BIO120H1 Lecture Notes - Lecture 20: Interspecific Competition, Intraspecific Competition, Logistic Function

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12 Jul 2017
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BIO120: Species Interactions From Two-Species Population Models to
Community Structure (Lecture 20)
Partial Classification of Species Interactions
-types of interactions classified (+ or -) by who suffers and who benefits
1. consumer-resource (+/-): one species eats another, derives energy from it
predator-prey
plant-herbivore
host-parasite
2. competition (-/-): typically thought of as on e species using up resources, exhausting
supply so that other species suffers; both species attacking same pool of resources, each
having negative effect on competitor
3. mutualism (+/+)
e.g. pollination biology: pollinators help plant populations by letting them exchange
gametes, plants help pollinators by providing rewards in form of pollen and nectar
-foci of study:
1. population dynamics (ecological effects on N’s, can species coexist)
2. evolutionary dynamics (adaptation, coevolution)
Interspecific Competition for Resources
-basic model: Lotka-Volterra equations for two species competing for resources
-simple outgrowth of logistic equation:
logistic already has braking term for intraspecific competition within species
adds second braking term for interspecific competition between species
1. rewrite logistic with subscripts to indicate Species 1
2. add a term to show effect on Species 1 by Species 2
3. write matching equation for Species 2
4. ji = per-capita effect on i by j (competition coefficient)
-these paired differential equations are the Lotka-Volterra model for combined
intraspecific and interspecific competition
Possible Outcomes of L-V Competition
-expect now to solve for N1 and N2 as f(t)
-instead, specify 4 possible equilibria:
1. the two species may stably coexist
2. species 1 may always win (N1 = K1, N2 = 0)
3. species 2 may always win (N2 = K2, N1 = 0)
4. identity of winner may depend on starting N’s
-outcomes depend on values of K’s and ’s
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-coexistence requires both species to inhibit their own growth more than they inhibit each
other’s
-can expand to consider n species
Law of Competitive Exclusion
-LV outcomes became widely interpreted as basically unstable
complete competitors cannot coexist
true for simple math models, but not so true in nature because various external factors
can prevent even unstable competition from going to completion
LV Models and the Real World
-LV models formed core of ecological theory
-experiments by Gause (1930s):
good description of competition by protozoa in artificial culture vessels; saw both
stable coexistence and competitive exclusion, can often be unstable
predator-prey strongly tended to be unstable (predators eat all prey, then starve), unless
habitat complexity added
did get some stability with competition
if he grew 3 species by themselves, got fairly good fits for logistic
combination of two species: different outcomes depending on species
red and yellow: competitive exclusion, species can’t coexist, one species outcompetes
other and drives out of community
red and green: stable coexistence (both below K’s)
How are Competitive Effects Maintained in Nature?
-competitive exclusion is less likely to go to completion, but abundances can be
drastically altered and distributions in space altered
-biological effects interact with physical effects: different outcomes in different
environments
-natural selection may select for higher competitive ability or for reducing resource-use
overlap
Tansely 1917 Garden Experiments
-two species of Galium: outcome depends on environment in which they compete
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