The Role of Environmental, Temporal, and Spatial Scale on the Heterogeneity of Fusarium Head Blight of Wheat

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Alissa B. Kriss, M.S.

Graduate Program in Plant Pathology

The Ohio State University

2011

Dissertation Committee:

Distinguished Professor in Plant Protection Laurence V. Madden, Co-Advisor

Assistant Professor Pierce A. Paul, Co-Advisor

Professor Michael A. Ellis

Associate Professor Clay H. Sneller

Fusarium head blight (FHB) of wheat is a disease of foremost importance in many parts of the world, including Europe and the US. In the US, FHB is predominantly caused by the fungal species Fusarium graminearum (teleomorph: Gibberella zeae), but in

Europe and other regions, a complex of Fusarium and Microdochium species is involved.

FHB reduces quantity and quality of yield by reducing grain weight and contaminating grain with mycotoxins [especially deoxynivalenol (DON)]. The fungus overwinters on crop residues in the field following harvest. Under favorable weather conditions, primary inocula (ascospores and conidia) are produced and transported to wheat spikes by wind and rain. Infection mainly occurs at anthesis or shortly thereafter, and subsequent colonization of the wheat spike often results in the production of DON by the fungal pathogen.

Fusarium head blight is known to be highly variable at several spatial and temporal scales, which is likely due, in part, to the variability in environmental conditions. Different statistical approaches were used to empirically quantify this heterogeneity in FHB and relate it to environmental conditions. First, window-pane methodology was utilized to determine the length and starting time of temporal windows where environmental variables were associated with the inter-annual variation in FHB in four US states over time periods of 23 to 44 years, and the spatio-temporal variation

ii across three European countries. Associations between biological variables and environmental variables were quantified with Spearman rank correlation coefficients.

Significance for a given variable across all time windows was declared using the Simes’ multiple-testing adjustment for P values; at individual time windows, significant correlations were declared when the individual (unadjusted) P values were less than

0.005. Atmospheric moisture- or surface-wetness-related variables (e.g., average daily relative humidity) were positively associated with FHB intensity for multiple window lengths and starting times in the US analysis, especially for the last 2 months of the growing season. Results from the European analysis confirm that FHB intensity was associated with the moisture variables, and also showed that biomass of the causal agents of FHB in the wheat spikes, and their associated mycotoxins in harvested grain were significantly associated with these same environmental conditions, although mycotoxin concentrations were only associated with post-anthesis conditions.

Second, cross-spectral analysis was used to characterize the coherency between inter-annual variation in FHB in Ohio and Indiana and global climate variability. Climate patterns investigated were the Oceanic Niño Index (ONI), the Pacific/North American

(PNA) pattern and the North Atlantic Oscillation (NAO), which are known to have strong influences on the Northern Hemisphere climate and weather. Significance for coherency was determined by a nonparametric permutation procedure. Results showed that the ONI was significantly coherent with FHB in Ohio, with a period of about 5.1 years (as well as for some adjacent periods). The estimated phase-shift distribution indicated that there was a generally negative relation between the two series, with high values of FHB (an indication of a major epidemic) estimated to occur less than 1 year after low values of

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ONI (indication of a La Niña). At periods between 2 and 7 years, the PNA and NAO indices were coherent with FHB in both Ohio and Indiana, although results for phase shift and period depended on the specific location, climate index, and time span used in calculating the climate index. Results suggest that global climate indices and spectral models could be used to identify potential years with high (or low) risk for FHB development, although based on the magnitude of the coherencies, the most accurate risk predictions will need to be customized for a region and will also require use of local weather data during key time periods for sporulation and infection by the fungal pathogen.

Third, a generalized linear mixed model (GLMM) was fitted to multilevel survey data for the incidence of FHB from the 2002 through 2011 growing seasons in the major wheat-producing regions in Ohio. Spatial heterogeneity of the complementary log-log link function of disease incidence among counties, fields within counties, and sites

(sampling units) within fields and counties was quantified through the estimated variance components of the GLMM and their profile-likelihood-based confidence intervals. The

GLMM was based on the assumption that the disease status of wheat spikes within sites was binomially distributed conditional on the random effects of county, field, and site.

Results confirmed that FHB is sporadic on a spatial scale, and that larger-scale (county and field) variability can dominate the spatial patterns, with very low variability among sites within fields. The intra-cluster correlation (for disease status of spikes within sites)—a function of the spatial variances and expected incidence—indicated that spikes from the same site were somewhat more likely to share the same disease status relative to the situation with complete spatial randomness.

Results from this dissertation should lead to the development of improved disease forecasting (predictive) systems and sampling procedures for precise estimation of FHB incidence.

Acknowledgements

I would like to thank the faculty, staff, and students of the Plant Pathology

Department for their support and assistance throughout my time at Ohio State. I particularly thank Dr. Laurence Madden and Dr. Pierce Paul, my co-advisors, for providing me with amazing opportunities during my time as a graduate student. In addition, I thank Dr. Madden for our many conversations, his guidance in all things related to my dissertation and unrelated, and his constant patience, and I thank Dr. Paul for sharing his passion for plant pathology with me and his continued support of my work. I would also like to thank my committee members, Dr. Clay Sneller (Department of Horticulture and Crop Science) and Dr. Michael Ellis, for their intellectual support and review of my dissertation, and Dr. Xiangming Xu (East Malling Research) for providing the data used in Chapter 3.

Additionally, I thank Mr. Lee Wilson for his advice and help whenever needed and all of the Agricultural and Natural Resources Extension Educators in Ohio that assisted with my survey.

Personally, I would like to thank my parents, Harold and Cheryl Kriss, for their love, support, and telling me starting at a young age that I could accomplish all of my goals. I also thank my sisters (Megan Gearhart, Cara Voorhorst, and Jennifer Hauber) and their families for always being there when I needed them.

Vita

2004 ...... B.S. Mathematics and Secondary Mathematics Education, Indiana State University

2004 – 2007 ...... Mathematics Teacher, Lowell Senior High School

2007 – present ...... Graduate Research Associate, The Ohio State University

2010 ...... M.S. Plant Pathology, The Ohio State University

Publications

Refereed Journal Articles 1. Kriss, A. B., Paul, P. A., and Madden, L. V. 2010. Relationship between yearly fluctuations in Fusarium head blight intensity and environmental variables: A window-pane analysis. Phytopathology 100:784-797. 2. Kriss, A. B., Paul, P. A., and Madden, L. V. 2011. Variability in Fusarium head blight epidemics in relation to global climate fluctuations as represented by the El Niño Southern Oscillation and other atmospheric patterns. Phytopathology (DOI: 10.1094/PHYTO-04-11-0125).

Abstracts in Journal 1. Kriss, A. B., Madden, L. V., Paul, P. A., and Xu, X. 2011. Climate, weather, and the heterogeneity of Fusarium head blight. Phytopathology 101:S221. 2. Madden, L. V., Kriss, A. B., Paul, P. A. and Xu, X. 2010. Data mining of weather and climatic data to improve risk prediction of Fusarium head blight. Page 85 in: Proceedings of the 2010 National Fusarium Head Blight Forum, Milwaukee, WI. 3. Kriss, A. B., Willyerd, K. T., Paul, P. A. and Madden, L. V. 2010. Fusarium head blight epidemic in Ohio: Our role in extension and outreach. Page 178 in: Proceedings of the 2010 National Fusarium Head Blight Forum, Milwaukee, WI.

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4. Kriss, A. B., Paul, P. A. and Madden, L. V. 2010. Multi-scale spatial heterogeneity in disease incidence of Fusarium head blight of wheat. Phytopathology 100:S65. 5. Kriss, A. B., Paul, P. A. and Madden, L. V. 2010. Role of El-Niño-Southern Oscillation and atmospheric teleconnection patterns on variability of Fusarium head blight in Ohio. Phytopathology 100:S66. 6. Kriss, A. B., Madden, L. V. and Paul, P. A. 2009. Multi-state assessment using window pane analysis confirming weather variables related to Fusarium head blight epidemics. Page 60 in: Proceedings of the 2009 National Fusarium Head Blight Forum, Orlando, FL. 7. Kriss, A. B., Madden, L. V., and Paul, P. A. 2009. More than 40 years of observations from Ohio confirm the importance of relative humidity and precipitation for Fusarium head blight epidemics. Phytopathology 99: S67. 8. Kriss, A. B., Madden, L. V., and Paul, P. A. 2009. Multi-state assessment using window pane analysis confirming weather variables related to Fusarium head blight epidemics. Phytopathology 99: S67. 9. Kriss, A. B., Madden, L. V., and Paul, P. A. 2008. More than 40 years of observations from Ohio confirm the importance of relative humidity and precipitation for Fusarium head blight epidemics. Page 39 in: Proceedings of the 2008 National Fusarium Head Blight Forum, Indianapolis, IN.

Fields of Study

Major Field: Plant Pathology Epidemiology

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Table of Contents

Abstract ………………………………………………………………….…...... ii Acknowledgments ………………………………………………………...... vi Vita …………………………………………………...... ….... vii List of Tables ……………………………………………………………...... xiii List of Figures …………………………………………………………...... xv

Chapter 1. Introduction ...... 1

Objectives ……………………...... 8

References ...... 11

Chapter 2. Relationship Between Yearly Fluctuations in Fusarium Head Blight Intensity and Environmental Variables: A Window-Pane Analysis

Introduction ……………………………………………………………...... 17

Materials and Methods …………………………………………………….... 21 Disease data ……………………………………………………….... 21 Meteorological data ………………………………………………... 22 Window-pane analysis – variable construction …………………...... 23 Window-pane analysis – statistics ………………………………...... 26 Window-pane analysis – multiple hypothesis testing ……………..... 27 Serial correlation for FHB ……………………………………….…. 30

Results ……………………………………………………………………..... 30 Annual variation in disease intensity ……………………………….. 30 Ohio window-pane analysis ……………………………………….... 31 Indiana, Kansas, and North Dakota window-pane analysis ……….... 35

Discussion ………………………………………………………….……….. 39

Summary ……..…………………………………………………….……….. 63

References ...... 65

Chapter 3. Quantification of the Relationship Between the Environment and Fusarium Head Blight, Fusarium Pathogen Density, and Mycotoxins in Winter Wheat in Europe

Introduction ……………………………………………………………….... 71

Materials and Methods ……………………………………………………... 74 Field data ………………………………………………...... 74 Fungal DNA and toxin quantification …………………………...... 75 Environmental variables …………………………………………..... 75 Window-pane analysis ………………………………………..…..... 76 Semi-partial correlations ………………………………...... 79 Multiple hypothesis testing ………………………..……...... 80

Results …………………………………………………………………….... 81 Overall significance and magnitude of correlations …………...... 81 Temporal patterns to correlations with environment – disease and fungal biomasses ………...... …….. 83 Temporal patterns to correlations with environment – mycotoxins ... 85 Semi-partial correlations ...... 86

Discussion ………………………………………………………………...... 87

Summary ……………………………………………………………..…….. 107

References ...... 109

Chapter 4. Variability in Fusarium Head Blight Epidemics in Relation to Global Climatic Fluctuations as Represented by the El Niño-Southern Oscillation and Other Atmospheric Patterns

Introduction ...... 114

Materials and Methods ...... 118 Disease data ...... 118 Climate indices ...... 118 Spectral analysis ...... 119 Cross-spectral analysis ...... 120 Nonparametric significance testing of coherency ...... 122

Results ...... 123 Univariate statistics ...... 123 Oceanic Niño Index and FHB ...... 125 North Atlantic Oscillation Index and FHB ...... 126 Pacific-North American Pattern and FHB ...... 127

Discussion ...... 129

Summary ...... 144

References ...... 146

Chapter 5. Characterizing Heterogeneity of Disease Incidence in a Spatial Hierarchy: A Case Study from a Decade of Fusarium Head Blight of Wheat in Ohio

Introduction ...... 151

Materials and Methods ...... 155 Data collection ...... 155 Data analysis – basic notation ...... 156 Data analysis – model fitting ...... 158 County (or field) level predictions ...... 161 Intra-cluster correlations ...... 164

Results ...... 167 Heterogeneity at multiple scales ...... 167 County-level predictions ...... 169 Intra-cluster correlations ...... 172

Discussion ...... 173

Summary ...... 189

References ...... 191

Bibliography ...... 199

Appendix A: Spectral Analysis and Cross-Spectral Analysis ...... 217

Spectral analysis ...... 217 Cross-spectral analysis ...... 219 Interpreting the phase shift ...... 221

References ...... 225

Appendix B: Intra-cluster Correlations for Binary Data in Hierarchical Random Effects Models ...... 226

General definition of the intra-cluster correlation ...... 226 Linearization approach ...... 228

Latent variable approach ...... 232 Numerical calculations based on equations ...... 232

References ...... 234

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List of Tables

Table 2.1. Window lengths and calendar dates for winter and spring wheat locations used in window-pane analysis of Fusarium head blight ...... 48

Table 2.2. Description of environmental variables, with units in brackets, used in window-pane analysis of Fusarium head blight ...... 49

Table 2.3. Adjusted significance levels based on Simes’ method, and maximum Spearman rank correlation coefficient between Fusarium head blight intensity rating and environmental variables for listed time window lengths based on 44 years of data from Ohio ...... 50

Table 2.4. Adjusted significance levels based on Simes’ method, and maximum Spearman rank correlation coefficient between Fusarium head blight intensity rating and environmental variables for 10, 15, 30, 60, and 120 day window lengths based on data from Indiana, Kansas, and North Dakota ...... 51

Table 3.1. Description of environmental variables, with units in parentheses, used in window-pane analysis of Fusarium head blight and associated mycotoxins in Europe ...... 95

Table 3.2. Global significance levels based on Simes’ method and the highest Spearman rank correlation coefficients between each of the listed environmental variables and Fusarium head blight (FHB) intensity, biomass of Fusarium graminearum, F. culmorum, and F. poae, for data collected at growth stage 77 (milky ripe) ...... 96

Table 3.3. Global significance levels based on Simes’ method and the highest Spearman rank correlation coefficients between each of the listed environmental variables and biomass of Fusarium graminearum, F. culmorum, and F. poae, for data collected at growth stage 92 (harvest) ...... 98

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Table 3.4. Global significance levels based on Simes’ method and the highest Spearman rank correlation coefficient or semi-partial Spearman rank correlation coefficient between each of the listed environmental variables and DON ...... 99

