Desired results Heres an approximation of reality The hare birth rate is constant as their food supply is unlimited Hares only die when eaten by a lynx and the number of hares eaten is proportional to how often hares amp lynxes meet ie the chance of a lynx catching a hare ID: 548488
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Slide1
Predicting predator-prey populationsSlide2
Desired resultsSlide3
Here’s an approximation of reality:
The hare birth rate is constant, as their food supply is unlimited. Hares only die when eaten by a lynx, and the number of hares eaten is proportional to how often hares & lynxes meet, i.e., the chance of a lynx catching a hare.
The lynx birth rate is also proportional to how often hares & lynxes meet, i.e., the food available for each lynx family. Lynxes only die from natural causes, and their death rate is constant.
Lotka
&
Volterra
, 1926
Dr.
Siemann
, EEBSlide4
Computational Thinking
Recipe (Algorithm)
Relevant input
Answer
Abstraction
Automation
Problem description
Computational goal
Information extraction
Algorithm design
Algorithm implementationSlide5
Hares’ & Lynxes’ Populations
Recipe (Algorithm)
???
???
Problem description
Computational goal
Information extraction
Algorithm design
Algorithm implementationSlide6
Algorithm Design – Decomposition
Generate population data.
Repeatedly,
G
enerate next populations of predator & prey.
Display population data.Slide7
Algorithm Design – Refinement
Store original populations.
Generate population data.
Repeatedly,
G
enerate next populations of predator & prey.
Store new populations.
Display stored population data.Slide8
Lotka
&
Volterra
, 1926
The hare birth rate is constant, as their food supply is unlimited. Hares only die when eaten by a lynx, and the number of hares eaten is proportional to how often hares & lynxes
meet, i.e., the chance of a lynx catching a hare.
The lynx birth rate is also proportional to how often hares & lynxes meet, i.e., the food available for each lynx family. Lynxes only die from natural causes, and their death rate is constant
.
Hare annual pop. change
Lynx annual pop. changeSlide9
Initially
(Year 0)
Year 1
Year 2
Year 3
# Hares
100
Hares
born
4
0
Hares
eaten
15
#
Lynxes
50
125
60
152
78
17
7
109
Lynxes
die
10
Lynxes
born
2
0
50
23
12
30
61
36
16
47
71
5
8
22
77
+
-
-
+
.4
.003
.004
.2
Hare annual pop. change
Lynx annual pop. change
Rounding
all #
s.Slide10
Algorithm Design – Refinement
Given
,
,
,
,
,
,
.
Store
in
. Store
in
.
Repeat for
:
Compute
Add
to end of
. Add
to end of
.
Plot
and
.
Slide11
Suggested Readings
Predator-prey models
Lotka-Volterra
equationWolves & Moose of Isle Royale
E
sp. the
Data sectionA technical paper about population cycles