[R-sig-eco] How to fit a logistic discrete function!

[Alexandre F. Souza]

Dear friends,

Sorry for the somewhat lengthy message, but I would really like to hear
your opinion on this.

I am organizing an undergraduation population ecology course and would like
to work the logistic equation as proposed by Bellows 1981 and presented by
Begon et al. 2006 in their Ecology textbook:

Nt+1 =(Nt*R)/((1+a*Nt)^b)

Where R is lambda, the discrete growth rate (R = Nt+1/Nt), and a and b are
constants.

The beauty of this equation, in contrast to other more traditional
formulatons, is because it bypasses the support capacity K, which is hard
to know in advance, and makes it a function of a and R as K = (R - 1)/a. So
K becomes a consequence of population properties and not an unrealistic
prerequisite. Furthermore, a is meaningful in its own right, measuring the
per capita susceptibility to crowding: the larger the value of a, the
greater the effect of density on the actual rate of increase in the
population. Finally, b is thought to portray undercompensation (b < 1),
perfect compensation (b = 1), scramble-like overcompensation (b > 1) or
even density independence (b = 0).

However, because the the equation is an iterative one, I am having a hard
time figuring out how to fit it to an empirical dataset made by a time
series of population counts. I believe this is key to make it more concrete
for the students, to show how to make it practical and not merely a
theoretical construct.

I could not find this equation used much often, and could not find an
example of how fitting it.

Does anyone have any suggestions?

Thank your very much in advance,

Alexandre




-- 
Dr. Alexandre F. Souza
Professor Adjunto III
Universidade Federal do Rio Grande do Norte
CB, Departamento de Ecologia
Campus Universitário - Lagoa Nova
59072-970 - Natal, RN - Brasil
lattes: lattes.cnpq.br/7844758818522706
http://www.docente.ufrn.br/alexsouza

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