Chapter 16: Competition It s all mine, stay away!
Species Interactions +/+ +/- -/-
Basic interaction -/- Pop growth rate of species 1 (dn 1 /dt) is decreased by interaction Pop growth rate of species 2 (dn 2 /dt) is decreased by interaction
Competition in general The use or defense of a resource that reduces the availability of the resource to others intraspecific: equilibrium population size interspecific: coexistence vs exclusion Density dependent process
Resources Consumable food space and other such Its consumption increases population growth Scarce resources tend to limit population growth (Leibig s law of the minimum ) Synergy between resources may be important
Limiting Resources Liebig s law of the minimum: each population increases until the supply of some limiting resource becomes depleted
Limitation by Interacting Resources Liebig s law does not apply if resources interact in their effects examples of interactions effects fertilized plants are better capable to respond to light than unfertilized plants various nutrients (e.g., nitrogen and phosphorus) interact in a synergistic fashion to promote plant growth
Tansley s Classic Study A.G. Tansley demonstrated competition between closely related species Two species of the genus Galium: G. saxatile is normally found on acid, peaty soils G. sylvestre is normally found on limestone hills and pastures Are they restricted to their habitats by competition?
Figure 16.1 Planted alone, each species performed better on its preferred soil, although each could grow on the other In mixture, each species overgrew and shaded the other on its preferred soil type
General Implications the presence or absence of species can be determined by competition with other species conditions of the environment affect the outcome of competition competition may be felt very broadly throughout the community the present segregation of species may have resulted from past competition
Mechanisms of competition Consumptive Preemptive Overgrowth Chemical Territorial Encounter
Modeling competition Density - dependent population growth Equilibrium conditions Non-equilibrium conditions Phase space for two species dynamics
Model dn/dt = rn( 1- N/K) add interspecific competition alpha = the rate at which individuals of the other species uses up the carrying capacity relative to individuals of its own species Species 1 dn 1 /dt = r 1 N 1 ( 1- N 1 /K 1 - α 12 N 2 /K 1 ) Species 2 dn 2 /dt = r 2 N 2 ( 1- N 2 /K 2 - α 21 N 1 /K 2 )
Review single species densitydependence dn/dt = rn( 1- N/K) Solve for equilibrium The population stops growing when carrying capacity is reached dn/dt = 0 rn( 1- N/K) = 0 1 = N/K N= K
Two species Species 1 dn 1 /dt = r 1 N 1 ( 1- N 1 /K 1 - α 12 N 2 /K 1 ) Combinations of species 1 and species 2 can fill the carrying capacity 0= 1- N 1 /K 1 - α 12 N 2 /K 1 0= K 1 /K 1 - N 1 /K 1 - α 12 N 2 /K 1 0= K 1 - N 1 - α 12 N 2 α 12 N 2 = K 1 - N 1 N 2 = (K 1 - N 1 )/ α 12 N 2 = K 1 / α 12 - N 1 / α 12 (y= b+ mx)
Two species Species 2 dn 2 /dt = r 2 N 2 ( 1- N 2 /K 2 - α 21 N 1 /K 2 ) Combinations of species 1 and species 2 can fill the carrying capacity N 1 = (K 2 - N 2 )/ α 21
Number of individuals of Species 2 Phase space: dynamics of species 1 K 1 /alpha 12 What happens if you start over here? Number of individuals of Species 1 K 1
Number of individuals of Species 2 Phase space: dynamics of species 2 K 2 Number of individuals of Species 1 K 2 /alpha 21
How many ways can the lines cross? Species 1 wins Species 2 wins Unstable coexistence Stable coexistence If K s are nearly equal, then stable coexistence is possible when the intraspecific effects are greater than the interspecific effects
Number of individuals of Species 2 K 1 /alpha 12 Lets see how the lines divide the space look at intercepts look at arrows look at combined arrows imagine moving the lines K 2 Number of individuals of Species 1 K 1 K 2 /alpha 21
Number of individuals of Species 2 Species 1 wins K 1 /alpha 12 K 2 K 2 /alpha 21 Number of individuals of Species 1 K 1
Number of individuals of Species 2 Species 2 wins K 2 K 1 /alpha 12 Number of individuals of Species 1 K 1 K 2 /alpha 21
Number of individuals of Species 2 Unstable equilibrium leads to one species winning. determined by where you are after departing from pt. K 2 K 1 /alpha 12 K 2 /alpha 21 Number of individuals of Species 1 K 1
Number of individuals of Species 2 Stable coexistence when: interspecific competition is weak (alpha<1) this occurs when competitors share resources or partition resources K 1 /alpha 12 K 2 Number of individuals of Species 1 K 1 K 2 /alpha 21
Some insights from the model Competitive exclusion is common Coexistence is the outcome only when interspecific competition is weak Species using the same resource continuum will partition it Limiting similarity among competitors
Competitive exclusion similar experiments conducted on a wide variety of species have tended to show the same thing - one species persists and the other dies out, usually within 30-70 generations Gause s Paramecium experiments
Competitive exclusion principle No two species can stably co-exist on the same exact resource Equilibrium theory Leads to character displacement Limiting similarity may structure communities Limiting similarity may determine the number of species that can co-exist on a resource continuum
Coexistence although similar species exist careful study usually reveals they differ in their habitat or diet requirements too much overlap unstable Unstable: too much overlap
Coexistence although similar species exist careful study usually reveals they differ in their habitat or diet requirements for stability overlap is limited stable: little overlap
Beak size reflects diet: seed size Seeds of different sizes form the resource continuum How does beak size change when species are alone vs in competition? Limiting similarity in Darwin s finches
Competition among animals in the intertidal zone Connell s studies barnacles compete for space Chthamalus is more tolerant of desiccation and thrives in the upper intertidal zone Balanus is less tolerant of desiccation but can displace Chthamalus in the lower intertidal zone
Figure 16.11: Competition, physical limits and predation Connell s studies in Scotland
The outcome of competition can be influenced by predators. Experiments by Robert Paine in the rocky intertidal (on Pacific coast) a key predator (starfish Pisaster) was removed competition among their prey (barnacles, mussels, limpets, chitons) increased diversity (no. of species) of these intertidal animals decreased predation reduces competitive exclusion
Summary Competition is the use or defense of a resource by two or more consumers Limiting resource Interference vs. exploitation Mathematical models build on the logistic model Competitive exclusion common but predation may prevent it Stable coexistence: when interspecific competition is weak leads to limiting similarity