Table 3.5. Global significance levels based on Simes’ method and the highest Spearman rank correlation coefficient or semi-partial Spearman rank correlation coefficient between each of the listed environmental variables and NIV ...... 101

Table 4.1. Coherency with associated period and phase difference for climate variables and Fusarium head blight intensity in Ohio or Indiana for the three largest coherency values if they were determined to be significant by the permutation procedure (α = 0.10) ...... 137

Table 5.1. Structure of the data for 2002 to 2011 with estimated mean disease incidence (complementary log-log (CLL) scale ( ) and original incidence scale ( ) with standard errors) and estimated variances (and standard errors) from the generalized linear mixed model for county ( ), field within county ( , and site within field and county ( ) for incidence of Fusarium head blight in Ohio over 10 years with measures of the intra-site correlation ...... 183

Table 5.2. Estimated best linear unbiased predictors (EBLUPs) at the county and field levels ...... 184

Table 5.3. Estimated parameters (β) with standard errors for a subset of the covariables evaluated ...... 185

Table A.1. Frequencies and periods for the 46 year time series in Ohio ...... 218

Table A.2. Simplified definitions and notations used ...... 224

Table B.1. Approximations of the intra-cluster correlation with the data and model used in Chapter 5 ...... 233

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List of Figures

Figure 2.1. Fusarium head blight intensity for Ohio (1964 to 2008), North Dakota (1986 to 2008), Indiana (1973 to 2008), and Kansas (1978, 1980, 1982 to 2007). The disease assessment scale was different among the four locations...... 52

Figure 2.2. Spearman rank correlation coefficients for the association between average daily relative humidity (ARH) and Fusarium head blight intensity in Ohio. Window lengths of 10 to 240 days are shown in separate graphs. The horizontal axis represents the starting time of the window of defined length, with day 0 representing 30 June, and day 280 representing 24 September. Horizontal lines are at the critical correlation coefficients for individual significance at  = 0.005 and 0.05. The critical correlation for  = 0.05 does not provide any adjustment for multiple correlated test statistics, and the critical correlation for  = 0.005 provides some adjustment for the multiple statistics...... 53

Figure 2.3. Spearman rank correlation coefficients for the association between A, total daily precipitation (TP), B, average daily temperature (AT), and C, number of hours temperature was between 15°C and 30°C and the mean relative humidity was greater than 80% (THRH80), and Fusarium head blight intensity in Ohio. Window lengths of 15, 30, 60, and 120 days are shown for each environmental variable. The horizontal axis represents the starting time of the window of defined length, with day 0 representing 30 June, and day 280 representing 24 September. Horizontal lines are at the critical correlation coefficients for individual significance at  = 0.005 and 0.05. The critical correlation for  = 0.05 does not provide any adjustment for multiple correlated test statistics, and the critical correlation for  = 0.005 provides some adjustment for the multiple statistics...... 55

Figure 2.4. Graphic summary of the time periods in which there were significant positive correlation coefficients between each of eight environmental variables (see Table 2) and Fusarium head blight (FHB) intensity (with individual correlations significant at P < 0.005) in four locations (states). Results are shown for 15-day and 30-day window lengths. The time line corresponds to days prior to 30 June (time 0) for Ohio, Indiana, and Kansas, and days prior to 15 August for North Dakota. The lines encompass the total time of a window where the summary variable (e.g., average relative humidity [ARH] for 15 days) was significantly related to FHB intensity, not just the starting time of the window. For instance, if ARH was significant with a 15-day window starting on day 20, then the line would go from 20 to 34. In contrast, Figures 2, 3, and 5 identify the starting time of each window...... 57

Figure 2.5. Spearman rank correlation coefficients for the association between A, average daily relative humidity (ARH) at 15-day windows, B, average daily relative humidity (ARH) and 30-day windows, C, total daily precipitation (TP) at 15-day and D, 30-day windows, and E, number of hours temperature was between 15°C and 30°C and the mean relative humidity was greater than 80% (THRH80) at 15-day and F, 30-day windows, and Fusarium head blight intensity in Indiana, Kansas, and North Dakota. The horizontal axis represents the starting time of the window of defined length, with day 0 representing 30 June, and day 280 representing 24 September. Horizontal lines are at the critical correlation coefficients for individual significance at  = 0.005 and 0.05. The critical correlation for  = 0.05 does not provide any adjustment for multiple correlated test statistics, and the critical correlation for  = 0.005 provides some adjustment for the multiple statistics...... 59

Figure 2.6. Spearman rank correlation coefficients for the association between FHB and average daily relative humidity (ARH) with 15-day windows (solid lines), and between FHB at a reference time and ARH for all other window starting times (gray bars) in Ohio (A) and North Dakota (B). The reference time was based on the window starting time with the highest correlation between ARH and FHB in each location. In A, the horizontal axis represents the starting time of the window, with day 0 representing 30 June. The reference time was 20. In B, the horizontal axis represents the starting time of the window, with day 0 representing 15 August. The reference time was 19...... 61

Figure 3.1. Spearman rank correlation coefficients at 15-day windows for the association between environmental variables (graph titles, Table 1) and A, Disease intensity; B, Fusarium graminearum biomass; C, F. culmorum biomass; and D, F. poae biomass quantified at GS77 (milky ripe) across three European countries. Horizontal axis represents the starting time of the 15-day window, with day 0 representing the beginning of anthesis. Negative numbers represent days before anthesis began and positive numbers represent days after anthesis began. Bold vertical bars represent correlation coefficients for individual significance at α = 0.005...... 103 xvi

Figure 3.2. Spearman rank correlation coefficients at 15-day windows for the association between environmental variables (graph titles, Table 1) and A, Fusarium graminearum biomass; B, F. culmorum biomass; and C, F. poae biomass quantified at GS92 (harvest) across three European countries. Horizontal axis represents the starting time of the 15-day window, with day 0 representing the beginning of anthesis. Negative numbers represent days before anthesis began and positive numbers represent days after anthesis began. Bold vertical bars represent correlation coefficients for individual significance at α = 0.005...... 104

Figure 3.3. Spearman rank correlation coefficients and semi-partial Spearman rank correlation coefficients at 15-day windows for the association between environmental variables (graph titles, Table 1) and A, deoxynivalenol (DON) concentration; B, DON adjusted for disease intensity, Fusarium graminearum biomass at GS77 and GS92, and F. culmorum biomass at GS77 and GS92; C, nivalenol (NIV) concentration, and D, NIV adjusted for disease intensity, F. graminearum biomass at GS77 and GS92, F. culmorum biomass at GS77 and GS92, and F. poae biomass at GS77 and GS92 across three European countries. Horizontal axis represents the starting time of the 15-day window, with day 0 representing the beginning of anthesis. Negative numbers represent days before anthesis began and positive numbers represent days after anthesis began. Bold vertical bars represent correlation coefficients for individual significance at α = 0.005...... 105

Figure 4.1. A, Scaled (transformed) Fusarium head blight intensity for Ohio (1965 – 2010) and Indiana (1973 – 2008). B, Spectral density of yearly values of FHB intensity in Ohio and Indiana. The square-root of disease intensity was used for all analyses. Interior tick lines on the lower Period axis are the Fourier frequencies (converted to periods) for Ohio and on the upper Period axis are the Fourier frequencies (converted to periods) for Indiana. The scaled disease data points overlap completely in 1986 and only one point can be seen...... 139

Figure 4.2. Time-series and corresponding spectral densities of winter (December to February) and spring (March to May) Oceanic Niño Index (ONI), North Atlantic Oscillation (NAO), and Pacific/North American pattern (PNA). On the spectral density plots, interior vertical lines on the Period axis are the Fourier frequencies (converted to periods) for Ohio...... 140

Figure 4.3. Coherency relationships among time series of annual FHB intensity values in Ohio and the Oceanic Nino Index (ONI), North American Oscillation (NAO), and Pacific/North American Pattern (PNA) from 1965 to 2010. Insert graphs are the amplitude of the cross-spectral density for each pair of time series. Interior vertical lines on the Period axis are the Fourier frequencies (converted to periods). Asterisks denote periods where the coherency is significant as determined by the permutation procedure (α=0.10)...... 141 xvii

Figure 4.4. Example phase relationship between the predicted winter Oceanic Niño Index (ONI) (solid line) and (scaled) predicted Fusarium head blight (FHB) intensity rating in Ohio (dashed line) for a period of 5.1 years. Predictions are given for an arbitrary 10-year time span. Three relevant estimated phase shifts are demonstrated. PS(+) = 3.451 years, PS(-) = 0.900 years...... 142

Figure 4.5. Coherency relationships among time series of annual FHB intensity values in Indiana and the Oceanic Nino Index (ONI), North American Oscillation (NAO), and Pacific/North American Pattern (PNA) from 1973 to 2008. Insert graphs are the amplitude of the cross-spectral density for each pair of time series. Interior vertical lines on the Period axis are the Fourier frequencies (converted to periods). Asterisks denote periods where the coherency is significant as determined by the permutation procedure (α=0.10)...... 143

Figure 5.1. 95% confidence bounds for the variance parameters at the A, county; B, field within county; and C, site within field and county levels for each year. Estimates with standard errors are in Table 5.2...... 186

Figure 5.2. Estimated best linear unbiased predictor (EBLUP) on the complementary log-log (CLL) scale for each county ( ) surveyed, based on the fit of equation 3 to the data for each year. Counties with EBLUPS below the estimated mean ( ) are in red and counties with EBLUPS greater than are in blue, with the darkest shades indicating very low or very high estimated incidence levels on the CLL scale. As an example, for the counties in dark red in 2002, = -3.69 - 1. The Spearman correlation (r) between county EBLUPs for pairs of adjacent years is next to each map. For instance, the correlation between county EBLUPS in 2002 and 2003 is next to the 2002 map. All correlations were not significant (P > 0.10). Because of nonsignificance, any spatial autocorrelation is not relevant...... 187

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Chapter 1

Introduction

Fusarium head blight (FHB) of wheat (Triticum aestivum L.) is a disease of foremost importance in many parts of the world, including North America, Asia, and

Europe. FHB can be caused by several different fungal pathogens worldwide, but the most important are Fusarium graminearum, F. culmorum, F. avenaceum and F. poae, which can produce a range of mycotoxins (12), and Microdochium nivale and M. majus

(28), which do not produce any known mycotoxins. The pathogens that cause FHB are dependent on climatic and weather factors and, therefore, vary from year to year within and between regions (42,63). Throughout most of the U.S., Fusarium graminearum

Schwabe (teleomorph: Gibberella zeae (Schwein.) Petch) is the most prevalent species, whereas in cooler areas of Canada and Europe, F. culmorum may be more common. In

Europe and other regions outside of North America, F. graminearum is just one of a complex of Fusarium species causing FHB (66). It should be noted that F. graminearum has been shown to be a species complex, with multiple lineages (45).

Fusarium head blight reduces quantity and quality of yield by reducing grain weight and size, and by contaminating grain with mycotoxins [especially deoxynivalenol

(DON)] produced by the colonizing fungal pathogen. Yield reduction results from the production of small, shriveled, light-weight kernels with corresponding reduction in test

1 weight (i.e., density) of the harvested grain (6,10). Since the mycotoxins are harmful to humans and livestock, the US has set an advisory level of 1 part per million (ppm) for products processed from wheat intended for human consumption (2), and in the European

Union, even more stringent thresholds have been imposed (1). However, during major epidemics, such as the pandemic in the Northern Great Plains in 1993, DON levels can exceed 40 ppm (39), rendering grain unfit for commercialization and consumption. Yield loss in weight or volume can also be significant; for instance, estimated yield loss totaled

4.78 million metric tons (39) in the northern plains states in 1993, and an epidemic in

Ohio in 1996 resulted in an estimated yield reduction of 40% (34).

Gibberella zeae is a facultative parasite that can overwinter as perithecia or mycelia on infested corn or small grain residue (52), or in Fusarium-damaged kernels

(32), for at least 2 years. In the spring or early summer, perithecia mature and ascospores are produced within the perithecia (5). Ascospores may be forcibly discharged and become airborne (59), and then disseminated by wind; the ascospores may also ooze out of the perithecia and be dispersed by rain splash (46). Also in infested plant material, macroconidia are produced and disseminated by rainfall. Inoculum on wheat heads

(spikes) may arrive in the form of ascospores, macroconidia, or hyphal fragments.

However, hyphal fragments are not readily disseminated and thus, only ascospores and macroconidia are of importance in the epidemiology of Fusarium head blight (9,62).

Infection of wheat flowers occurs at and shortly after anthesis (3, 55), since the anthers are extruded at this time, thus providing the fungus with an entry point. After infection, the fungus colonizes the wheat spike, moving horizontally to other florets within the same spikelet and vertically to other spikelets above and below the point of infection.

Phytotoxic trichothecene mycotoxins, such as DON, that are produced have been clearly implicated as virulence factors in pathogenesis (54).

It has been known for over eight decades that FHB disease intensity and mycotoxin levels in grain are highly variable in nature (3,14,39,62), both spatially and temporally (14,62). The heterogeneity in FHB intensity occurs at multiple scales. Spatial variability within each year can be at small scales, such as between sites within a field, or at very large scales, such as between fields (65), between counties, or between states and countries (41). Similarly, variability can be observed at different temporal scales, such as between assessment times within years (67), between years, or even between decades

(39,62).

As early as 1929, Christensen et al. (14) suggested that meteorological conditions were the principal determinates of FHB intensity. Since then, many authors have drawn the same general qualitative conclusion (16,18,36,47,53,68). Particular weather conditions have been associated with several components of the disease cycle. For instance, maturation of perithecia and formation of ascospores in infested wheat and maize residue are favored by periods of warm temperatures and high relative humidity

(24,27,51). Ascospores and macroconidia are transported to wheat spikes by wind (26) or water splash (46), and density of spores on wheat spikes (reflecting both dispersal and spore production on debris) has been associated with high relative humidity, high rain intensity, and moderate temperatures in empirical studies (47). High relative humidity has also been associated with increased disease intensity (3,7,8,57) resulting from an increase in infection of the wheat spikes, and colonization and production of DON have been related to atmospheric moisture (16,17,18,58). However, there is yet uncertainty

3 regarding the effect of moisture and rainfall on DON. There is a considerable degree of heterogeneity found for all reported relationships (16,17).

