# BIOC50H3 Lecture : lecture note 20 for BGYB50

LECTURE 20:

- Competition affects per capita survivorship, susceptibility to disease, and, very

predictably, body size and weight (Yoda’s Law: individual body weight and density are

correlated inversely; in a log-log plot of these parameters, a linear relationship is

frequently found, with a slope of -3/2; example: forest stands: trees are smaller when

there are many of them compared to only a few; conversely, if trees “want” to grow

larger, they will have to reduce their own density through self-thinning)

- In order to describe the competitive interactions between populations of two species, we

need to modify the logistic equations for those populations by incorporating the per

capita competitive effect (!) each has upon the other

- ! gives the relative “muscle power” of the two species populations in relation to each

other

- Subscripts to ! denote the directionality of the competition effect (!12 = the per capita

competitive effect on species 1 of species 2; !21 = the per capita competitive effect on

species 2 of species 1); e.g. !12 = 0.5, if the average individual in the population of

species 2 is half “as strong” as the average individual in the population of species 1; in

other words, multiplying N2 by !12 converts any given number of individuals of

population 2 to a number of “N1 equivalents”

- The logistic equations then become:

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## Document Summary

In order to describe the competitive interactions between populations of two species, we need to modify the logistic equations for those populations by incorporating the per capita competitive effect () each has upon the other. gives the relative muscle power of the two species populations in relation to each other. These are known as the lotka-volterra equations for competition. Clearly, populations 1 and 2 will stop to grow when dn1/dt = 0, and dn2/dt = 0, respectively. The same can be done for species 2, and both lines (isoclines) and intercepts can be graphed in the same plot (which, by convention, has n1 as the x-axis and n2 as the y- axis) www. notesolution. com. The isoclines in these graphs delineate the areas where the numbers of populations 1 and 2 can increase (to the left of the respective isoclines) or have to decrease (to the right of the isoclines)