Lecture 11 - Competition
Intraspecifics lectures of Dr.Laurel Fox (UCSC)
Specifically, interspecific competition
That is, competition that occurs between two or more species that is driven by limitation (short supply) of requisite resources. To affect a species it need only be competition for one limiting resource.
Competition is any interaction between two or more species over a limiting resource that causes a decrease in population growth of one of the species.
Competition can take two forms:
Resource competition (also referred to as scramble or interference competition).
Interference competition (or contest competition).
Direct interaction by one species resulting in harm to the other.
Work on the nature of competition and its significance in explaining the distribution of species have resulted in some of the best paradigms in ecology and evolution.
Although Darwin recognized the importance of competition in nature he never clearly defined it.
The first to empirically explore competition was the Russian biologist Gause (1930's). His work was inspired by two mathematicans Lokta (American, 1925) and Volterra (Italian, 1926) would independendently derived the same result - species competing for the same resource(s) cannot coexist.
Results from Gause's laboratory studies confirmed this result - became known as the "Competitive Exclusion Principle"
We start with the mathematical model derived by Lotka-Volterra.
Using the logistical equation, they modeled the outcome of two species competing for the same resource. Goal was to find conditions where coexistence was possible.
For species 1:
dN1/dt = r1N1(K1-N1/K1)
For species 2:
dN2/dt = r2N2(K2-N2/K2)
In the model, the fraction of the habitat still unoccupied is equal to K-N/K.
Suppose we say that the competitive abilities of species 1 and 2 are asymmetrical.
Let's say that 3 individuals of species 2 have the same negative effect (inhibitory effect) on species 1 as a single individual of species 1 has on itself (intraspecific competition).
So, 3 individ. of species 2 = 1 individ. of specie 1
So now,
N1 + N2/3 = total competition effect (intra- and
intra inter interspecific) on species 1 as N approaches K.
The constant (in this case 1/3) is called a competition coefficient denoted as a 1,2 or sometimes just a = 0.3.
So, if we multiply a 1,2 x N2 it will convert it to a number of "N1 equivalents"
e.g. N2/3, and N2=9, then 9/3=3 and a 1,2= 0.3, N2 = 9
if a 1,2= 0.3 and N2 =100 then "N1 equivalents" = 30
if a 1,2= 3 and N2 =100 " " " = 300
so when a 1,2 <1, it means that species 2 has less inhibitory effects on species 1 than species 1 has on itself. And vice versa a 1,2 >1 more inhibitory effect.
Now, in the logistical equation model for species 1 we can add the effects of species 2 in the system.
(for a 1,2 ) dN1/dt = r1N1 [K1-(N1+ a 1,2 N2)/K1]
conversely,
(for a 2,1 ) dN2/dt = r2N2 [K2-(N2+ a 2,1 N1)/K2]
The model assume that r and K are constant, although they can be different for each species.
Also assumes:
Now what are the conditions that might lead to coexistence? Species population growth is assumed to be limited by the same resources used by both species.
Equilibrium is population growth occurs when
dN/dt = 0, i.e. no change in population growth.
When we set dN/dt=0, where dN/dt=rN(K-N/K)
0=K-N when N=K.
For species 1, N1=K1 - a 1,2 N2 ,
where K1-(N1+ a 1,2 N2)/K1 = dN/dt
N1 + a 1,2 N2 = K1 or, N1= K- a 1,2 N2
For species 2, N2 =K2 - a 2,1 N1
These two equations represent the conditions which the population sizes of species 1 and species 2 do not change.
For species 1:
When N1 = 0, N2= K1/a 1,2 where, 0= K1 - a 1,2 N2
K1=a 1,2 N2
N2= K1a 1,2
and when N2=0, N1=K1,
see graph 1
For species 2:
When N2=0, N1=K2/a 2,1 and when N1=0, N2=K2
See graph 2
The slopes of the curves will indicate the intensity of competition:
See graphs 3, 4
Interspecific competition is more intense in example 1 because the abundance of the species 2 has a far greater effect on species 1, i.e. N2 equivalents to N1, a 1,2>> 1