Management of FHB with host resistance is a highly desirable goal (14,40). FHB resistance is a quantitative trait (9,60), and the development and release of resistant cultivars have been a slow process, with only moderate (partial or incomplete) levels of resistance being obtained so far (13). Resistant spring wheat cultivars have been available for a little over a decade (4), and resistant soft red winter wheat cultivars (e.g., ‗Malabar‘,

‗Bromfield‘) are now being released and grown in the ―corn belt‖ states such as Ohio

(29). However, grain yield and quality losses can still be experienced with these cultivars during major epidemics of FHB (30). Moreover, growers may choose to not use the more resistant cultivars because they tended to have—or were perceived to have—lower yield and quality than susceptible cultivars, and partly because of the sporadic nature of the disease (39) (Paul, unpublished). For instance, one of the most commonly grown cultivars in Ohio is Pioneer 25R47 since it is consistently high yielding, but it is also susceptible to FHB (11). With sporadic epidemics, growers may drift away from the use of more resistant cultivars if FHB intensity or DON contamination were very low during the previous year or two in a given region.

Other disease-management strategies, including cultural practices related to tillage and crop rotation (23) and fungicide application, are also often recommended for control of FHB. Use of a single application of a fungicide (especially of the triazole class) at anthesis (when the most effective fungicide applications have been timed) is a management tactic that can be beneficial to reduce losses during scab-favorable years

(48,49,50). However, the use of a fungicide may not be economical during low disease or

DON years. Therefore, accurate disease warnings or FHB risk predictions based on environmental (or other) conditions are crucial, so that fungicides are used only when conditions are favorable for epidemics (18,20).

Various models have been developed for FHB prediction, usually based on empirical analyses of observations of disease and meteorological conditions

(18,21,31,36,43,53,56). However, some models are of the (mechanistic) systems type, based on sub-models for environmental effects on individual disease-cycle components

(20,44,56). The current national FHB prediction system (utilized in 30 US states) is based on use of empirical logistic regression models and local weather conditions for the week before anthesis (Feekes growth stage 10.5.1) to predict risk of major FHB epidemics

(18,19,20). It is assumed that the forecaster is identifying periods favorable for spore production immediately before anthesis (19). Risk predictions are made at the start of anthesis because this is the best time to apply a fungicide, when it is most needed and effective (33). Validation of the national FHB prediction system showed that the model was 75-80% accurate in terms of sensitivity and specificity across a large number of location-years and wheat marketing classes.

Other predictive models for FHB and DON have been created for diverse regions around the world. Hooker et al. (31) identified weather variables that were associated with the occurrence and accumulation of DON in wheat heads in fields in southern

Ontario, Canada, over a 5-year period. They partitioned the time from 7 days before anthesis to 10 days after anthesis into three periods. It was shown that DON was higher when there were 1 or 2 days of rainfall >5 mm in the period before anthesis, but lower when there were multiple days with cool temperatures during this same period. DON

5 increased with moderate levels of rainfall and decreased with days exceeding 32°C for the periods of 3-6 days and 7-10 days after the start of anthesis. Their model predicted low levels of DON well, but did not accurately predict DON levels in major epidemic situations. Del Ponte et al. (21) developed a predictive model for FHB based on 5 years of data from Passo Fundo, Brazil. Their model took into account the host (flowering process), pathogen (ascospore density), and environment (temperature and relative humidity). Rossi et al. (56) created a systems model for both the risk of FHB and the risk of mycotoxin content under European conditions. Components of the model were based on very limited experiments on conditions favoring the disease-cycle components. The model calculated a daily infection risk based on (sub-)models for sporulation, spore dispersal, and infection of host tissue. A sporulation rate function was based on temperature and incubation time of Gibberella zeae. A spore dispersal function was calculated from air temperature, rainfall, and number of days with high relative humidity.

The infection rate function in the overall model was based on temperature, wetness, and the host growth stage. Zhao et al. (69) proposed a novel approach of using sea temperatures to predict incidence levels of FHB in China. They showed that there was a lagged correlation between the average water temperature over several months before an epidemic and the resulting FHB incidence.

A better understanding of the spatial and temporal variability in FHB can aid in: the elucidation of factors that influence epidemics; development and refinement of disease forecasting (prediction) systems, especially for risk of disease outbreaks or high levels of mycotoxin; the development of efficient sampling protocols (37) for risk assessment and model validation; and development of experimental designs for field

6 studies with increased precision and power (25). Therefore, this research project was developed to address aspects of the heterogeneity of FHB over short- and long-term temporal and spatio-temporal scales. There is currently only limited quantitative information on the spatial distribution of FHB intensity at the within-field or between- field levels (22,65), and no research is available on the degree of spatial heterogeneity over multiple spatial scales for several years with differing environmental conditions.

Therefore, this project deals, in part, with the simultaneous characterization of spatial heterogeneity at multiple spatial scales. However, the primary emphasis in this dissertation is on the role of environment – including both weather and climate – on the variability in FHB and mycotoxins. Currently, there is uncertainty over the environmental conditions that are most associated with FHB epidemics and DON, the starting and ending times, and time durations, over which environmental conditions are most predictive of disease and DON, as well as the specific form of environmental variables that are constructed from meteorological measurements. This dissertation addresses this topic using FHB and mycotoxin data from the US and Europe. Moreover, besides the effects of (short-term) weather conditions, the (long-term) climate may be associated with

FHB epidemics, and knowledge of global climate indices may be useful in characterizing longer-term temporal variability (over years or decades) of FHB. Such a characterization could, in principle, ultimately contribute to predictions of FHB epidemics that could be made sooner than those predictions currently made based on weather conditions.

The overall goal of this dissertation was to empirically quantify the relationship between climatic and weather variation and the variation in Fusarium head blight intensity at different scales. To address this goal, a range of data sets consisting of

7 biological or physical data were utilized, including: observations of FHB intensity, or the impact of epidemics, over multiple years in several states; data on intensity of FHB in wheat spikes, biomass of Fusarium graminearum, F. culmorum, and F. poae, and concentration of the mycotoxins DON and nivalenol (NIV) from multiple locations from three European countries over 4 years; disease incidence data collected at multiple spatial scales in Ohio over a decade; environmental data collected from meteorological stations or from automated data loggers within fields; and global and regional climate indices calculated by the National Oceanic and Atmospheric Administration. The motivation of this study was to ultimately improve disease-prediction models and develop more efficient sampling procedures by developing a more thorough understanding of the spatio-temporal variation in FHB, and the factors that affect these variations. A series of studies presented herein addressed different aspects of the spatial and temporal variability in FHB.

This dissertation is divided into four chapters after this introductory one. The following chapters describe:

2. An empirical examination of the FHB-environment relationship across multiple

years (or decades) in four states in the US;

3. An empirical examination of the FHB-fungal biomass-mycotoxin concentration-

environment relationship across multiple location-years in Europe;

4. A determination of the variability in FHB epidemics in two US states in relation

to global climate fluctuations as represented by the El Niño-Southern Oscillation

(ENSO) and other atmospheric patterns;

5. An examination of the multi-scale spatial variability in FHB incidence at multiple

locations in Ohio, obtained from a state-wide survey over 10 years.

In this dissertation, several statistical approaches were used to either quantify or account for the heterogeneity in Fusarium head blight (FHB), including: a data-mining algorithm known as ‗Window-pane‘ analysis (15), spectral and cross-spectral analysis

(64), and generalized mixed-model analysis (35). In particular, window-pane analysis was used to investigate the effects of environment on the inter-annual variation in FHB in four US states (Chapter 2) and the spatio-temporal variation across three European countries (Chapter 3). Window-pane approaches involve a large number of correlated test statistics, so novel approaches for dealing with the multiple-testing problem inherent in this analysis were considered. Then, spectral analysis and cross-spectral analysis (61) were used to determine whether there was coherency between variation in FHB over multiple decades and global climatic patterns (Chapter 4). Because there is no integrated explanation in a single reference of the multiple steps involved in conducting this type of statistical modeling, nor how to interpret model-fitting results, a detailed protocol for conducting spectral and cross-spectral analysis using SAS software is provided

(Appendix A). Finally, a generalized linear mixed model (38) was fitted to multi-scale survey data for the incidence of FHB in Ohio in order to quantify large and small-scale heterogeneity in disease incidence and evaluate variables that may affect the heterogeneity (Chapter 5). The intra-cluster correlation coefficient (ICC) is key to characterizing heterogeneity at the lowest scale in a hierarchy (e.g., the similarity in disease status of individual spikes within sampling units in fields). However, because of

9 the discrete nature of disease incidence, and properties of generalized linear mixed models, there are different approaches for approximating the ICC. Thus, a discussion on the approximations for the ICC is also provided (Appendix B).

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Chapter 2

Relationship Between Yearly Fluctuations in Fusarium Head Blight Intensity

and Environmental Variables: A Window-Pane Analysis

Introduction

Epidemics of Fusarium head blight (FHB) of wheat (Triticum aestivum L.), also known as wheat scab, are caused by several fungal species, but primarily by

Fusarium graminearum Schwabe (teleomorph: Gibberella zeae (Schwein.) Petch) in the United States (6,11,39,57,65,67). The economic importance of this disease is due to reduction in yield and contamination of grain with toxins (37). Yield reduction results from the production of small, shriveled, light-weight kernels with corresponding reduction in test weight of the harvested grain (3,7,60). Moreover, F. graminearum usually produces mammalian mycotoxins, especially deoxynivalenol

(DON), during colonization of the wheat spikes, which can result in high levels of toxins in the harvested grain (29,44,53). All sectors of the wheat industry experience losses caused by FHB (68), although the magnitude of the losses vary greatly among locations and years (33,35).

Management of FHB with host resistance is a highly desirable goal (11). FHB resistance is a quantitative trait (6,57), and the development and release of resistant

17 cultivars have been a slow process, with only moderate levels of resistance being obtained so far (9). Resistant spring wheat cultivars have been available for a little over a decade (2), and resistant winter-wheat cultivars are now being released (27).

However, losses can still be experienced with these cultivars during major epidemics of FHB (31). Moreover growers may not use the more resistant cultivars because they tend to have—or are perceived to have—lower yield and quality than susceptible cultivars, and partly because of the sporadic nature of the disease (35) (Paul, unpublished). With sporadic epidemics, growers may drift away from the use of more resistant cultivars if there were few FHB problems during the previous year or two in a given region. Other disease-management strategies, including cultural practices and fungicide application, are also often recommended for control of FHB. Use of a single application of a fungicide (especially of the triazole class) at anthesis (when the most successful fungicide applications have been timed) is a management tactic that can be beneficial to reduce losses during scab-favorable years (42,43,45). However, the use of a fungicide may not be economical during low disease years. Therefore, accurate disease warnings or predictions are crucial, so that fungicides are used only when conditions are favorable for epidemics (18,20).

The sporadic nature of FHB epidemics has been well known for over eight decades (1,11,35,63). As early as 1929, Christensen et al. (11) suggested that meteorological conditions were the principal determinates of disease intensity. Since then, many authors have drawn the same general qualitative conclusion

(16,18,34,41,48,70). Particular weather conditions have been associated with several components of the disease cycle. For instance, maturation of perithecia and formation

18 of ascospores in infested wheat and maize residue are favored by periods of warm temperatures and high relative humidity (23,26,46). Ascospores and macroconidia are transported to the wheat spike by wind (24) or water splash (40), and density of spores on wheat spikes (reflecting both dispersal and spore production on debris) has been associated with high relative humidity, high rain intensity, and moderate temperatures in empirical studies (41). Infection of wheat flowers occurs at and shortly after anthesis, and relative humidity has been associated with increased disease intensity (1,4,5,51). Colonization of the wheat spike and production of DON have been related to atmospheric moisture (16,17,18,55), but there is yet uncertainty regarding the effect of moisture and rainfall on DON. There is a considerable degree of heterogeneity found for all reported relationships (16,17).

Various models have been developed for FHB prediction, usually based on empirical analyses of observations of disease and meteorological conditions

(18,21,32,34,36,48,50), although some models are of the systems type, based on sub- models for environmental effects on disease-cycle components (20,38,50). The current national FHB forecaster (for 24 US states) is based on empirical logistic regression models, and utilizes local weather conditions for the week before anthesis

(Feekes growth stage 10.5.1) to predict risk of major FHB epidemics, so management decisions (e.g., application of a fungicide) can be made in a timely manner

(18,19,20). It is assumed that the forecaster is identifying periods favorable for spore production immediately before anthesis (19). Less researched is whether the annual variability in FHB disease level and yield loss in a region can be related to variability from year-to-year in environmental conditions over short or long time scales during

19 different periods of the growing season. Historical records of FHB intensity (broadly defined) over multiple decades in Ohio and three other U.S. states provide data sets that can be used to address this issue.

To investigate possible correlations between environmental variables and annual variations in FHB intensity, we utilized an empirical method that was first formalized by Coakley and colleagues in 1982 (15), now commonly-called ‗window- pane‘ analysis. This methodology—a form of data mining—has since been expanded in different ways for use with wheat (13,14,47,64), potato (25), rice (10), and banana

(12) diseases. This analysis can be used to determine the length (duration) and starting (or ending) time of the temporal windows where environmental variables are significantly associated with disease intensity.

The objectives of this research were to: (i) determine environmental variables most associated with annual fluctuations of FHB intensity in wheat in Ohio; (ii) determine time-window lengths and starting/ending times when FHB intensity was most highly correlated with environmental variables; and (iii) compare correlation results found for Ohio with those found for three other states, Indiana, Kansas, and

North Dakota. Because the window-pane methodology involves the calculation of a large number of correlated test results, approaches to adjust for the multiple-testing problem were explored and utilized in the investigation.

Materials and Methods

Disease data. In Ohio, FHB intensity in the state (broadly defined to include estimated yield impact) was rated on an ordinal scale from 0 to 9 at the end of each wheat season for 44 years (1965 to 2008). In each year, FHB intensity was assigned the rating score relative to the score assigned the previous years, based on observed disease levels and yield losses in variety trials and reports coming in from across the state. In addition to FHB, other diseases and yield-impacting (biotic and abiotic) stresses were also rated on the 0 - 9 scale; so, for any given year, the magnitude of one problem was determined relative to the occurrence of other (potential) problems evaluated in that same year. The rating was made by either a wheat breeder or field- crop pathologist in Wooster, OH. A year such as 1996, with widespread FHB outbreaks and resulting yield losses (>40%) (33), serves as a reference standard when assigning FHB scores.

