Lecture 15
 from last time: prove that the decline of a population above its carrying capacity is
faster than
the corresponding increase below K
Review of terms
 competition: use or defense of a resource that reduces availability of that resource
for another
individual
2 types:
1. exploitation
2. interference
LotkaVolterra models of competition
 mathematical derivation
Species 1
Species 2
dN
1
/dt = r
1
N
1
(K
1
N
1
/K
1
)
dN
2
/dt = r
2
N
2
(K
2
N
2
/K
2
)
dN
1
/dt = r
1
N
1
(K
1
N
1

α
12
N
2
/K
1
)
dN
2
/dt = r
2
N
2
(K
2
N
2

α
21
N
1
/K
2
)
α
12
and
α
21
are competition coefficients
α
12
= per capita effect of species 2 on species 1, measured relative to effect of species 1 on
itself
α
21
= per capita effect of species 1 on species 2, measured relative to effective of species 2 on
itself
if 1 and 2 are equal, adding another species of 2 will have same effect of adding a species 1
let species 1 = wildebeest
dN
w
/dt = r
w
N
w
(K
w
N
w

α
wb
N
b
/K
w
)
α
wb
= effect of one buffalo on one wildebeest
if
α
wb
= 1, intraspecific competition = interspecific competition
if
α
wb
> 1, interspecific competition> intraspecific competition
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α
wb
< 1, interspecific competition < intraspecific competition
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 Winter '08
 R.Howard
 Biology, per capita, Interspecific competition, intraspecific competition, Biological interactions

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