#### Abstract

Idaho is ranked 5^{th} in the United States in overall wheat production and makes over $500 million in profit annually from wheat. Many pests have detrimental effects on wheat; some of the most predominant ones are aphids. Four species of aphids having economic effects on wheat crops in Idaho are: *Diuraphis noxia*, *Metopolophium dirhodum*, *Rhopalosiphum padi*, *Sitobion* *avenae*. Predictive regression models could be useful for better understanding of the occurrence of these aphid species. Count data for the four species were collected over 17 years via suction traps at 12 locations in wheat fields throughout Idaho. Species specific nonlinear logistic growth models were fitted to each suction trap location to model the aphid accumulation process during the wheat growing season. The nonlinear model used was parameterized to provide inference on three main aphid characteristics, the onset of trapped aphid accumulation, the rate of increase in aphid accumulation, and the maximum accumulated abundance of trapped aphids. Suction trap locations were further aggregated into 5 environments using hierarchical clustering based on climate data. Species specific models were then fitted to each of the 5 environments. Within each environment, the maximum yearly aphid abundance was determined to have a lag (1) autocorrelation structure across years, indicating a biotic feedback. A full nonlinear logistic growth model was then fitted to the entire data set using dummy variable regression to investigate potential climatic environmental patterns in the aphid accumulation process. Predicted models were validated both externally and internally. External validation used suction trap locations in Idaho that were excluded from the model building process to assess the predictive capabilities of the specified models. Internal validation was conducted using bootstrap simulation of the residuals for each model. Statistical models similar to those developed in this study can aid in understanding and evaluating the dynamics of the abundance of cereal crop aphid species in Idaho.

#### Keywords

Nonlinear Regression, Logistic Growth Models, Autocorrelation, Suction Traps

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Merickel, John W.; Shafii, Bahman; Eigenbrode, Sanford D.; Williams, Christopher J.; and Price, William J.
(2015).
"MODELING THE OCCURRENCE OF FOUR CEREAL CROP APHID SPECIES IN IDAHO,"
*Annual Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/2015/proceedings/3

MODELING THE OCCURRENCE OF FOUR CEREAL CROP APHID SPECIES IN IDAHO

Idaho is ranked 5^{th} in the United States in overall wheat production and makes over $500 million in profit annually from wheat. Many pests have detrimental effects on wheat; some of the most predominant ones are aphids. Four species of aphids having economic effects on wheat crops in Idaho are: *Diuraphis noxia*, *Metopolophium dirhodum*, *Rhopalosiphum padi*, *Sitobion* *avenae*. Predictive regression models could be useful for better understanding of the occurrence of these aphid species. Count data for the four species were collected over 17 years via suction traps at 12 locations in wheat fields throughout Idaho. Species specific nonlinear logistic growth models were fitted to each suction trap location to model the aphid accumulation process during the wheat growing season. The nonlinear model used was parameterized to provide inference on three main aphid characteristics, the onset of trapped aphid accumulation, the rate of increase in aphid accumulation, and the maximum accumulated abundance of trapped aphids. Suction trap locations were further aggregated into 5 environments using hierarchical clustering based on climate data. Species specific models were then fitted to each of the 5 environments. Within each environment, the maximum yearly aphid abundance was determined to have a lag (1) autocorrelation structure across years, indicating a biotic feedback. A full nonlinear logistic growth model was then fitted to the entire data set using dummy variable regression to investigate potential climatic environmental patterns in the aphid accumulation process. Predicted models were validated both externally and internally. External validation used suction trap locations in Idaho that were excluded from the model building process to assess the predictive capabilities of the specified models. Internal validation was conducted using bootstrap simulation of the residuals for each model. Statistical models similar to those developed in this study can aid in understanding and evaluating the dynamics of the abundance of cereal crop aphid species in Idaho.

## Comments to Editor

Review of “Modeling the Occurrence of Four Cereal Crop Aphid Species in Idaho” A submission to the Proceedings of the 27th Annual K-State Conference on Applied Statistics in Agriculture

Note:Reviewer’s comments are in regular type, authors’ responses are in bold (Italics).This is a well-written paper. I recommend its acceptance for the proceedings pending addressing a small number of minor issues listed below. The authors have provided line numbers and I will identify the issues with the line number.

We greatly appreciate the reviewer positive comment and recommendation. We have addressed all of his/her comments below. Please note that line numbers correspond to the original submission.Line 165 -I believe the right hand brace in the first expression should be placed after the zero.

.We disagree. Placing the right hand brace after the 0 would be redundant. We left the expression unchangedLine 454 - It would be much easier to read, interpret, and compare all these graphs if they had the same vertical scale. There are four different scales for the four rows, which doesn’t seem helpful.

We agree with reviewer’s suggestion. Graphic displays now have the same scale.Line 489 - Delete the ‘s’ from Figures 5.

Done.Line 540 - “lag 1 is -0.33952” does not agree with the value in the table above. I think a 9 was left out of this number.

Corrected the specified values on both lines 540 and 542.Line 580-581 - it would be good to identify what the various lines/curves represent. I believe they are individual years, and I don’t think you need to label the curves, but in the legend it ought to be mentioned that there is a different line for each year. (There is a similar issue at line 736.)

Incorporated the suggestion as part of the plot.Line 667 - provide units (I think it is degree days) for the numbers 180, 228, 191, and 292.

Done.Line 670 - should “greater” be “later”?

We believe greater is more appropriate in this context.Lines 673-676 – I don’t follow the argument made here. Driven by climate factors makes sense, but the notion that populations are therefore (maybe) localized does not follow for me. Can you make a better argument for this?

.We have further elaborated on this point in the paragraph starting at line 764 in the ConclusionsLines 691-692 - The minus sign (at the end of line 691) is somehow detached from the number on the next line. Suggestion incorporated. Line 736 - Problem is mentioned above.

Done.