stochastic models for population growth

[Vassily Shvets]

Hello,
Having measured two populations' characteristics at one particular time[with great precision] with R, I would like to extend this to measuring the same populations starting at t1, and then again at t2, and try to develop a growth model (something like dpop1/dt=r*pop^(...),dpop2/dt=r*pop^(...)). I think the idea is to create a model that will predict the growth of a population(N(mu, sigma)) within a margin of error. This kind of modeling isn't well known or publicized in terms of R, am I right?
regards,
s

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Michael D-2]

It's not too clear to me what you plan to do.
You want to model population growth using a normal distribution?

You should consider the classic differential equation of population growth
and look at variants with species interaction.

For modeling a single species you want to have

dP/dt = r*P (r is rate of increase accounting for birth and death)

which is P(t)=c1 e^(rt)
(c1 you solve from your initial conditions)

Then you can look to add a N(0,s) random component for


If you want to do some competition for resources/predator-prey modeling
there's already lots done on those.

As far as an R library you can download and just enter a few parameters...
I'm sure there's something in:
http://cran.r-project.org/web/views/Environmetrics.html


Michael D

On Thu, Jan 20, 2011 at 23:57:18 -0800 (PST), Vassily Shvets <
shv736_at_yahoo.com<shv736_at_yahoo.com?Subject=Re:%20[R]%20stochastic%20models%20for%20population%20growth>

>wrote:
>
> Hello,
> Having measured two populations' characteristics at one particular
> time[with great precision] with R, I would like to extend this to measuring
> the same populations starting at t1, and then again at t2, and try to
> develop a growth model (something like
> dpop1/dt=r*pop^(...),dpop2/dt=r*pop^(...)). I think the idea is to create a
> model that will predict the growth of a population(N(mu, sigma)) within a
> margin of error. This kind of modeling isn't well known or publicized in
> terms of R, am I right? regards,
> s

        [[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

[Vassily Shvets]

Hello,

It's not easy to express clearly what I have in mind. I've been working with a couple of titles -Stochastic Models in Biology, for one, but both date back a decade or more.
I'll try to illustrate the model a little more.
A reasonably comparable situation is Bolker's analysis of how many flowers are created on a given plant among a patch of plants, then comparing patches of plants at different locations. Then, I believe it's possible to determine the degree to which number of flowers appears to be dependent on other variables, like plant height, or root depth.
Finally, I would like to add to these analyses, one which, having determined a stochastically(if I'm using this word correctly) distributed parameter for the average number of flowers for each patch (patch 1(N(mu, sigma)), patch 2(N(mu, sigma)),...) would constitute a growth model for each patch over time, I think maybe something like:
 
df(patch 1) =r1*f0+ exp^(r1*t)
dt
df(patch 2) =r2*f0+ exp^(r2*t)
dt
It would be nice to be able to add the other effects here: plant height, and others, as further parameters in each equation.
I think it's likely these models have been done in biology, though I don't seem to find exactly how to do it in Bolker's book, and as a non-biologist, I 'm not sure where to look to find it. Maybe one can see that I'd like to be able to transfer this kind of model to use with other kinds of data from other fields!
-regards,
s
--- On Sun, 1/23/11, Michael D <[hidden email]> wrote:


From: Michael D <[hidden email]>
Subject: Re: [R] stochastic models for population growth
To: [hidden email], [hidden email]
Received: Sunday, January 23, 2011, 3:41 AM


It's not too clear to me what you plan to do.
You want to model population growth using a normal distribution?

You should consider the classic differential equation of population growth and look at variants with species interaction.

For modeling a single species you want to have

dP/dt = r*P (r is rate of increase accounting for birth and death)

which is P(t)=c1 e^(rt)
(c1 you solve from your initial conditions)

Then you can look to add a N(0,s) random component for


If you want to do some competition for resources/predator-prey modeling there's already lots done on those.

As far as an R library you can download and just enter a few parameters... I'm sure there's something in:
http://cran.r-project.org/web/views/Environmetrics.html


Michael D

On Thu, Jan 20, 2011 at 23:57:18 -0800 (PST), Vassily Shvets <shv736_at_yahoo.com>wrote:
Hello,
Having measured two populations' characteristics at one particular time[with great precision] with R, I would like to extend this to measuring the same populations starting at t1, and then again at t2, and try to develop a growth model (something like dpop1/dt=r*pop^(...),dpop2/dt=r*pop^(...)). I think the idea is to create a model that will predict the growth of a population(N(mu, sigma)) within a margin of error. This kind of modeling isn't well known or publicized in terms of R, am I right? regards,
s


        [[alternative HTML version deleted]]


______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.