In Indiana, disease was assessed for 36 years (1973 to 2008) in cultivar nurseries by Purdue University researchers. Observations used here were obtained from the susceptible ―check‖ cultivars. For all years, FHB disease index (field severity) was estimated as the mean percentage of spike area with symptoms

(including the spikes with no symptoms). In Kansas, mean disease index was assessed for 28 years (1978, 1980, 1982 to 2007) by Kansas State University, Kansas

Department of Agriculture, and USDA-ARS personnel, based on surveys of wheat in the state. No assessment was made in 1979 and 1981. So-called ―trace‖ amounts of

FHB were recorded for some of the years; we assigned these an index value of 0.001.

In North Dakota, the impact of FHB was rated at the end of each season for 23 years

(1986 to 2008) based on results from field surveys for yield losses by North Dakota

State University extension agents and specialists. Estimated yield losses for the disease were expressed on an ordinal scale from 0 to 9, with a 0 for no visible evidence of the disease and a 9 for the highest estimated yield loss observed in the state (2.4 million metric tons) over the years of observations. Although the ordinal scale used in both Ohio and North Dakota ranged from 0 to 9, the individual values do not necessarily have equivalent meaning in each location. However, for the chosen statistical analysis (see below), only the order of the values within a location matter in the interpretation of analytical results.

Meteorological data. For Ohio, weather data were gathered from weather stations near Wooster by the National Climatic Data Center (NCDC) and the Ohio

Agricultural Research and Development Center (OARDC). Daily maximum and minimum temperature and total precipitation were available for all years. Daily average temperature was calculated as half the sum of the maximum and minimum from 1964 to 1982, and as the arithmetic mean of hourly data thereafter. Maximum, minimum, and average relative humidity were available from 1982 to 2008. A nearby weather station (WBAN 14895) provided 3-hour relative humidity data from 1964 to

1981, which was used to find the daily maximum, minimum, and average relative humidity. This weather station was also used for missing data (total of 22 days) in

Wooster for all other years. Average daily dew point was calculated from the average temperature and relative humidity (69) (when dew point measurements were not directly available). In general, atmospheric moisture for hourly data was provided as

22 dew point temperature (in combination with ambient air temperature); relative humidity was then determined using a standard formula based on air temperature and dew point (National Oceanic and Atmospheric Administration. 2009. National

Climatic Data Center). Based partly on previously published results for FHB and other diseases, several combinations of the weather variables were investigated in the construction of environmental variables for different time windows (Table 2.1), as described below. For the other states, weather data were gathered from weather stations near Lafayette, Indiana, Manhattan, Kansas, and Fargo, North Dakota, by the

NCDC and the Indiana State Climate Office, the Kansas State University Research and Extension Weather Data Library, and the North Dakota Agricultural Weather

Network, respectively. As with Ohio, relative humidity was calculated from air temperature and dew point depression (when relative humidity was not provided). All data missing from Lafayette, Indiana, and Manhattan, Kansas, were collected from nearby weather stations (WBAN 93819 and WBAN 13996).

Window-pane analysis—variable construction. The concept underlying window-pane analysis is the specification of a time window of defined length or duration, and the construction of summary environmental variables (e.g., means) for the specified window. This time window (e.g., 30 days) is moved (or slid) along the total time frame of interest (e.g., a year or a growing season), in daily increments, so that the environmental data from the entire time frame is ultimately considered in the data analysis. With a defined starting time and window length, the ending time of the window is automatically determined. Time windows of environmental data were constructed separately for each year. The ―beginning‖ of the time frame in the

23 analysis for Ohio data was considered the approximate time of wheat maturity (30

June; for convenience of expression, given as time ―0‖), and the windows proceeded backwards over this time frame in daily increments to end at the approximate time of planting (24 September; time ―280‖).

Summary environmental variables were calculated for a wide range of time– window lengths and starting times of the windows for each year. The fixed time windows had lengths of 10, 15, 30, 60, 90, 120, 150, 180, 210, 240, and 280 days

(Table 2.1). As an example, the first window of length 10 began on 30 June (time 0) and ended on 21 June; the second 10-day window began on 29 June (time 1) and ended on 20 June; and the final 10-day window began on 3 October (time 270) and ended on 24 September. Two successive time windows (of the same length) share all but one day of data. There were a total of 270 windows of length 10 for each year, with smaller numbers of windows of longer lengths (Table 2.1). The construction of summary variables for the different window lengths and starting times was done with the 2007 version of Microsoft Excel.

The above-described window lengths for Ohio were also used for Indiana,

Kansas, and North Dakota. The same starting time was used for the windows for

Indiana and Kansas. However, to correspond to the spring wheat growing season in

North Dakota, a starting time of 15 August (time 0) was used; time windows ended in mid-January (time 210) for this state. Although for spring wheat the growing season starts around late April or early May of the same year (around time 105), we still continued time windows back further in time to capture periods when overwintering is occurring. For all states, the time frame was linked to the calendar dates and not to 24 specific crop growth stages. This is because there can be a range of dates for a particular growth stage in any given area, and because cultivars vary in maturity, and consequently, the time of occurrence of any specific growth stage. In addition, records were not kept in the historical data for the times of specific stages in several of the years. We do refer to the growth stages that typically occur during approximate time periods in a given location, based on historical norms and experiences of the local experts.

For each window length and start time, several summary environmental variables were calculated (Table 2.2), based on either averages or summations of temperature (e.g., AT), relative humidity (e.g., ARH), negative dew point depression, precipitation, or combinations of these. Some variables were based on the summation of times (days or hours) where certain conditions were met (e.g., T1530). Most variables were based on the recorded daily meteorological conditions (or from the daily average or summations when hourly or every 3-hour data were available); however, HRH90, THRH90, HRH80, and THRH80 were based strictly on hourly values. Construction of the summary variables was based, in part, on the variables used in other studies (34,41). The environmental variables for the longer time windows generally represent climatic conditions, and can be used to relate overall climate to FHB epidemics. In contrast, the environmental variables for the shortest time windows, which are more weather-like summaries of the environment, could be used to associate environment with particular components of the disease cycle (e.g., spore production, infection, spike colonization, etc.).

Window-pane analysis—statistics. The relationship between each summary environmental variable and disease intensity was quantified with an estimated

Spearman rank correlation coefficient (r) (61) for each of the window lengths and starting times. This rank-based nonparametric correlation was used due to the ordinal nature of the FHB intensity data in Ohio and North Dakota, and because of the nonnormal data in the other locations. The Spearman correlation coefficient determines the degree to which a monotonic relationship exists between a pair of variables (58); with this type of correlation, only the order of the variables matters, and not the actual values.

The summary environmental variables were exported to SAS (SAS, Inc., Cary,

NC) for analysis. The CORR procedure was then used to estimate the Spearman correlation coefficient and significance level (P) across all years, based on a one- sided test for each variable at each of the time window lengths and starting/ending times. That is, the correlation was based on N = 44, 36, 28, and 23 observations for

Ohio, Indiana, Kansas, and North Dakota, respectively. For instance, with the Ohio data set, there were 44 values of the environmental variable HRH90 with window starting time of 0 and a length of 10 days; the correlation of these environmental observations and the yearly FHB intensity values was estimated with the CORR procedure. Then, the correlation was estimated between FHB intensity and the 44

HRH90 values with a window starting time of 1 and window length of 10 days. In the same fashion, the correlations were estimated for all the window starting times and window lengths, for HRH90 and then for all the other environmental variables

(and then for all the other locations). One-sided tests were performed because we

26 hypothesized that the effect of an environmental variable would be manifested in only a single direction. Windows (for a given length) with nonzero association between disease intensity and an environmental variable were identified with the magnitude of the individual P value for the different starting times of the windows. When one is dealing only with a single test result, in general, a positive correlation is declared if P

< , where  is the pre-specified significance level for an individual test. For window-pane analysis, multiple correlated test statistics are obtained, which require adjustments to the simple hypothesis-testing problem.

Window-pane analysis—multiple hypothesis testing. This analysis involves a large number of test statistics; for instance, with the 10-day window length, there are 270 windows (and, hence, 270 correlations) for the 280-day time frame. Because of the multiple testing of correlations, the global (experiment-wise, family-wise) significance level (Pg)—for an effect ―somewhere‖ across all the windows—will be higher than the critical significance level () set for the individual-test decisions (66).

As a consequence, there can be too many ―false positives‖ (i.e., falsely declaring correlations to be greater than 0) across the collection of test results. Additionally, the calculated statistics are correlated with each other with this type of analysis, because they involve the same disease data, because adjacent and nearby time windows share multiple days of the same environmental data, and because large-scale climatic patterns will affect weather data over successive days. These correlations of the test statistics complicate the methodology for multiplicity adjustments, compared to when there are collections of independent tests, and there is no clear-cut best approach to use for the adjustment (66). However, the degree of the adjustment for multiplicity is

27 much less for correlated tests results than for independent tests (49). The problem with all multiple-testing adjustments is low or very low statistical power of the test results (i.e., in order to control the probability of a false positive, the probability of correctly detecting a true positive result can become very small) (66). Some authors even argue against adjustments when the primary interest is in the individual test results, such as whether or not a particular correlation is greater than 0 (52,54). This issue has not been formally addressed in previous uses of window-pane analysis

(47,64).

We dealt with the multiple-testing problem in three separate ways. First, for each environmental variable and window length, we performed a global test of significance across all window starting times using the Simes‘ method (59). This is a test for the global null hypothesis (H0(g)) that none of the individual correlations are significant, and the alternative (Ha(g)) that at least one is greater than 0. The Simes‘ method is based on the ordering of individual P values (Pj) from low to high in a collection of k

(possibly) correlated test results, where j represents the j-th smallest individual P value (j = 1, …, k). If g is the pre-specified global significance level for the collection of tests (g = 0.05 in our study), H0(g) is rejected if Pj ≤ jαg/k for any of the j tests. Based on the number of tests and the order of the achieved significance levels,

~ an adjusted individual Pj value can also be obtained ( Pj ) as explained in Westfall et al. (66); the global P value (Pg) is the minimum of the values. Values of Pg less than αg (0.05) are considered significant for the global test. With the Simes‘ method, no decision is made on the significance of the individual test results (i.e., estimated

28 correlation coefficients here); therefore a significant result in our case (Pj ≤ jαg/k for any j) only means that one or more of the correlations is larger than 0.

Second, the individual estimated correlation coefficients were compared with critical values corresponding to individual pre-specified significance levels ( values) of 0.005 instead of 0.05. That is, the j-th individual correlation was considered to be greater than 0 if Pj < 0.005. Use of  = 0.005 makes it harder to declare that a correlation exceeded 0, which provided some protection from excessive number of false positives for the individual correlation results. As with all multiple-testing adjustments, however, the correction does lead to an increased number of false negatives (falsely accepting the null hypothesis) or reduced power (66). Although there is no formal linkage between the global test adjustment (first approach) and the individual test adjustment (second approach), in most (but not all) explored cases, when there was global significance, there were also significant individual correlations, and when there was not global significance, there were no significant individual correlations (Kriss, data not shown).

Third, a separate ad-hoc method followed by Pietravalle et al. (47) was utilized to reduce the chances of falsely declaring a positive result due to spurious results

(caused by unexplained variation and correlations). A significant positive relation during a given time period between an environmental variable and FHB intensity was declared only if there were clusters of successive correlations that were individually significant (at P < 0.005). The individual significance levels were determined using the approach in the previous paragraph. The principle is that because of the high correlation of the environment in nearby windows, as discussed previously, a single

29 large correlation of environment with FHB intensity surrounded by small or 0 correlations would likely be a false positive. There is no formal (probabilistic or other) rule regarding the required length of correlation clusters; we chose clusters of five. We primarily used this third method to confirm the results of the global significance level (based on the Simes‘ method) for a given variable and window length.

It should be noted that the magnitude of the Simes‘ adjustment is a function of the number of test results in the collection being considered. In particular, the adjustment for short-time windows is much greater than for long time windows. Thus, in general, individual correlations must be larger for short time-windows than for long time- windows in order for there to be a significant global test result.

Serial correlation for FHB. Trends in FHB intensity from year-to-year were characterized using (Spearman) serial correlations. After first ranking the data for each location, the ARIMA procedure in SAS was used to estimate the first-order correlation coefficient and its standard error.

Results

Annual variation in disease intensity. There was considerable year-to-year heterogeneity in FHB intensity for Ohio, Indiana, Kansas, and North Dakota (Fig.

2.1). Although one cannot directly compare the magnitude of intensity values across locations (because of the different scales or types of measurements utilized), the large numbers of zeros for Kansas indicate that this location had the lowest amount of

FHB. Within each state, disease intensity from year-to-year was highly variable, with low-moderate serial correlation between successive years. For instance, the first-order serial Spearman correlation and their corresponding standard error was 0.304 (0.15),

0.319 (0.17), 0.104 (0.20), and 0.314 (0.21) for Ohio, Indiana, Kansas, and North

Dakota, respectively. The apparent decreasing trend in disease in North Dakota, starting around 15 years ago, was not supported by a significant correlation coefficient. Also, in any given year, disease intensity was variable among states.

There were several years where high FHB intensity in one state did not coincide with high disease levels in other states, and vice versa. However, there was more similarity in FHB intensity between Ohio and Indiana, possibly because of the proximity of the states (Fig. 2.1).

Ohio window-pane analyses. In Ohio, yearly fluctuations of FHB intensity were significantly and positively correlated with several environmental variables.

Table 2.3 provides the adjusted global P value (Pg) and the maximum individual

Spearman correlation coefficient for each weather variable and window length. The table also indicates if the maximum correlation was significant at an individual P value of < 0.005, and if there was at least one cluster of five successive correlation coefficients that were significant. In general, variables that represented atmospheric moisture or wetness conditions in some sense (e.g., relative humidity, precipitation) were significantly and positively correlated with FHB intensity, and variables based on temperature alone were not. The mean average daily relative humidity (ARH), for instance, was significantly correlated to FHB intensity for all window lengths (Pg <

0.05). Also, there were clusters of at least five significant positive r values at all window lengths between 10 and 240 days.

Individual Spearman correlation coefficients from the window-pane analysis are depicted in the form of graphs for each window length. The specific example of

ARH is shown in Figure 2.2 for 10 different window lengths. (For the window length of 280 days, there is only a single window, encompassing the entire time frame). The horizontal axis represents the starting time of each window of a given length (where time 0 is the end of the season), and each vertical bar represents the (estimated) correlation coefficient for the association between FHB intensity and ARH for the given window. The number of bars depends on the length of the window (Table 2.1).

