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Lotka-Volterra Models

Discussion of the distribution and abundance of living organisms and how these properties are affected by interactions between the organisms and their environment

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Lotka-Volterra Models

Postby BioCore » Mon Nov 10, 2008 5:08 pm

Hi,

I am trying to complete an assignment, but in the background information there is one piece of information that is very confusingly written, and I can not seem to find out some other source to help.

Specifically I am talking about the coefficients of competition. This is what they say for alpha as an example:
"If individuals of species 2 have less effect on an individual of species 1 than on members of their own species, α<1."
Now when they say the part in bold, are they referring to the intraspecific effects of species 1 on itself or of species 2 on itself? It sounds as if it is referring to species 2, but I think it means species/population 1. Am I correct? Thanks again.
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Re: Lotka-Volterra Models

Postby JAP1st » Mon Nov 10, 2008 6:18 pm

Hi, are you sure the a < 1 is actually alpha?

I'm asking because if it is alpha (representing the independent growth rate of the prey's population) then a lesser effect of the predators population (P1) on the preys population (P2) would result in a higher alpha (although alpha is actually being considered as the natural growth rate of the P2 in absence of predation).

I think a < 1 is more likely to represent the predation rate coefficient, and thus the statement you cite would make more sense (the lesser the effect of P1 on P2 and higher the intraspecific competition of P1, the lesser the predation coefficient).

I'm not quite familiar with this model, but different authors change the symbols of the equation.

Here are some further web references that might help you:

http://home.comcast.net/~sharov/PopEcol/lec10/lotka.html
http://www.stolaf.edu/people/mckelvey/envision.dir/lotka-volt.html
http://mathworld.wolfram.com/Lotka-VolterraEquations.html

I hope it helps (and please correct me if I'm wrong, my community ecology subject in college was not quite well imparted).

Greetings,
JAP
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Postby BioCore » Mon Nov 10, 2008 6:55 pm

Actually this model that we are studying currently does not take predation into account between the two populations. The two populations, are just species whose growth is limited by resources and competition for these resources. By the way the description I put up there was from background info, as in a general meaning and not the assignment information.

In the assignment itself, alpha is 1 which mean that the effect of species 2 on species 1 is same as that of its own population. And Beta is 0.5, in other words the interspecific effect on population 2 is less than the intraspecific competition.

Also I believe I have understood variables myself, when it says up there: "If individuals of species 2 have less effect on an individual of species 1 than on members of their own species, α<1.", they are referring to the intraspecific competition, that is talking about species 1.
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Re:

Postby JAP1st » Mon Nov 10, 2008 7:43 pm

Huh, it is actually quite confusing. I also think the statement refers to alpha as the intraspecific competition, although syntax intuition tells me otherwise (Do not pay attention to my poor mathematical skills).

BioCore wrote:And Beta is 0.5, in other words the interspecific effect on population 2 is less than the intraspecific competition.

I would interpret it as
beta = (SP1onSP2 < SP2onSP2) = 0.5 < 1
where SP2onSP1 is the interspecific effect on population 2 by population 1, and SP2onSP2 is the intraspecific effect on population 2 by itself.

Biocore wrote:alpha is 1 which mean that the effect of species 2 on species 1 is same as that of its own population.

Thus, I interpret this as
alpha = (SP2onSP1 = SP1onSP1) = 1
where SP2onSP1 is the interspecific effect on population 2 by population 1, and SP1onSP1 is the intraspecific effect on population 1 by itself.

Therefore, alpha and beta would be sort of reciprocal (alpha focused on the effects on SP1, and beta focused on the effects on SP2). The result of the interaction between alpha and beta would be that the interspecific effect on SP1 by SP2 is greater than the interspecific effect on SP2 by SP1 (assuming the intraspecific interactions for SP1 and for SP2 are of an equal magnitude).

And thus,
BioCore wrote:"If individuals of species 2 have less effect on an individual of species 1 than on members of their own species, α<1."

would mean
alpha = (SP2onSP1 < SP1onSP1) < 1
which would be the opposite result.

Unless, of course, an interaction of the kind aplha' = (SP2onSP1 < SP2onSP2) < 1 actually meant something in the model.

I believe I may have confused both of us even more, which has happened to me quite frequently, hehe. So.. sorry beforehand.
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Postby BioCore » Mon Nov 10, 2008 7:56 pm

That is ok, I just read your comment a couple of times and I think I understand it better. Thanks again Jap.
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