Download Bio 152 L. R. Fox INTERSPECIFIC COMPETITION Review from your

Bio 152
L. R. Fox
INTERSPECIFIC COMPETITION
Review from your Basic Ecology Class
This handout summarizes some basic theory and recent examples of competition. It should be a review
from an introductory ecology course, and a slightly different way of explaining the interactions as
presented by Morin (pp34-39).
1. THE COMPETITION MODELS
A general competition model assumes that each of 2 competing species (in the simplest case) are
growing logistically in the same environment and that they are competing for, and are limited
by, the same resources. The model is a pair of equations, one for each species, derived from the simple
logistic model.
New Symbols
1 subscript to identify Species 1 (S1)
2
α12
subscript to identify species 2 (S2)
competition coefficient measuring the effect of S2 on S1; it expresses N2 as the number of
individuals of S2 which would have the same depressive effect on the resources needed by N1
individuals of S1
α21 competition coefficient measuring the effect of S1 on S2 (expressed as units of S2)
Model
(1)
dN1 = r1N1 (K1 - N1 - α12 N2)
dt
K1
dN2 = r2N2(K2 - N2 - α21 N1)
dt
K2
Note: In competitive situations, α12 and α21 are positive, but the model is quite general, and mutualistic
and symbiotic interactions, predation, or no interaction at all can be described by different combinations
of zero, positive and/or negative values of those coefficients.
Derivation:
This model is derived directly from the logistic equation by modifying the number of resource "spaces"
(K) used when 2 species are present. In single-species logistic growth,
(2)
N is the number of intraspecific
dN = rN(K-N)
dt
K
competitors at any given time
1
A second species can be added simply by using subscripts to identify each species and adding an
expression for the competitive effect of S2.
(3)
dN1 = r1N1 (K1 - N1 ) - f (N2))
dt
K1
The simplest assumption to make about how the species interact is that there is a linear relationship, that
each individual in S1 uses resources as some number of individuals in S2. (This works the same way as
currency transactions, where, for example, the British pound in worth about $1.50 on the world market.)
α12
N1
N2
(4)
N1 = m N2 (straight line through the origin)
N1 = α12 N2
The competition coefficient, α12 , is simply the slope of this line. Substituting this value back into
equation (3) gives a complete competition equation (e.g., equation 1)
An analogous equation can be written to describe the dynamics of S2 in competition with S1.
Properties
The value of the competition coefficients (α12 and α21 ) indicates the intensity of competition between
these two species. The higher the value, the stronger the interactions.
6 -N1
α12 = 3
α12 = 1
3 -α12 = .3
|
3
N2
|
6
2
The competitive "worth" of each individual of S2 compared to S1 members:
α12
3
1
.3
Effect
S2 strong competitor of S1
S2 has same effect as individuals of S1
S2 has little effect on S1 ; weak competitor
Competition
inter- > intrainter- = intrainter- < intra
The main competition model then is a set of 2 equations, each describing the growth of a species in a
way that accounts for both intraspecific and interspecific competition.
The outcomes of competition can be found by solving this set of equations (1), when population
growth is 0. In (5), neither population is growing.
(5)
dN1 = 0 = dN2
dt
dt
Intuitively, if K1 = K2, then the possible outcomes depend only on the relative strengths of interspecific
interactions.
II. GRAPHICAL INTERPRETATION
At equilibrium, neither population is growing, eq. (5). So, for S2,
dN2 = r2N2(K2 - N2 - α21 N1) = 0
dt
K2
0 = K2 - N2 - α21 N1
(6)
N2 = K2 - α21 N1
This is an equation of a straight line (y=mx+b):
K2
N2
y intercept: K2
x intercept: K2
α21
slope:
- α21
N1
K2
α21
The line itself describes the boundary for growth of S2. Anywhere on this line, S2 does not grow, but
maintains a given density (N2) for each level of abundance (N1) of S1. Anywhere below this line, S2
increases in abundance. Anywhere above this line S2 populations must decline.
The slope of the line is entirely determined by the strength of competition (α21) of S1 on S2. As
competition gets weaker, α21 declines and eventually may even become 0 when S1 has no effect on S2.
This shifts the curve along the x-axis. The y-intercept (K2) remains the same!!
3
K2
K2
K2
K2
α21
K2
α21
small
medium
infinite
competitive
effect S1 on S2
strong
weaker
no comp
α21
large
smaller
K2
α21
0
Finally, when the growth of both S1 and S2 are considered at the same time, there are a variety of
interactions depending on the competition coefficients and on K1 and K2. You can see these directly from
the graphs just drawn.
1. If one species has a higher equilibrium growth potential (dN/dt =0) than the other (over all possible
abundances) it always wins, as long as the assumptions of the model are met.
Here, S1 always wins.
This is Competitive Exclusion of S2 by S1.
N2 K2
N1
K1
2. As competition gets weaker (the effect of S1 on S2 declines) and α21 gets smaller, the slope of the line
for S2 moves to the right along the x-axis (see above). Once interspecific competition gets so weak these
lines cross (but only in the way shown below!!), both species can survive because FOR EACH SPECIES,
intraspecific competition is now stronger than interspecific competition.
4
Both species can coexist
at stable densities where
the two lines cross. This is a
stable equilibrium because it is
reached no matter what are the initial
population sizes (see arrows).
K2
K1
III. THE IMPORTANCE OF COMPETITION
Many ecologists have argued that competition is the main ecological process structuring communities,
either because of present-day interactions or because of previous competitive encounters. The
"importance" of competition was addressed in a debate published in a journal (The American Naturalist)
in 1983, and issued separately the next year (edited by G. Salt). One paper in this debate, by Joseph
Connell, actually evaluated the experimental demonstrations of competition in the previous 10-15 years
and was able to quantify the current relevance of competition pressures.
% of competition in field experiments:
# of
% of expts/species showing
expts/sp
interspecific competition
1(1 sp in study)
93 - probably artifact
1(>1 sp)
48
2
50
3-5
37
6-13
9
--mean =
43 (w/ >1 sp)
# Species
15
65
63
58
14
--215
These data show that competitive interactions are clearly important, though their assessment as the 'major'
interaction declines as more experiments are done with a species to assess variation in interactions in
space or in time.
% of experiments showing interspecific competition:
trophic level terrestrial
marine
fresh-water
Plants
30
68
50
Herbivores
20
69
no expts
Carnivores
11
60
67
--------Totals
26%
67%
60%
(286 spp)
(49spp)
(5spp)
mean
35
31
20
32%
(340spp)
These data show the distribution of examples of competition across trophic levels and habitats. Twothirds of the experiments in marine systems (almost entirely from the rocky intertidal)
have demonstrated competitive interactions. Fresh-water systems may also show high competitive levels,
but only 5 experimental studies had been done in any fresh-water communities. About 25%
of studies in terrestrial systems showed competitive interactions, with more occurring among plants
(30%) than among carnivores (11%).
5