J. H. Connell, Ecology, 1961. The influence of interspecific
competition and other factors on the distribution of the p
f
f
barnacle Chthalamus stellatus.
Lotka‐Volterra Competition
Alfred J. Lotka (1880 – 1949), Vito Volterra (1860 – 1940)
LLotka‐Volterra
tk V lt
models (including competition): Per capita growth d l (i l di
titi ) P
it
th
rate of any species depends linearly on the densities of other species in the community.
 N1   N2 
1 dN1
 r1  1 

N1 dt
K1


 N2   N1 
1 dN2
 r2  1 

N2 dt
K

2

Isoclines are not necessarily straight lines
from Gilpin & Justice, Nature, 1972
Resource competition
David Tilman
competition among algae in chemostats
Photo credit Thomas Massie
What are “resources”?
Tilman: “A resource is defined as a consumable factor for which increases in its availability lead to increased per capita reproductive rates, through at least some range of its d ti
t th
h tl t
f it
availability. … It is through the depression of resource levels caused by consumption that species compete with each other, and thus that resources may influence the structure of communities. ”
Examples (for plants): Water, light (PAR), nutrients, space (for sessile plants)
Temperature is not a resource (why?)
Resource competition, a la Tilman
For each resource:
Rate of change of resource
=
Resource supply
‐
Biotic consumption
=
Resource‐
dependent
dependent reproduction
‐
Mortality
For each consumer:
Per capita rate of change
Resource competition, a la Tilman
For each resource:
Rate of change of resource
=
Resource supply
‐
Biotic consumption
=
Resource‐
dependent
dependent reproduction
‐
Mortality
For each consumer:
Per capita rate of change