© 2014 by Princeton University Press

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© 2014 by Princeton University Press Module 4.1 Competition Angela B. Shiflet and George W. Shiflet Wofford College © 2014 by Princeton University Press

Competition Competition is the struggle between individuals of a population (intraspecific) or between species (interspecific) for the same limiting resource.

Species Competition Example: Sparrows & juncos - ground feeders As one grows, other shrinks (both compete the same limited food source) Sparrow: Junco:

Species Competition Recall that in an unconstrained growth model (module 2.2), it ignores competition and limiting factors, and dP/dt = births – deaths = r1P – r2P, that is, P = P0e(r1 – r2)t. If competition is considered, we can model the number of deaths of each species as being proportional to its population size and the population size of the other species.

Sparrows versus Juncos Ps - pop. of sparrows Pj - pop. of juncos ∆(deaths of each species) Depends on interactions between Proportional to what? Proportional to Ps Pj ∆(sparrow death) = ? (sparrow death proportionality constant) Ps Pj ∆(junco death) = ? (junco death proportionality constant) Ps Pj

WTS (whitetip shark) vs. BTS (blacktip shark)

WTS (whitetip shark) vs. BTS (blacktip shark) dW/dt = aW - bWB, dB/dt = cB - dWB, W0 = 20, B0 = 15, a = 1, b = 0.27, c = 1, d = 0.2 Equilibrium solutions: a = bB and c = dW

WTS (whitetip shark) vs. BTS (blacktip shark) The computational scientist uses actual field data to establish reasonable parameters for a model.

WTS (whitetip shark) vs. BTS (blacktip shark)