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12-15-2014 05:35 PM

I am trying to fit dispersal functions to seed trap data gathered in the field. Seed traps were placed at intervals of increasing distances from a single seed source. I am trying to fit dispersal functions to the data that describes the probability of a seed landing at a particular distance. Below is the code I created for fitting a Negative Exponential (NE) function with PROC NLMIXED. The parameter *a *needs to be estimated. The parameter *D *is the distance from the seed source. The xb line is the NE function. Mu gives the expected seed count at a distance by multiplying the dispersal function (xb) by trap area (tarea) and by the total number of seeds dispersed (q). The variable tarea is offset variable and both tarea and q are known quantities. There is a random effect (u2) because I replicated the study at 3 sites.

**proc** **nlmixed** data=count; title "NE";

parms a=**.0001**,**.001**,**0.01**,**0.1**,**1**,**10**,**100**,**1000**,**10000**, **100000**,**1000000** s2u=**1**,**10**,**100**,**1000**,**10000**;

xb=((**1**/(**2*****3.1415***(a****2**)))*(exp(-(D/a)))) +u2 ;

mu=exp(xb)*tarea*q;

model count~ poisson(mu) ;

random u2~normal(**0**,s2u)subject=source;

predict mu out=results;

**run**;

My questions are: 1) is the code correct for calculating the parameters of the dispersal function?

2) Is the random effect in the correct location? Could it be placed at mu=exp(xb)*tarea*q + u2;?

If anyone has experience with dispersal functions and could offer any insight, I would be very thankful!

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Posted in reply to ChrisLoebach

12-16-2014 07:48 AM

The placement of u2 will depend on your assumption regarding the variability due to site. Where you have it now, it enters essentially as a multiplicative error--probably a reasonable assumption given the distribution. Moving it to the alternative you propose means an additional (above residual) additive error. You might want to consider one other alternative--that the parameter a comes from a distribution with error dependent on site. This would result in:

xb=((**1**/(**2*****3.1415***(a****2**)))*(exp(-(D/(a + u2))))

This sort of parameterization is more common in pharmacokinetic models where there is additional variability due to patient/subject, but may be appropriate here.

Hope this helps some.

Steve Denham