For instance, there are 270 vertical bars for the 10-day windows; the first bar is at 0, and the last is at time 270 (the first day of the last window calculated). For short window lengths (e.g., 10 to 30 days), ARH was significantly (P < 0.005) correlated with FHB intensity during and shortly before late May/mid June (10 to 25), and around late April (70), early March (120), and late December (185). At the 30- day window length (and longer), significant correlations could also be seen for windows around the end of the season (0 to 15). The time period from 0 to 25 days encompasses the approximate time of DON production and fungal colonization of the spike; the period from 25 to 45 the approximate time of infection (anthesis and later); the period from 45 to 120 the approximate time for inoculum production; and the period from 120 to 220 the approximate time of pathogen winter survival

(63).

For ARH, as the window length increased, the individual correlation coefficients and the maximum coefficient across all window start-times tended to decrease (Fig. 2.2; Table 2.3). However, the global Simes‘-based test was significant at all window lengths. Maximum daily relative humidity (MRH), average negative daily dew point depression (NDPD), and hours with relative humidity above 80%

(HRH80) (Table 2.2) showed similar trends as found with ARH (Table 2.3), although the Pg values were slightly above 0.05 for a few window lengths. Because of the similarity of results to that found for ARH, individual correlation coefficients are not shown for these variables. Interestingly, hours of relative humidity greater than 90%

(HRH90) were not significantly correlated with FHB intensity (Pg > 0.05), although there were some significant individual correlations (P < 0.005) for shorter time windows.

Precipitation variables were also significantly correlated with FHB intensity in

Ohio (Pg < 0.05, individual P < 0.005) for selected window lengths. The total daily amount of precipitation (TP) was significantly associated with FHB intensity for 15- and 30-day windows, and the incidence of precipitation (IP) was significantly associated with FHB intensity for 15-210 day windows (Table 2.3). Each of these variables had clusters of five or more sequential r values that were individually significant. The correlation coefficients at four selected window lengths are shown in

Figure 2.3A to demonstrate the patterns. The highest correlations were predominantly located at starting times from 0 to 30 (Fig. 2.3A), which includes anthesis through crop maturation. In general, the magnitude of the correlations decreased as the window length increased above 60 days.

Temperature-based variables that were not coupled with aspects of moisture or wetness, such as average daily temperature (AT), were not significantly correlated

(Pg > 0.05, individual P > 0.005) with annual FHB intensity for any time window

(Fig. 2.3B; Table 2.3). The same nonsignificant results were found for the T1530,

DD15, DD9, NDD15, and NDD9 temperature variables (defined in Table 2.2), and the tabular and graphic results are not displayed for these latter variables to save space. On the other hand, when temperature was coupled with other variables to create a composite environmental variable, such as the number of hours with relative humidity greater than 80% and temperature between 15°C and 30°C (THRH80; see

Table 2.2), significant correlations were found at several window lengths (Fig. 2.3C;

Table 2.3). For THRH80, at short window lengths (10 and 15 days), the maximum correlation coefficients were slightly lower than those found when temperature was not incorporated into the corresponding environmental variable. However, at window lengths of 30 days or longer, the maximum correlations were substantially higher when temperature was considered jointly with relative humidity than when temperature was not considered. In fact, for window lengths of 120 days or longer, the maximum correlation coefficients for THRH80 were higher than the maximum for any other variable at these long window lengths (Table 2.3). Similar to previously mentioned moisture variables, the highest correlations between FHB intensity and

THRH80 were around anthesis, with other moderately high correlation coefficients at time 70 (Fig. 2.3C). Results for the composite variable T1530P were similar to those found without the use of temperature (IP), and individual test results are not shown.

A graphic depiction of the time windows with individually significant correlation coefficients (at P < 0.005) is provided in Figure 2.4 for two shorter window lengths. The variables AT and THRH90 are not included in the summary because of their general lack of significant associations with FHB intensity in Ohio.

The horizontal lines encompass the time range of the windows with significant correlations between the environmental variable and FHB intensity, not just the starting time of the windows. As shown in the first row of graphs, substantial portions of the late season (anthesis to approximate maturity) had significant correlations, although the exact times varied a little. For relative humidity variables, the earlier time periods with high correlations are also evident (as shown more specifically in

Figure 2.2 for ARH).

Indiana, Kansas, and North Dakota window-pane analyses. Similar results to those found in Ohio were also found in the three other states. In each location, environmental variables based on atmospheric moisture and/or wetness conditions

(e.g., ARH, HRH80) tended to be positively correlated to FHB intensity (Pg < 0.05) for one or more windows (Table 2.4), especially for windows of shorter length (60 or fewer days). At least two moisture/wetness variables were significant for each location. There were fewer globally significant results for North Dakota, possibly because of the smaller number of years in the analysis, which can have a large impact on the power to detect a true positive correlation (71). For this state, several of the results of the Simes‘ tests were borderline significant (i.e., 0.05 < Pg < 0.10).

Although there were a few exceptions, maximum correlation for a given variable tended to be highest—and individually significant at P < 0.005—at one of

35 the shorter window lengths (10, 15, 30, or 60 days), and the magnitude of the correlation coefficients generally declined as window lengths increased above 60 days. Thus, to save space, only the results for five window lengths are shown in Table

2.4.

Based on global significance level, Pg, in these three states, there were no significant correlations found between the temperature-only variables and FHB intensity for any time window (Table 2.4). The results were the same for the other temperature-only variables listed in Table 2.3 (Kriss, data not shown). In Indiana, however, a few individual correlations with the 10- and 15-day window lengths were found to be significant (at an individual P of < 0.005), although there were no clusters of five or more individually significant correlations involving temperature (Table

2.4). As in Ohio, incorporating temperature into a moisture variable (e.g., THRH80) did generally increase the magnitude of the correlations found for HRH80 with the different time windows.

In terms of the overall results across all starting times of the windows, some specific differences between the states could be seen (Tables 2.3 and 2.4). For

Indiana, the smallest Pg and largest maximum r (over all the starting times) were found for 60-day windows for several variables (ARH, MRH, NDPD, TP, and IP), whereas shorter windows tended to have the smallest Pg and largest maximum r for the other locations (including Ohio). Also, the highest correlations (across all variables and window lengths) tended to be higher for Kansas and North Dakota compared with Ohio or Indiana. The largest correlations found per location (among all variables) were 0.677, 0.681, 0.787, and 0.704 for Ohio, Indiana, Kansas, and

North Dakota. Moreover, based on the global test, the atmospheric-moisture-based

MRH and NDPD were not significant (Pg > 0.05) for Kansas, although these were significant globally for the other locations; also, rainfall-based TP and IP were not significant for North Dakota, although they were significant elsewhere.

The individual correlation coefficients for three select environmental variables

(ARH, TP, and THRH80), chosen for demonstration purposes, and two (short) window lengths are shown in Figure 2.5. For ARH at a short window length (15 days), there were high and individually significant (P < 0.005) positive correlations around 10 and 45 in Indiana, 35 in Kansas, and 20, 120, and 180 in North

Dakota (Fig. 2.5A). At the somewhat longer window length (30 days), there were high and individually significant (P < 0.005) positive correlations around 30 in

Indiana and Kansas (Fig. 2.5B). Similar patterns were found for the TP variable, with high and significant correlations around 30 to 45 in Indiana, and 25 to 40 in

Kansas (Figs. 2.5C and D), but with no significant correlations in North Dakota.

However, some of the correlations around 25 and 30 were very close to being significant at P < 0.005. With 30-day window lengths, significant positive correlations were found for about the same time periods as found for the 15-day windows, and the correlations for North Dakota were also significant. For THRH80, the highest correlations corresponded to the time near crop maturity (for either window length). In Indiana, these high positive correlations were around 10, and in

Kansas around 0 to 10 (Figs. 2.5E and F). In North Dakota, the high correlations were around 0 to 20. It should be noted that even when a variable did not have a significant association with FHB intensity globally (across all window starting times; 37

Pg < 0.05), there could still be individual positive correlation coefficients that were significant at P < 0.005.

The similarity of the individual correlation results across locations can be seen graphically in Figure 2.4 for eight of the environmental variables. With the 30-day window length, the significant positive correlation coefficients between environment and FHB intensity near the end of the growing season (from shortly before anthesis to crop maturity) can be clearly seen for most of these moisture/wetness-related variables. There were just a few noticeable differences among the locations. In

Kansas, the significant correlations did not extend as close to time 0 as they did in the other locations. This may be due to the earlier flowering dates of wheat in Kansas as compared to the other states (relative to the chosen time for crop maturity). In North

Dakota, fewer of the variables were significant (at P < 0.005) as compared to the other states. The variable HRH90 (see Table 2.2) was individually significant late in the season only in Ohio (although it was not globally significant here), and MRH was significant late in the season only in Indiana. Moreover, only in Ohio and North

Dakota were there significant correlations at starting times of around 100 or earlier

(for a small number of variables).

With 15-day window lengths, greater temporal resolution could be seen in the timing of significant correlation coefficients, with more periods of noncontiguous high correlations being evident (relative to the 30-day windows). In Ohio and North

Dakota, there also were more periods before day 80 with high correlations. With the higher resolution, the positive correlations around or right before anthesis were evident for most locations, at least for several variables. The very late-season

38 correlations (near crop maturity), found with 30-day windows were less evident with

15-day window lengths.

Discussion

A window-pane analysis (15) based on use of the nonparametric Spearman correlation coefficient (61) was used in the current investigation to identify environmental variables that were associated with annual fluctuations of FHB intensity. As with any type of correlation analysis, the power to detect significant relationships is a function of the number of observations; thus, the power (for an environmental variable that truly was associated with FHB intensity) would be highest for Ohio (N=44), followed by Indiana (N=36), Kansas (N=28), and finally

North Dakota (N=23). Equivalently, the magnitude of r required to reject the null hypothesis in favor of the alternative (at a specified ) is inversely related to N; for instance, a much larger r was required for North Dakota than for Ohio to declare a significant positive correlation (at a fixed ). Nevertheless, results for North Dakota were generally similar to those in the other states, although there were fewer significant correlation coefficients.

In all states, there was no evidence of a significant correlation between FHB intensity and any of the temperature variables (e.g., AT) for any time window. This may initially be considered surprising given that others (1,23,63) have shown that various components of the pathogen life cycle (e.g., rate of sporulation and spore density on spikes) are dependent on temperature. However, in the absence of wetness

(from rain or dew) or high atmospheric moisture levels (e.g., high relative humidity), temperature alone may be relatively unimportant for the disease. Moreover, during critical portions of the season (e.g., around anthesis), temperature may not vary enough from year-to-year within a location for there to be a detectable level of association of temperature variables with FHB intensity. Based on other diseases of field crops, temperature variables alone may be of greatest potential value in predicting overwintering of the pathogen (62). However, the correlations during for the winter months were low and also not significant here.

As anticipated from several other studies (18,36,41,50), moisture and/or wetness-related variables (e.g., ARH, TP) were found to be significantly correlated with FHB intensity over the multiple years of observations in Ohio and the other locations. Additionally, variables that combined aspects of moisture/wetness with temperature (e.g., TRH80) were also correlated with FHB intensity, and sometimes the estimated correlation coefficients were higher when temperature was incorporated into the moisture/wetness variable than when it was not. In general, the r values were higher for the shorter window lengths (e.g., 15 or 30 days) than for the longer lengths

(e.g., 120 days or longer). Moreover, with the shorter time windows, the highest positive correlations were found for time periods from around 60 days before crop maturity (time 60) to around (or close to) crop maturity (time 0), with the exact results dependent on location and the window length. With 15-day window lengths, there were more distinct time windows identified with high r-values, and correlations very late in the season (10 to 0) were usually not significant (Fig. 2.4). This would suggest that the high correlations for windows that included time 0—found with the

30-day window—were based more on the environmental conditions more than 10 days before maturity rather than the conditions immediately before or at time 0. The results on moisture/wetness effects on disease development support the findings of several other authors (8,16,18,34,41,50). In particular, the high correlations from around 60 to 30 days likely reflect the influence of atmospheric moisture on production of ascospores and conidia in debris, and the subsequent dispersal to wheat spikes (63). In this regard, Gilbert et al. (26) found the rate of ascospore germination was at a maximum at 90% relative humidity, and Paul et al. (41) found that moisture- related variables had a significant relationship with spore density on wheat spikes immediately before, at, and after anthesis. High correlations from around 40 to 10 days likely represent the influence of moisture/wetness variables (or combined moisture/temperature variables) on infection efficiency of spores and spike colonization (with DON production) (8,16,63). De Wolf et al. (18) found the combined effect of temperature and moisture/wetness was related to FHB disease risk during the time periods for sporulation and spike infection. However, they found the number of hours that temperature was between 15 and 30°C and relative humidity was greater than or equal to 90% had a stronger relationship than the number of hours with temperature between 15 and 30°C and relative humidity greater than 80%. In the present study, using different data, we find the opposite to be true. In the current study, this may reflect lower accuracy of relative humidity observations from some weather stations, where hourly relative humidity was determined using a standard formula based on measured air temperature and dew point. The accuracy of these

41 measurements is about  1°C, which can lead to decreasing (relative) accuracy as relative humidity approaches 100%.

No single best environmental variable was identified in this investigation for its correlation with FHB intensity; rather, several inter-correlated moisture/wetness variables were found to give very similar results. This is not surprising because the environmental variables were correlated with each other. Furthermore, as discussed above, no single window length (for starting times between 60 and 0) was best overall, although shorter windows (60-day, and especially 30- and 15-day) generally gave the highest correlations compared to longer windows (especially 120-days or more). The general decline in individual correlation coefficients (at particular window starting times), or decline in the maximum correlation for a particular location (across all starting times), with increasing window lengths suggests that FHB intensity is affected more by shorter-term weather patterns than by longer-term climatic conditions (over multiple months). The shorter window lengths can be more directly connected to particular crop stages and components of the disease cycle, as discussed above. Ideally, window length could be refined further, especially by further shortening of the window length, by linking window start or end times to the timing of particular growth stages (e.g., anthesis) in a given location. However, with this system and available data, such additional refinement is not possible because: growth- stage timing (such as anthesis) varied somewhat within a region, cultivars varied with regard to the time when stages were reached, and there was no recording of the exact time of various crop growth-stages in many location-years. Therefore, as window- length decreased (with starting times based on a calendar date), there would be an

42 increasing likelihood that the (very) short windows would line up with crop growth- stages in some years and not others, or for some cultivars and not others. Thus, window lengths of 15 or 30 days, or possibly 60 days in some circumstances, appeared to be the most appropriate time lengths for relating environment to FHB intensity in this multi-year and location investigation.

