in generation 4 + more brown beetles each generation)
The generation before, plus the brown beetles gained: more brown beetles survive to breed. A steady gain is a simplification: real gains depend on how many brown beetles there are.
b₅
=
14
+
4
b₅
=
18
Check
Put the numbers back in. Both sides should match.
6 = 2 + 4 ✓
10 = 6 + 4 ✓
14 = 10 + 4 ✓
18 = 14 + 4 ✓
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Asexual or sexual reproduction?
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Natural selection or artificial selection?
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