Dear Augusto,
A product is zero only if one of the multipliers is zero.
r2=0 and/or N2=0 are mathematically correct, but biologically
meaningless solution of the equation.
If r2>0 and N2>0 than the only solution is
(1 - alpha21*N1 - alpha22*N2)=0
Best wishes
Zoltan
2013.08.13. 22:09 keltezéssel, Augusto Ribas írta:
Hello dear list members, i was reading the book Primer of Ecology with R
from M Henry H Stevens and got a simple doubt, its not about R but hope
someone could spare one moment with it, its a little off-topic but maybe
could of general interest.
On the chapter 5, more specifically 5.2.1 he start to teach about
iscoclines for 2 populations.
He set the change of one species to zero and solve for the other. My doubt
is about this part:
We have logistic growth for one species and one competitor:
Dn2/dt = r2*N2 * (1 - alpha21*N1 - alpha22*N2)
Then he set Dn2/dt=0, zero change and solve for N2, and we got:
0 = r2*N2 * (1 - alpha21*N1 - alpha22*N2)
The next step is:
0 = 1 - alpha21*N1 - alpha22*N2
And we end with:
N2 = 1/alpha22 - N1 * alpha21 / alpha22
And this end in a line equation that is the iscocline for this 2 species
system, the isocline line for species 2.
I got this part, my doubt is what happens between this two steps:
0 = r2*N2 * (1 - alpha21*N1 - alpha22*N2)
To
0 = 1 - alpha21*N1 - alpha22*N2
How the r2*N2 that multiply everything in the parenthesis vanishes? does it
is simply put on the other side and when divided by zero it becomes zero?
Or there is something more about this?
I dont know if i got this right.
--
Botta-Dukát Zoltán
--------------------------------
Ökológiai és Botanikai Intézet
Magyar Tudományos Akadémia
Ökológiai Kutatóközpont
--------------------------------
2163. Vácrátót, Alkotmány u. 2-4.
tel: +36 28 360122/157
fax: +36 28 360110
botta-dukat.zol...@okologia.mta.hu
www.okologia.mta.hu
Zoltán BOTTA-Dukát
--------------------------------
Institute of Ecology and Botany
Hungarian Academy of Sciences
Centre for Ecological Research
--------------------------------
H-2163 Vácrátót, Alkomány u. 2-4.
HUNGARY
Phone: +36 28 360122/157
Fax..: +36 28 360110
botta-dukat.zol...@okologia.mta.hu
www.okologia.mta.hu
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