The most surprising result perhaps was the identification of significant correlation coefficients for some moisture-related variables for time windows considerably before anthesis in Ohio and North Dakota (at times of about 160, 185 or earlier) (Fig. 2.4). However, Lu et al. (34) also reported on significant relationships between FHB intensity and moisture/wetness- related variables in the fall and/or winter (times of approximately 150 or 210). The correlations in our investigation may reflect a true relationship between wintertime environmental variables and pathogen winter survival. Alternatively, the results could reflect high autocorrelation of environmental variables over long time spans. For instance, the high correlation between FHB intensity and ARH at 185 could be (partly) due to a high correlation between ARH at 185 and 20 (the window around anthesis). To explore this, we plotted the correlations of ARH at one time period with other time periods for Ohio

(Fig. 2.6A) and North Dakota (Fig. 2.6B) for 15-day window length, using the time with the highest correlation near anthesis between ARH and FHB as the starting point. For North Dakota, there was some evidence that the autocorrelations in ARH could be responsible for significant correlation between ARH and FHB at around time 180; that is, the correlation between ARH and FHB and also between ARH and

ARH were high for time 180 [see Figs. 2.2 and 2.6B]). However, the high 43 correlation between FHB and ARH at about time 120 did not line up with a high correlation between ARH at 120 and ARH at 19 (the reference time). The evidence for this autocorrelation effect was also weaker in Ohio (Fig. 2.6A). That is, there were several time periods with high autocorrelations of ARH (e.g., at 90 and 160), but there was low correlation between FHB and ARH during these times. Further investigations are needed to clarify the role of very early environmental conditions on

FHB.

We utilized the Simes‘ multiplicity-adjustment procedure to test the global null hypothesis of no effect of an environmental variable across all windows of a particular length, primarily because it performs well with positively correlated test statistics (27). Where there was a significant result based on the Simes‘ procedure

(i.e., Pg < g, with g = 0.05), one-to-several individual correlations generally were found to be individually significant at P < 0.005 during the time periods identified above. Exceptions to the linkages of the different multiplicity corrections could be explained in terms of the degree of adjustment in the Simes‘ method for global hypothesis testing. The magnitude of the adjustment was very small with the very long window lengths because there were few separate P values in the collection (in the extreme, with the 280-day window, there was only one individual P value). For some long window lengths, therefore, sometimes the global test was significant but individual correlations were not significant (at P < 0.005) (Kriss, data not shown). A less conservative individual P value could be warranted in these cases, but we did not pursue this because the estimated correlation coefficients generally declined in magnitude with increasing window length. With short window lengths, there are 44 many P values over the 280-day time frame, and the Simes‘ adjustment is correspondingly large; that is, the evidence has to be very strong for one or more positive correlations in a collection of correlations in order to reject the global null hypothesis. Thus, occasionally the global test was not significant even though there were one or more individual correlations significant at P < 0.005. This was most likely to occur for the North Dakota data, partly because of the smaller number of years in the analysis compared to the other locations.

In conclusion, annual variations in FHB intensity were associated with several inter-related variables that summarized environmental conditions related to moisture and wetness over window lengths of various durations, but especially shorter-length windows in the 2 months prior to crop maturity. Results were generally consistent with previously shown or postulated effects of environment on components of the disease cycle (16,23,26). Furthermore, the correlation results support the use of real- time disease forecasting systems based on environmental conditions (18,19) for this sporadic disease. The findings of this investigation can be used as a guide in determining possible updates to the current national FHB forecaster. Because the models in the national forecaster are based on data from a short 7-day window ending at anthesis, use of this system requires an estimate of the time of anthesis (18). This is one of the major challenges in use of the system (19,32) because time of anthesis is less routinely determined or reported than time of heading. It is unknown how forecaster accuracy suffers when the anthesis time is misspecified. The current investigation showed that it may be feasible to use environmental summaries from less strictly defined window start or end times (relative to a single phenological wheat

45 stage) to identify disease risk, and to use windows either closer to crop maturity or of longer lengths than currently used. Anthesis is about the latest time that a fungicide can be applied for FHB control. However, forecasts closer to crop maturity can be of benefit for estimating the magnitude of yield loss or DON contamination before the crop is harvested or sold at grain elevators. Because environment has been determined to be a significant factor in disease development, future work could include the use of climatic models (28) to predict years with high probability of moisture/wetness events during critical time windows. Climate models generally deal with longer-term environmental summaries (of the order of 1 month and longer) (28); therefore, the estimated positive correlations between FHB intensity and environment from longer-length time windows (30 or more days) are directly applicable to any consideration of climate change or climatic patterns and subsequent disease development. Although the environment during critical time windows clearly affects

FHB epidemics, grain yield, resulting toxin contamination of grain, the relationship between FHB intensity and the environment is variable, and the disease responses are also strongly influenced by resistance of the cultivars grown, use of fungicides, and cultural practices such as rotation and type of tillage (22,56). Cultivars with quantitative (partial) resistance are slowly being released and adopted by growers, although many factors influence whether a grower will use a less susceptible cultivar

(31,35). Moreover, growers may not be willing to utilize cultural practices that may reduce the intensity of this disease. Thus, the disease will likely continue to exhibit sporadic patterns over multiple years, based on the favorability (or lack of favorability) of environmental conditions. Knowledge of the relationship between

FHB intensity and environment aids in predicting major epidemics and in making decisions on the use of fungicide for disease control.

Table 2.1. Window lengths and calendar dates for winter and spring wheat locations used in window-pane analysis of Fusarium head blight Winter wheata Spring wheatb Window Number Start date (end date: 24 Number Start date (end date: 18 January) length of windows September) of windows 10 270 30 Jun , 29 Jun, …, 4 Oct, 3 Oct 200 15 Aug, 14 Aug, …, 28 Jan, 27 Jan 15 265 30 Jun, 29 Jun, …, 9 Oct, 8 Oct 195 15 Aug, 14 Aug, …, 2 Feb, 1 Feb 30 250 30 Jun, 29 Jun, …, 24 Oct, 23 Oct 180 15 Aug, 14 Aug, …, 17 Feb, 16 Feb 60 220 30 Jun, 29 Jun, …, 23 Nov, 22 Nov 150 15 Aug, 14 Aug, …, 19 Mar, 18 Mar 90 190 30 Jun, 29 Jun, …, 23 Dec, 22 Dec 120 15 Aug, 14 Aug, …, 18 Apr, 17 Apr 120 160 30 Jun, 29 Jun, …, 22 Jan, 21 Jan 90 15 Aug, 14 Aug, …, 18 May, 17 May 150 130 30 Jun, 29 Jun, …, 21 Feb, 20 Feb 60 15 Aug, 14 Aug, …, 17 Jun, 16 Jun 180 100 30 Jun, 29 Jun, …, 23 Mar, 22 Mar 30 15 Aug, 14 Aug, …, 17 Jul, 16 Jul 210 70 30 Jun, 29 Jun, …, 22 Apr, 21 Apr 1 15 Aug 240 40 30 Jun, 29 Jun, …, 22 May, 21 May 280 1 30 Jun a For winter wheat locations (Ohio, Kansas, Indiana), the time windows began 30 June (around physiological maturity) and proceeded

48 backward

to 24 September of the previous year (about the time of planting). b For Spring wheat (North Dakota), the time windows began 15 August (around physiological maturity) and proceeded backward to 18 January.

Table 2.2. Description of environmental variables, with units in brackets, used in window-pane analysis of Fusarium head blight

Weather Description variables AT Average mean daily temperature [°C] Number of days with average mean daily temperature between T1530 15°C and 30°C DD15 Total degree days (base 15) over window length [°C] DD9 Total degree days (base 9) over window length [°C] NDD15 Total negative degree-days (base 15) over window length [°C] NDD9 Total negative degree-days (base 9) over window length [°C] AD Average mean daily dew point [°C] ARH Average mean daily relative humidity [%] MRH Average maximum daily relative humidity [%] NDPD Average mean negative dew point depression [°C] TP Total precipitation over window length [mm] IP Number of days with precipitation over window length Number of days with average mean daily temperature between T1530P 15°C and 30°C and precipitation over window length HRH90 Number of hours with relative humidity > 90% Number of hours with temperature between 15°C and 30°C and THRH90 relative humidity > 90% HRH80 Number of hours with relative humidity > 80% Number of hours with temperature between 15°C and 30°C and THRH80 relative humidity > 80%

Table 2.3. Adjusted significance levels based on Simes‘ methoda, and maximum Spearman rank correlation coefficient between Fusarium head blight intensity rating and environmental variables for listed time window lengths based on 44 years of data from Ohio Variableb 10 15 30 60 90 120 150 180 210 240 280

Adjusted global P value (Pg) AT 0.713 0.681 0.496 0.456 0.296 0.201 0.242 0.311 0.292 0.24 0.473 ARH 0.006 0.006 0.005 0.010 0.005 0.005 0.004 0.004 0.004 0.008 0.012 MRH 0.033 0.027 0.022 0.015 0.010 0.009 0.009 0.009 0.013 0.012 0.018 NDPD 0.019 0.011 0.033 0.03 0.071 0.062 0.048 0.047 0.064 0.058 0.062 TP 0.257 0.037 0.005 0.095 0.172 0.115 0.041 0.135 0.223 0.110 0.148 IP 0.064 0.004 <0.001 <0.001 <0.001 <0.001 0.002 0.012 0.040 0.059 0.056 HRH90 0.095 0.125 0.074 0.089 0.100 0.084 0.123 0.124 0.117 0.094 0.162 THRH90 0.161 0.135 0.184 0.141 0.091 0.080 0.067 0.056 0.053 0.036 0.054 HRH80 <0.001 <0.001 0.002 0.018 0.048 0.026 0.037 0.046 0.067 0.067 0.080 THRH80 0.015 0.001 <0.001 0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 0.004 c Maximum Spearman correlation coefficient AT 0.326 0.277 0.305 0.315 0.293 0.273 0.274 0.261 0.161 0.153 0.111 ARH 0.554 0.559 0.532 0.521 0.491 0.496 0.481 0.468 0.456 0.424 0.374 50

MRH 0.484 0.459 0.442 0.462 0.436 0.432 0.419 0.408 0.395 0.367 0.355 NDPD 0.527 0.558 0.519 0.471 0.435 0.414 0.395 0.373 0.378 0.322 0.284 TP 0.435 0.522 0.577 0.419 0.381 0.381 0.443 0.344 0.315 0.309 0.222 IP 0.470 0.573 0.609 0.677 0.638 0.587 0.541 0.463 0.405 0.338 0.290 HRH90 0.413 0.427 0.416 0.416 0.373 0.349 0.353 0.296 0.264 0.251 0.215 THRH90 0.450 0.431 0.396 0.399 0.391 0.392 0.392 0.388 0.382 0.374 0.292 HRH80 0.618 0.666 0.567 0.458 0.406 0.448 0.418 0.375 0.364 0.315 0.267 THRH80 0.549 0.596 0.658 0.606 0.609 0.627 0.627 0.621 0.606 0.555 0.421 a Adjustment for multiple correlated test statistics. Single adjusted global P value (Pg) for the collection of time windows, each with different starting and ending dates, of the listed window lengths. Values of Pg less than 0.05 (αg) are considered significant. b Variables are defined in Table 2. c Italic font indicates individually significant correlations at P < 0.005. Bold indicates there is at least one cluster of five contiguous correlation coefficients with individual P values of < 0.005.

Table 2.4. Adjusted significance levels based on Simes‘ methoda, and maximum Spearman rank correlation coefficient between Fusarium head blight intensity rating and environmental variables for 10, 15, 30, 60, and 120 day window lengths based on data from Indiana, Kansas, and North Dakota Indiana Kansas North Dakota Variableb 10 15 30 60 120 10 15 30 60 120 10 15 30 60 120 Adjusted global P value (Pg) AT 0.431 0.350 0.678 0.605 0.440 0.992 0.997 0.998 0.978 0.991 1.000 0.991 0.983 0.966 0.987 ARH 0.055 0.110 0.069 0.016 0.379 0.091 0.042 0.093 0.100 0.169 0.054 0.079 0.109 0.144 0.098 MRH 0.084 0.109 0.139 0.020 0.392 0.787 0.674 0.746 0.650 0.735 0.078 0.104 0.083 0.040 0.043 NDPD 0.007 0.025 0.024 0.004 0.093 0.131 0.076 0.144 0.094 0.237 0.077 0.086 0.088 0.115 0.074 TP 0.011 0.012 0.011 <0.001 0.110 0.016 0.013 0.004 0.041 0.007 0.247 0.191 0.067 0.082 0.127 IP 0.363 0.203 0.109 0.055 0.135 0.001 <0.001 <0.001 0.001 0.007 0.260 0.323 0.204 0.156 0.417 HRH90 0.095 0.185 0.202 0.199 0.312 0.088 0.098 0.074 0.037 0.058 0.441 0.422 0.258 0.125 0.083 THRH90 0.075 0.076 0.171 0.184 0.221 0.270 0.140 0.105 0.148 0.123 0.284 0.202 0.038 0.004 0.006 HRH80 0.011 0.022 0.108 0.018 0.206 0.020 0.006 0.012 0.001 0.017 0.093 0.036 0.124 0.138 0.034 THRH80 0.002 0.005 0.102 0.092 0.338 0.013 0.002 0.005 0.002 0.024 0.074 0.032 0.010 0.004 0.004 Maximum Spearman correlation coefficientc

51 AT 0.456 0.454 0.336 0.229 0.231 0.359 0.312 0.262 0.256 0.073 0.215 0.223 0.134 -0.020 -0.262

ARH 0.532 0.489 0.482 0.534 0.379 0.562 0.604 0.525 0.489 0.465 0.618 0.619 0.517 0.542 0.503 MRH 0.506 0.466 0.449 0.531 0.321 0.397 0.365 0.364 0.275 0.241 0.640 0.608 0.601 0.600 0.489 NDPD 0.609 0.562 0.530 0.573 0.421 0.538 0.573 0.506 0.472 0.450 0.577 0.572 0.506 0.521 0.513 TP 0.592 0.572 0.577 0.681 0.440 0.663 0.648 0.697 0.594 0.661 0.571 0.522 0.610 0.567 0.465 IP 0.433 0.460 0.468 0.489 0.412 0.729 0.787 0.762 0.687 0.597 0.598 0.569 0.535 0.562 0.367 HRH90 0.495 0.468 0.381 0.429 0.356 0.564 0.567 0.488 0.535 0.507 0.495 0.558 0.490 0.521 0.490 THRH90 0.513 0.497 0.458 0.426 0.368 0.543 0.562 0.557 0.490 0.481 0.514 0.574 0.617 0.703 0.652 HRH80 0.607 0.567 0.454 0.528 0.378 0.630 0.659 0.633 0.723 0.622 0.606 0.621 0.538 0.493 0.566 THRH80 0.636 0.594 0.470 0.448 0.371 0.661 0.718 0.670 0.694 0.577 0.622 0.663 0.675 0.704 0.653 a Adjustment for multiple correlated test statistics. Single adjusted global P value (Pg) for the collection of time windows, each with different starting and ending dates, of the listed window lengths. Values of Pg less than 0.05 (αg) are considered significant. b Variables are defined in Table 2. c * Indicates individually significant correlations at P < 0.005. Bold indicates there is at least one cluster of five contiguous correlation coefficients with individual P values of < 0.005.

