here is a summary of the replies I got to my question. Any further idea will be very appreciated too.

----- Original Message -----

From: Francisco Jesús Moral García

To: ai-geostats@...

Sent: Tuesday, February 11, 2003 11:57 AM

Subject: AI-GEOSTATS: Distribution of a plague

Dear list members,

Now, I am studying the distribution of a plague (Helicoverpa armigera Hb.) in tomato parcels, using geostatistics techniques.

I have got information related to the numbers of captures of the insect in each trap. All traps are regularly disposed in the considered parcel.

So, I have, initially, discrete data, and I would like to get the continuous distribution or a map of the plague distribution in the parcels.

I have a result, using ordinary punctual kriging and supposing that the variable is continuous, which it is not true.

Can you tell me if it is a good way? if not, which is the correct way to get the distribution? Any reference about a similar work or any idea will be very appreciated.

Thak you in advance

Francisco Moral

----------------------------------------------------------------------------------

1)

Holla Francisco

I would recommend and modelling strategy which takes into account the fact

that you have a discrete variable, probably to be modelled with a Poisson

distribution.

One possible approach is to use a geostatistical model with a Poisson

distribution. This would extend the usual geostatistical model in the

same way that generalised linear models extends the usual linear model.

There is a software implementation for Poisson and Binomial models in the

geoRglm package for the R software:

http://www.est.ufpr.br/geoRglm

from Paulo Justiniano Ribeiro Jr

-----------------------------------------------------------------------

2)

Hi,

You can either use the methodology of Gotway and Stroup and krig the

counts in a glm setting as Poisson random variables or use indicator

kriging and estimate the attack risk. Another possibility is to krig

insect density but that is a bit of a fudge.

from Nicholas Lewin-Koh

--------------------------------------------------------------------

3)

Why don't you try the kernel density smoothing method? It's appropriate for discrete data (e.g., an event location). It's been used for a variety of epidemiological analyses. My CrimeStat program has a single- and duel-kernel density routine with a number of different kernels (functions) that can be used as well as several options for bandwidth selection. The software and manual are freely downloadable at:

http://www.icpsr.umich.edu/nacjd/crimestat.html

Ned Levine

------------------------------------------------------------

4)

Here are some relevant references

Lecoustre, R., Fargette, D., Fauquet, C., and de Reffye, P. 1989. Analysis and mapping of the spatial spread of African cassava mosaic virus using geostatistics and the kriging technique. Phytopathology 79:913-920.

Liebhold, A. M., Rossi, R. E., and Kemp, W. P. 1993. Geostatistics and geographic information systems in applied insect ecology. Annual Review of Entomology 38:303-327.

Barnes, J. M., Trinidad-Correa, R., Orum, T. V., Felix-Gastelum, R., and Nelson, M. R. 1999. Landscape ecology as a new framework for improved management of plant viruses and their insect vectors in agroecosystems. Ecosystem Health 5:26-35.

Byrne, D. N., Rathman, R. J., Orum, T. V., and Palumbo, J. C. 1995. Localized migration and dispersal by the sweet potato whitefly, Bemisia tabaci, Oecologia 105:320-328.

Nelson, M. R., Felix-Gastelum, R., Orum, T. V., Stowell, L. J., and Myers, D. E. 1994. Geographic information systems and geostatistics in the design and validation of regional plant virus management programs. Phytopathology 84:898-905.

Nelson, M. R., Orum, T. V., Jaime-Garcia, R.,

and Nadeem, A. 1999. Applications of geographic information systems and geostatistics

in plant disease epidemiology and management. Plant Dis. 83:308-319.

Orum, T. V., Bigelow, D. M., Nelson, M. R.,

Howell, D. R., and Cotty, P. J. 1997. Spatial and

temporal patterns of Aspergillus flavus strain

composition and propagule density in Yuma

County, Arizona, soils. Plant Dis. 81:911-916.

a.. 1994, A. Stein,C.G. Kocks, J.C. Zadocks, H.D. Frinking, N.A. Russen and Myers, D.E., A geostatistical analysis of the spatial temporal development of downy mildew epidemics in cabbage. Phytopathology 84,1227-1239

Donald E. Myers

http://www.u.arizona.edu/~donaldm

----------------------------------------------------------------------------------------------

5)

Hi,

The problem with density is the error propagation can be huge unless

done really carefully. Density at a point is not very meaningful, so you

should probably use block kriging for that and make sure you have robust

density estimators from your trap data.

for predicting risk look at the disease literature. I think Diggle has

several papers on it. Also look at the bark beetle literature.

Here are some references.

131 Autologistic Model of Spatial Pattern of Phytophthora Epidemic in

Bell Pepper: Effects of Soil Variables on Disease Presence

Marcia L. Gumpertz, Jonathan M. Graham, and Jean B. Ristiano

157 A Generalized Linear Model Approach to Spatial Data Analysis and

Prediction

C. A. Gotway and W. W. Stroup

both in Journal of Agricultural, Biological, and Environmental

Statistics (JABES) vol 2(2) 1997

from Nicholas Lewin-Koh

[Non-text portions of this message have been removed]