barnacle Chthalamus stellatus . Lotka Volterra Competition Alfred J. - - PowerPoint PPT Presentation

• 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) L tk V lt d l (i l di titi ) P it th Lotka‐Volterra models (including competition): Per capita growth rate of any species depends linearly on the densities of other species in the community.

1 1 2 1

1 1 dN N N r N dt K          

1 1 2 2 1 2

1 1 N dt K dN N N r N dt K            

2 2

N dt K  

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 d ti t th h t l t f it reproductive rates, through at least some range of its

• 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

• f resource

= Resource supply ‐ Biotic consumption For each consumer: Per capita rate = Resource‐ dependent ‐ Mortality

• f change

= dependent reproduction ‐ Mortality

Resource competition, a la Tilman For each resource: Rate of change

• f resource

= Resource supply ‐ Biotic consumption For each consumer: Per capita rate = Resource‐ dependent ‐ Mortality

• f change

= dependent reproduction ‐ Mortality