[R-sig-dyn-mod] Describing a modelling process (SIMEON LISOVSKI)

[Stephen Paul Ellner]

Simeon, 

instead of using approxfun and 
      B <- birth(t)
you could just do B <- dnorm(t,50,25) inside the model function. It's the same effect, but all the models will run faster.  

And I might describe that by saying 

Birth rate was assumed to vary seasonally, increasing steadily to a peak at day 50 and then decreasing. I used a Gaussian bell-shaped curve to describe this pattern, specifically $B(t)=h \phi(t; \mu=50, \sigma=25)$ where $\phi$ is the probability density function of a Gaussian distribution with the given mean and standard deviation. The maximum birth rate (births/day) is then $B(50)=h/(25\sqrt{2 \pi})$. 

Steve

Stephen P. Ellner 
Department of Ecology & Evolutionary Biology, E339 Corson Hall
Cornell University, Ithaca NY 14853-2701
Phone (607) 254-4221 FAX (607) 255-8088

-----Original Message-----
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Message: 1
Date: Mon, 19 May 2014 15:23:32 +0000
From: SIMEON LISOVSKI <slisovski at deakin.edu.au>
To: "r-sig-dynamic-models at r-project.org"
	<r-sig-dynamic-models at r-project.org>
Subject: [R-sig-dyn-mod] Describing a modelling process
Message-ID: <04899C52-E6A5-4984-9EAD-FC78949AD254 at deakin.edu.au>
Content-Type: text/plain

Hi all,
 I am running a deSolve based simulation (epidemiological & demographic model).
Some demographic parameters like birth follow a normal distribution to better reflect the natural dynamic. Basically implemented as follows:

## B =  birth
## h =  total numbers of juveniles
## my = mortality rate

model <- function (t, y, p) {
  with(as.list(c(y, p)),{

      B <- birth(t)

      dN = B*h - my*y[1]
    return(list(c(dN)))
  })
}

birth <- approxfun(x = 0:100, y = dnorm(0:100, 50, 25))

out <- ode(y = 100, times = 0:100, parms = c(my = 4e-2, h = 5), func = model) plot(out, ylab = "Population size", xlab = "Time?)

My question is rather post-modeling related. I am struggling to explain this in the method section of a manuscript. Basically I would like to receive a recommendation how to describe this process formally and mathematically right i.e. birth follows a normal distribution derived by multiplying the number of hatchlings with a density function of a normal distribution ?. ?!

Thanks,
Simeon