"Functional response" curves?

[Dan Edelstein]

Hi all,

I have a customer (biology grad student) who wants to estimate what's
referred to as a "functional response" curve.  This apparently is the
standard way of modelling predators' response to changing concentrations
of prey.  With my social science background, I just can't seem to relate
what's outlined in the literature she's showed me to any statistical
methods I'm familiar with, let alone how to implement it in SPSS.  Her
data consists of just three variables, number of prey exposed, number
eaten, and replicate number.  I found a reference to using SPSS nonlinear
regression (the standard "functional responses" apparently are logarithmic
("Type II") and logistic ("Type III") curves), but the literature shows
various steps and tests, and I'm not sure how to approach it.  Has anyone
done this in SPSS, and would be willing to offer advice?  I think I need
to know how to structure the data into observations and variables, and
then what procedures to run.

Thanks.

Dan

----------------------------------------------------
Daniel M. Edelstein
Academic Data Centre Manager
Leddy Library
University of Windsor
[phone], ext. 4722

Given the character of metadata, there is little likelihood of seeing a
metadatum in the wild.

[Marta García-Granero]

Hi Dan

DE> I have a customer (biology grad student) who wants to estimate what's
DE> referred to as a "functional response" curve.  This apparently is the
DE> standard way of modelling predators' response to changing concentrations
DE> of prey.  With my social science background, I just can't seem to relate
DE> what's outlined in the literature she's showed me to any statistical
DE> methods I'm familiar with, let alone how to implement it in SPSS.  Her
DE> data consists of just three variables, number of prey exposed, number
DE> eaten, and replicate number.  I found a reference to using SPSS nonlinear
DE> regression (the standard "functional responses" apparently are logarithmic
DE> ("Type II") and logistic ("Type III") curves), but the literature shows
DE> various steps and tests, and I'm not sure how to approach it. Has anyone
DE> done this in SPSS, and would be willing to offer advice?  I think I need
DE> to know how to structure the data into observations and variables, and
DE> then what procedures to run.

Although I haven't worked with functional response curves, I think
they can be solved easily with non linear regression (as a matter of
fact, a quick googling showed a couple of references of the use of
SPSS and NLR to fit those curves, like this one
http://www.esapubs.org/archive/ecol/E086/158/appendix-A.htm ). I can
give an example (from real data)

My goal was to fit the following equation:

             Aw
m=--------------------------
  alpha·Aw²+beta·Aw+epsilon

Using the following data:

* Dataset *.
DATA LIST LIST/ id (F8) Aw (F8.2) m (F9.5).
BEGIN DATA
 1 .04 .04160
 2 .08 .06300
 3 .12 .07470
 4 .16 .08360
 5 .20 .09419
 6 .24 .10500
 7 .28 .11380
 8 .32 .12180
 9 .36 .13060
10 .40 .14120
11 .44 .15250
12 .48 .16380
13 .52 .17500
14 .56 .18640
15 .60 .19780
16 .64 .21170
17 .68 .22580
18 .72 .24270
19 .76 .26260
20 .80 .28310
21 .84 .32050
22 .88 .37080
23 .92 .53650
24 .96 .75500
END DATA

The syntax was generated using the GUI, and then pasted:

* NonLinear Regression.
Set Printback on.
MODEL PROGRAM alpha=1 beta=1 epsilon=1 .
COMPUTE PRED_ = Aw/(alpha*(Aw**2)+beta*Aw+epsilon).
Set Printback off.

NLR m
  /PRED PRED_
  /SAVE PRED
  /CRITERIA SSCONVERGENCE 1E-8 PCON 1E-8 .

If the parameters can't be negative (or have any other restriction),
then you have to use CNLR instead of NLR:

CNLR m
  /PRED PRED_
  /BOUNDS alpha >= 0; beta >= 0; epsilon >= 0
  /CRITERIA STEPLIMIT 2 ISTEP 1E+20 .

HTH,
Marta Garcia-Granero