9 9 Ohio North Dakota 8 8 7 7 6 6 5 5 4 4 3 3 2 2

FHB (0-9 rating scale) rating (0-9 FHB 1 1 0 0 1965 1970 1975 1980 1985 1990 1995 2000 2005 1990 1995 2000 2005

35 2.5 Indiana Kansas 30 2.0 25

20 1.5

15 1.0 10 0.5 5

FHB Index (field severity) (field Index FHB 0 0.0 1975 1980 1985 1990 1995 2000 2005 1980 1985 1990 1995 2000 2005

Year Year

0.6 0.6 10-day windows 15-day windows 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -0.1 -0.1 0.6 0.6 30-day windows 60-day windows 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0.6 0.6 90-day windows 120-day windows 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0.6 0.6 Spearman correlation coefficient correlation Spearman 150-day windows 180-day windows 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0.6 0.6 210-day windows 240-day windows 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -280 -240 -200 -160 -120 -80 -40 0 -280 -240 -200 -160 -120 -80 -40 0

Time in days (crop maturity = 0) Figure 2.2

0.6 0.6 A Ohio TP: 15-day windows 0.5 0.5 Ohio TP: 30-day windows 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 0.6 0.6 Ohio TP: 60-day windows Ohio TP: 120-day windows 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -0.1 -0.1 -0.2 -0.2 0.5 0.5 B Ohio AT: 15-day windows Ohio AT: 30-day windows 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 0.5 0.5 Ohio AT: 60-day windows Ohio AT: 120-day windows 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -0.1 -0.1 -0.2 -0.2 C 0.7 0.7 0.6 Ohio THRH80: 15-day windows 0.6 Ohio THRH80: 30-day windows 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 0.7 0.7 Ohio THRH80: 60-day windows 0.6 0.6 Ohio THRH80: 120-day windows 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 -0.1 -0.1 -0.2 -0.2 -280 -240 -200 -160 -120 -80 -40 0 -280 -240 -200 -160 -120 -80 -40 0

Time in days (crop maturity = 0)

Figure 2.3

Ohio: 15-day windows Ohio: 30-day windows ARH ARH MRH MRH NDPD NDPD TP TP IP IP HRH90 HRH90 HRH80 HRH80 THRH80 THRH80

Indiana: 15-day windows Indiana: 30-day windows ARH ARH MRH MRH NDPD NDPD TP TP IP IP HRH90 HRH90 HRH80 HRH80 THRH80 THRH80

Kansas: 15-day windows Kansas: 30-day windows ARH ARH

Weather variable Weather MRH MRH NDPD NDPD TP TP IP IP HRH90 HRH90 HRH80 HRH80 THRH80 THRH80

North Dakota: 15-day windows North Dakota: 30-day windows ARH ARH MRH MRH NDPD NDPD TP TP IP IP HRH90 HRH90 HRH80 HRH80 THRH80 THRH80

-280 -240 -200 -160 -120 -80 -40 0 -280 -240 -200 -160 -120 -80 -40 0

Time in days (crop maturity = 0)

Figure 2.4

15-day windows 30-day windows A: ARH B: ARH 0.6 Indiana 0.6 Indiana 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 0.6 Kansas 0.6 Kansas 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 North Dakota North Dakota 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 C: TP D: TP 0.6 Indiana 0.6 Indiana 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 0.6 Kansas 0.6 Kansas 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 0.6 North Dakota 0.6 North Dakota 0.4 0.4 0.2 0.2 0.0 0.0 Spearman Correlation Coefficient Correlation Spearman -0.2 -0.2 -0.4 -0.4

E: THRH80 F: THRH80 0.6 Indiana 0.6 Indiana 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 0.6 Kansas 0.6 Kansas 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 0.6 North Dakota 0.6 North Dakota 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 -280 -240 -200 -160 -120 -80 -40 0 -280 -240 -200 -160 -120 -80 -40 0 Time in days (crop maturity = 0) Figure 2.5

1.0 A 0.8

0.6

0.4

0.2

Spearman correlation coefficient correlation Spearman 0.0

-0.2 -250 -200 -150 -100 -50 0 Number of days prior to 30 June

1.0 B 0.8

0.6

0.4

0.2

0.0

Spearman correlation coefficient correlation Spearman -0.2

-0.4 -200 -160 -120 -80 -40 0

Number of days prior to 15 August

Figure 2.6

Summary

Window-pane methodology was utilized to determine the length and starting time of temporal windows where environmental variables were associated with annual fluctuations of Fusarium head blight (FHB) intensity in wheat. Initial analysis involved FHB intensity observations for Ohio (44 years), with additional analyses for

Indiana (36 years), Kansas (28 years), and North Dakota (23 years). Selected window lengths of 10 to 280 days were evaluated, with starting times from approximate crop maturity back to the approximate time of planting. Associations were quantified with

Spearman rank correlation coefficients. Significance for a given variable (for any window starting time in a collection of starting times) was declared using the Simes‘ multiplicity adjustment; at individual time windows, significant correlations were declared when the individual (unadjusted) P values were less than 0.005. In all states, moisture and/or wetness-related variables (e.g., daily average relative humidity [RH] and total daily precipitation) were found to be positively correlated with FHB intensity for multiple window lengths and starting times, but the highest correlations were primarily for shorter-length windows (especially 15 and 30 days) at similar starting times during the final 60 days of the growing season, particularly near the time of anthesis. This period encompasses spore production, dispersal, and fungal colonization of wheat spikes. There was no evidence of significant correlations between FHB and temperature-only variables for any time window; however, variables that combined aspects of moisture/wetness with temperature (e.g., duration

of temperature between 15 and 30°C and RH>80%) were positively correlated with

FHB intensity. Results confirm that the intensity of FHB in a region depends, at least in part, on environmental conditions during relatively short critical time periods for epidemic development.

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Chapter 3

Quantification of the Relationship Between the Environment and Fusarium Head

Blight, Fusarium Pathogen Density, and Mycotoxins in Winter Wheat in Europe

Introduction

Fusarium head blight (FHB) of wheat (Triticum aestivum L.) is a disease of foremost importance in many parts of the world, including North America, Asia, and

Europe. FHB can be caused by many different pathogens worldwide but the most important are Fusarium graminearum, F. culmorum, F. avenaceum and F. poae, which can produce a range of mycotoxins (4), and Microdochium nivale and M. majus (13), which do not produce any known mycotoxins. In the US, F. graminearum is the predominant pathogen causing FHB on wheat, but in Europe, a complex of pathogens can cause the disease (11). In a recent study by Xu et al. (43) of the prevalence of FHB- causing pathogens in four countries over 2 years, F. poae was found to have the highest overall frequency, followed by F. graminearum. However in recent years, prevalence of

F. graminearum appears to be increasing in Europe, especially in the cooler regions

(37,43).

The economic importance of FHB is due to reduction in yield and contamination of grain with mycotoxins (21). Yield reduction results from the production of small,

71 shriveled, light-weight kernels with corresponding reduction in test weight of the harvested grain (1,2). Moreover, F. graminearum, F. culmorum, and F. poae produce mycotoxins, especially deoxynivalenol (DON) and nivalenol (NIV), which may contaminate the harvested grain (14). In a study by Xu et al. (42) where several FHB- causing pathogens and their associated mycotoxins were identified, DON was most strongly associated with the presence of F. graminearum, and NIV was most significantly associated with the presence of F. culmorum. However, isolates of both F. graminearum and F. culmorum can produce DON or NIV, while F. poae can produce only NIV

(16,38,40).

Kriss et al. (17) explored the annual variability in FHB intensity and its impact on yield in four US states over periods of 23 to 44 years as a function of variability in environmental conditions. Using a „window-pane‟ analysis (6), they found moisture- or wetness-related variables (determined from weather-station measurements) to be positively correlated with FHB intensity at multiple time periods over the growing season, but especially during the last 2 months of the season. Significant correlations were found for a range of time-duration intervals (windows), and the highest correlations were generally evident for the shorter time intervals. Xu et al. (41) investigated the relationship between environmental conditions and the presence/abundance of the complex of FHB-causing species in several European countries over 4 years. They considered environmental summary variables for a very limited number of time windows, from the start of anthesis to 7 days after the end of anthesis and from the start of anthesis to harvest. They also found that the presence/abundance on wheat heads and/or grain of pathogens that cause FHB were related to moisture variables. Results from the European

72 and US analyses are consistent with other published results on environmental effects on this disease and the components of the life cycles of the pathogens, such as moisture effects on spore production and infection and colonization of wheat spikes (3,7,12,24,34).

Quantification of the inter-relationships among environment and FHB intensity, pathogen abundance (as measured by fungal biomass), and mycotoxin contamination can shed light on the epidemiology of this disease and could lead to improved forecasting systems (9) for disease intensity or for mycotoxin levels in harvested grain. For instance, there is considerable interest currently in elucidating the effects of post-flowering environment (especially moisture) on fungal colonization and production of DON and other mycotoxins (7,8), although there is no consensus on the direction or magnitude of the effects. The dataset described in Xu et al. (41) provides an opportunity to quantify some of the relationships for European winter-wheat cropping systems. We expanded on the earlier work of Xu et al. (41) in several ways. First, we explored a wider range of window start times and durations of time windows. Second, we considered a larger set of environmental-summary variables that could, in some cases, potentially capture nonlinear relationships or more complex temperature/wetness effects on the biological responses.

Third, we considered environmental effects on disease intensity, fungal biomass, and mycotoxin concentrations, focusing on DON and NIV and the biomass of the predominant fungal species known to produce these mycotoxins.

We utilized window-pane methodology, a form of data mining, for the current study to quantify the strength of the empirical associations within the European dataset.

Since the original development by Coakley et al. (6), this protocol has been generalized and used in several investigations (5,26,33). In a recent study with FHB data in the US

(17), the window-pane methodology was expanded by formally addressing the multiple- testing problem that is common with data-mining techniques. In the current investigation, besides focusing on biological and environmental data from a different continent, we extend this approach to consider multiple biological variables (disease intensity, fungal biomass, and mycotoxins), and within-field environmental measurements. The specific objectives of this research were to: (i) determine environmental variables most correlated with disease, fungal biomass, and DON and NIV in wheat grain; (ii) determine time- window lengths and start/end times – relative to the onset of anthesis – during the last 2 months of the season when disease and mycotoxins were most highly correlated with environmental variables; and (iii) adjust correlations involving mycotoxins and environment for confounding effects of disease and fungal biomass on the mycotoxins.

Because DON and NIV were of ultimate interest, we generally restricted analyses to the predominant FHB fungal species that produce these mycotoxins.

Materials and Methods

Field data. Numerous winter wheat fields in four countries across Europe

(Hungary, Ireland, Italy, and the United Kingdom) were assessed for FHB, fungal biomass, and mycotoxin accumulation from 2001 to 2004 (41). These sites represent a wide range of climatic conditions in important winter wheat production areas in Europe where FHB can cause serious damage. In addition to climatic conditions, these sites also differed in other agronomic characteristics, such as cultivar, tillage, cropping history, and soil type. All cultivars used were susceptible to FHB. The data from Italy was not 74 included in this investigation because in-field environmental data was not collected for most of the sites. Any other specific location-years with missing environmental data due to malfunctioning loggers were also not included. A total of 150 location-years were used here (47 in 2001, 46 in 2002, 29 in 2003, and 28 in 2004). Details on the field sampling protocols are described in Xu et al. (41). Sampling was conducted at growth stage (GS)77

(milky ripe) and GS92 (harvest) (44). Intensity of FHB (percent of spikelets with FHB symptoms) was determined at GS77 at all location-years, except for fields in Hungary in

2001 and two fields in the UK in 2003. There were no missing samples at harvest from the selected 150 location-years.

Fungal DNA and mycotoxin quantification. Xu et al. (41) quantified-fungal biomass for six FHB-causing species (Fusarium graminearum, F. culmorum, F. avenaceum, F. poae, Microdochium nivale, and M. majus) at GS77 and GS92 using quantitative PCR (qPCR) as described by Simpson et al. (31). Here biomass results for F. graminearum, F. culmorum, and F. poae were used since they produce the mycotoxins deoxynivalenol (DON) and/or nivalenol (NIV). DON (ppb) and NIV (ppb) were also quantified at harvest as discussed in detail by Xu et al. (41).

Environmental variables. Temperature (°C), rainfall (mm), relative humidity

(%) and surface wetness were recorded electronically at intervals of 2 h or less using electronic data loggers at each location (41). All locations had environmental data available around anthesis, but the total time span of data available at each location differed. In Hungary, environmental data ranged from 37 days pre-anthesis to 55 days post-anthesis. The UK locations had environmental data available from 18 days pre- anthesis to 94 days post-anthesis, and Ireland had the longest time range available, from

86 days pre-anthesis to 149 days post-anthesis. However, these are the extremes for each county, and the majority of fields did not have associated environmental data for such long time spans. The average number of days with available environmental data in

Hungary, the UK, and Ireland was 55, 70, and 127 days, respectively. Due to differences in overall temperatures, anthesis lasts approximately one week in Hungary and approximately two weeks in Ireland and the UK (41).

Window-pane analysis. As described by Kriss et al. (17) and Pietravalle et al.

