SME
Grade 9 Science · Biology
Ecosystems: energy pyramids, matter cycles, succession and biodiversity
Use this for “Grasses store 12,000 kcal and 8% passes up each level. How much energy reaches the owls?”
Diagram
8% of 12,000 kcal = 960 kcal
8% of 960 kcal = 76.8 kcal
8% of 76.8 kcal = 6.14 kcal
This is an example. Type your own values to start a new problem.
E₂ (kcal)
=
E₁ (kcal)
×
p
÷
100
E₃
Energy in the shrews
calculated · kcal
E₄
Energy in the owls
calculated · kcal
Formulas
E₂
=
E₁
×
p
100
960
=
12,000
×
8
100
E₃
=
E₂
×
p
100
76.8
=
960
×
8
100
E₄
=
E₃
×
p
100
6.14
=
76.8
×
8
100
Assumptions
•
The trophic efficiency p varies, about 5–20%; the rest of the energy is used in respiration or lost as heat.
•
Biomass pyramids usually follow the energy pyramid, but a numbers pyramid can stand upside down: one oak feeds thousands of caterpillars.
•
Energy flows one way through the levels; matter cycles.
Step-by-step
WE KNOW
E₁ = 12,000 kcal, E₂ = 960 kcal
FIND
trophic efficiency (p), energy in the shrews (E₃), energy in the owls (E₄)
Step 1 · Find trophic efficiency (p)
Use E₂ = E₁ × p ÷ 100
The energy passed up as a percent of the level below.
p
=
100
×
E₂
E₁
p
=
100
×
960
12,000
p
=
96,000
12,000
p
=
8%
Step 2 · Find energy in the shrews (E₃)
Use E₃ = E₂ × p ÷ 100
Only
p
%
of
the
energy
in
the
grasshoppers
is
stored
in
the
level
above.
E₃
=
960
×
8
100
E₃
=
7,680
100
E₃
=
76.8
kcal
Step 3 · Find energy in the owls (E₄)
Use E₄ = E₃ × p ÷ 100
Only
p
%
of
the
energy
in
the
shrews
is
stored
in
the
level
above.
E₄
=
76.8
×
8
100
E₄
=
614.4
100
E₄
=
6.14
kcal
Check
Put the numbers back in. Both sides should match.
960
=
12,000
×
8
100
✓
76.8
=
960
×
8
100
✓
6.14
≈
76.8
×
8
100
✓
Topic check
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