(26), the concept underlying window-pane analysis is the specification of a time window of defined length (or duration), and the construction of summary environmental variables

(e.g., means) for the specified window. This time window (e.g., 30 days) is progressed

(or slid) along the total time frame of interest (e.g., a year or a growing season), in daily steps, so that environmental data from the entire time frame is ultimately considered in the data analysis. Two successive time windows (of the same length) share all but one day of data. With a defined starting time and window length, the ending time of the window is automatically determined. Time windows of environmental data were constructed separately for each year and location. The date when anthesis (GS60) began was recorded for each location-year; this growth stage was used to align all of the location-years and, for convenience, was set as day “0”. Positive numbers indicate days after anthesis and negative numbers indicate days prior to anthesis. The presented day is the edge of the window that is closest to the beginning of the season. For example, a listed time window of -10 days for a time window of 30 days in length covers the period from 10 days before anthesis to 19 days after anthesis (day 19). This is opposite of what

76 was done in Kriss et al. (17) where we referred to the edge of the window closest to harvest as the “starting” time of the window.

Summary environmental variables were calculated for windows of lengths 5 to 30 days (increments of 5 days), but because of high similarity of results for windows of similar lengths, we limit results shown to 5, 15, and 30 days. Table 3.1 lists all the summary environmental variables considered within the present study. Summary variables were not calculated if there was any missing data within the window. The construction of summary variables for the different window lengths and starting times was completed with a macro written for SAS (SAS, Inc., Cary, NC). The summary variables were averages of daily values (e.g. average daily temperature [AT]) or summations of hours where certain conditions were met (e.g., number of hours with measureable precipitation [IP]). Construction of most of the summary variables was based, in part, on the variables used in other studies (19,24). However, LTRH80 and

LTRH90 (Table 3.1) are unique summary variables; relative to THRH80 and THRH90, they give more weight to hours where the temperature is closer to the optimum for F. graminearum growth and development as compared to hours when temperature is farther from the optimum. For instance, THRH80 can be viewed as a variable where each hour in the summation receives a weight of 0 or 1 (the latter only occurring when temperature is in the prescribed 15-30 C range and RH is greater than 80%). In contrast, the hourly weights for LTRH80 can be 0, 1, or a continuous value between 0 and 1 (depending on the closeness of temperature to 25 C) (Table 3.1). This variable is consistent with work showing that infection or sporulation rate increases with temperature (roughly) between 9 and 25 C (23,28).

The relationship between each summary environmental variable and disease intensity, fungal biomass, and mycotoxin concentration was determined for each of the window lengths and starting times. Analysis was based on the pooled location-year data

(a separate analysis for each biological variable and each window of each environmental variable). The association between variables was quantified with the nonparametric

Spearman rank correlation (r) (32) using the CORR procedure of SAS (SAS, Inc., Cary,

NC). The Spearman correlation measures the strength of the monotonic relation between two variables, and is robust to the presence of outliers and is applicable for any continuous or ordinal scale. In addition, correlations were only considered if at least 35 location-years had non-missing data for a given window (of given length and starting time). Therefore, each correlation was determined from a possible range of between 35 and 150 location-years. Because of the varying number of observations for each window starting time, there is not a single critical value for significance.

Because of differences among location-years in the start and end of environmental monitoring, the smallest number of location-year observations was generally for windows that were the greatest time before or after anthesis. Windows used in the analysis had start days that began 23 days before anthesis. This was the first day where at least 35 location-years had environmental data available. However, the most extreme pre-anthesis time windows were primarily from Ireland, since this is the country where more pre- anthesis data were available. However, by starting day -13, there was close to an equal number of location-years within each country with environmental data available for the analysis. For biological variables recorded at GS77, windows extended forward to 25 days post-anthesis. For biological variables recorded at GS92, windows extended forward

78 to 60 days post-anthesis. Results for windows late in the season were generally from the

UK and Ireland, since there was limited environmental data available from Hungary for this period because grain had already been harvested by then.

Semi-partial correlations. Semi-partial Spearman correlation coefficients were calculated to quantify the monotonic association between the mycotoxins and environment after adjusting for the monotonic effect of other biological variables on the mycotoxins. A semi-partial correlation coefficient quantifies the strength of the relationship between two variables while the influence of one or several other variables is removed from only one of the two variables in the pair that are being correlated (29).

Specifically, semi-partial Spearman rank correlation coefficients were calculated between each environmental variable (Table 3.1), for each window length and starting time, and the concentration of a mycotoxin (DON or NIV) after any association that the mycotoxin had with disease intensity or fungal biomass was removed. As an extreme example, suppose that the quantity of DON was correlated perfectly with disease intensity, but that disease intensity was a function of the environment. Although there would be a nonzero correlation between DON and environment (because disease is related to the environment), the semi-partial correlation between DON and environment (adjusting for disease effects on DON) would be zero. Semi-partial correlations allow one to assess the environmental effects on mycotoxin concentrations due to effects other than those expected towards the biological variables that affect mycotoxin concentrations.

Semi-partial Spearman correlations were calculated with specialized programs written in SAS using the formulas in Sheskin (29) after first adjusting for disease intensity alone, then adjusting for disease intensity and fungal biomass quantified at

GS77, and then adjusting for disease intensity and fungal biomass quantified at GS77 and at GS92. This sequence represents adjustments for increasing numbers of variables that could be influencing mycotoxin accumulation.

Multiple hypothesis testing. With a single test result, a significant correlation is declared if P ≤ α, where α is the prespecified significance level for an individual test and

P is the achieved significance level of the individual test. Because of the large number of test statistics calculated, by definition, in a window-pane analysis, adjustments to the simple hypothesis-testing problem are needed to avoid excessively large type I error rates and false positive proportions (39). Because the test statistics are highly correlated, there is no simple solution to the multiple-testing problem; we dealt with the issue in three separate ways, as described in detail in Kriss et al. (17). First, we performed a global test of significance across all window starting times for a given environmental variable by calculating the adjusted P value (Pg) using the Simes‟ method (30). This is a test for the global null hypothesis (H0(g)) that none of the individual correlations are significant, and the alternative (Ha(g)) that at least one is different from 0. Values of Pg < αg (with αg =

0.05) are considered significant for the global test. Second, the individual estimated correlation coefficients were compared with critical values corresponding to individual prespecified significance levels (α values) of 0.005 (instead of 0.05). Third, the ad-hoc method of Pietravalle et al. (26) was used to reduce the chances of declaring spurious results for a window as being true significant results. A significant relation during a given time period between an environmental variable and FHB intensity was declared only if there were clusters of five successive correlations that were individually significant (each at individual P < 0.005). Unlike in Kriss et al. (17), we performed two-sided tests for the

80 correlations. These procedures were followed for the Spearman correlation coefficients and for the semi-partial Spearman correlation coefficients.

Results

Overall significance and magnitude of correlations. Multiple environmental variables were significantly correlated with disease intensity, fungal biomass, and mycotoxin levels. Tables 3.2 to 3.5 provide the adjusted global P value (Pg) and the highest individual Spearman correlation coefficient across all window starting times for each environmental variable and window length. The tables also indicate whether the presented correlation was significant at an individual P ≤ 0.005, and if there was at least one cluster of five successive correlation coefficients that were significant. All environmental variables tested were significantly correlated (Pg ≤ 0.05) with at least one of the FHB intensity, fungal biomasses, or mycotoxin variables. In general, when significant, temperature had negative relationships with the biological variables, and moisture or wetness variables had positive relationships.

For disease intensity, significant correlations were found for multiple environmental variables that included a measure of relative humidity (e.g., ARH,

LTRH90, HRH80); for the environmental variables with the strongest associations, the general trend was for decreasing correlation with increasing window length (Table 3.2).

Combining temperature with duration of relative humidity measurements in a simple way

(THRH90, THRH80) did not improve the correlations compared to the duration measurements (HRH90, HRH80), and using the more complex weighted function (e.g.,

LTRH90, LTRH80) resulted in similar correlations to those without temperature (e.g.,

HRH80).

Fusarium graminearum and F. culmorum had significant (global) and negative correlations with mean daily temperature (AT) (Tables 3.2 and 3.3). Interestingly, for F. graminearum, the significant correlations with temperature were found when the fungus was isolated at milky ripe (GS77), but not at harvest (GS92). This is in contrast to F. culmorum, where the significant negative correlations were detected from the samples taken at GS92 and not at GS77.

Fusarium graminearum was the only fungal species investigated that had a significant relationship with mean daily relative humidity (ARH) (Tables 3.2 and 3.3).

Other moisture and wetness-related variables had varying relationships with the different

Fusarium pathogens. There were some significant, although not consistent, correlations between F. graminearum or F. culmorum and HRH90 and HRH80. When temperature was coupled with relative humidity variables to create composite variables (e.g.,

THRH90, LTRH80), significant correlations were found at multiple window lengths for

F. graminearum (GS92) (Table 3.3). Fusarium poae did not have the same strong relationships with temperature and relative humidity as the other Fusarium pathogens, but it was also significantly correlated with mean daily surface wetness (AW) (Table 3.3) and both mean daily precipitation (AP) and number of hours of precipitation (IP) (Tables

3.2 and 3.3). The relationship between F. poae and precipitation was unique among the three species in that significant negative correlations were identified.

Deoxynivalenol (DON) (Table 3.4) and nivalenol (NIV) (Table 3.5) had significant negative correlations with AT and significant positive correlations with ARH

82 and other moisture and wetness-related variables (e.g., HRH80, AW). For DON, when temperature was coupled with relative humidity (e.g., LTRH80, LTRH90), there were significant correlations for multiple window lengths, but the magnitude of these correlations was generally lower than for relative humidity alone.

Temporal patterns to correlations with environment – disease and fungal biomass. Although individual Spearman correlation coefficients were determined for each window length and starting time for each environmental variable, only a subset of the individual correlations are displayed in order to save space. Specific examples of disease intensity and fungal biomasses of the three Fusarium species are shown in

Figures 3.1 and 3.2 for 15-day window lengths. The example graphs were selected to demonstrate some of the most highly significant correlations or interesting time patterns to the correlations. The horizontal axis represents the starting time of each window of a given length and each vertical bar represents the (estimated) Spearman correlation coefficient for the association between the biological variable and environmental variable.

The highest individual Spearman correlation between disease intensity and ARH was 0.583 at day -16 (P < 0.0001) of window length 15. This indicates that the average daily relative humidity from day -16 to day -2 (i.e., from 2 to 16 days prior to the beginning of anthesis) was significantly positively associated with disease intensity. With all of the humidity-related variables, there were two main clusters of windows with significant correlations (Fig. 3.1). One was near anthesis (with starting times around days

-20 to -10) and the other was after anthesis began (with starting times around days 0 to

10). The relative-humidity based variables that did not include temperature (e.g., ARH,

HRH80, and HRH90) had the strongest correlations around anthesis, and the variables that coupled temperature with relative humidity (e.g., LTRH80) had the strongest correlations post-anthesis.

Fusarium graminearum biomass at GS77 was significantly associated with several different environmental variables for a range of window starting times (Fig. 3.1).

For F. graminearum (GS77) and AT, all individual correlations were negative and significant (P ≤ 0.005) for the 15-day windows (Fig. 3.1). This significance was also found for all the 30-day windows; correlations for several windows, but not all, were also significant for the 5-day windows (data not shown). Significant positive relationships were found for moisture or wetness-related variables (e.g., ARH, HRH80, AP) at window start days around 15 days before anthesis through slightly after anthesis. In most cases, the correlations for windows prior to anthesis were not significant for the moisture- related variables.

For F. graminearum quantified at harvest (GS92), there were clusters of significant correlations with humidity-related variables (e.g., ARH, HRH90) approximately 5 to 25 days post-anthesis (Fig. 3.2). These higher correlations were later than the corresponding one for F. graminearum quantified at GS77. Combining temperature with humidity measurements (e.g., LTRH90) yielded significant positive correlations for windows that started around day 35.

Fusarium poae biomass was significantly correlated with surface wetness and rainfall variables, and the correlation pattern was generally consistent between GS77 and

GS92 (Figs. 3.1 and 3.2). Clusters of negative correlations around anthesis to 10 days post-anthesis were found for the relationships between F. poae and precipitation (AP)

(Figs. 3.1 and 3.2). In contrast, F. poae biomass at GS92 had positive relationships with surface wetness (AW) towards the end of the growing season (around days 20 to 35).

Significant negative correlations between F. culmorum biomass at GS92 and temperature were identified before anthesis (Fig. 3.2), and positive correlations with

HRH90 and HRH80 were evident at the end of the season (approximately day 25). These correlations at the end of the season mostly reflected locations in Ireland and the UK. In general, individual correlations were only assessed when the Simes global test was significant (Table 3.3). The correlations with AW in Figure 3.2B demonstrate the situation where the global test was not significant (P = 0.06) but some individual correlations were significant at the individual P value of 0.005. These small correlations were considered to be false positives.

Temporal patterns to correlations with environment – mycotoxins. DON concentrations and AT were negatively correlated at around 25 days after anthesis (Fig.

3.3). NIV was significantly negatively correlated with AT around the same time period as found for DON, but there was also an expanded period of significant correlations from approximately day -5 to day 25 days post-anthesis (Fig. 3.3). At similar time periods, there were significant positive correlations between ARH and both DON and NIV. Other moisture and wetness-related variables were also significantly associated with DON and

NIV for several window starting times (Fig. 3.3; Tables 3.4 and 3.5). In particular, hours with relative humidity >80% (HRH80) had significant correlations with the two mycotoxins approximately 5 days before anthesis to a month after anthesis for all window lengths tested. For DON, a similar result was found for hours with relative humidity >90% (HRH90), although these individual correlations were lower than those

85 for HRH80 (data not shown). Other wetness or moisture variables were significantly correlated with DON over the same general time span, but for a much smaller number of window starting times than found for ARH and HRH80 (Fig. 3.3). The correlations for time windows substantially before anthesis were not significant for any of the environmental variables.

Semi-partial correlations. Tables 3.4 and 3.5 provide the adjusted global P value

(Pg) and the individual Spearman correlation coefficient with the lowest P value for the relationship between the mycotoxin concentration and each environmental variable and window length after adjusting for one or more other biological variables. The semi-partial correlations usually decreased as adjustments were made for increasing numbers of biological variables that could be affecting the mycotoxins, but the decrease was often minor (e.g., LTRH80 and DON) and the outcome of the global tests of significance often did not change. In a few cases, the semi-partial correlations actually increased slightly

(e.g., AW and NIV) compared with the regular correlations. This likely happened because of missing values in the data set. Some observations (location-years) were not used in determining the adjusted correlations that were used for the regular correlations; these dropped observations could move the statistics slightly up or down.

Significant semi-partial correlations (Pg < 0.05, individual P < 0.005) were found for the relationship between toxins and humidity-related variables (e.g., ARH, HRH80) when adjusted for disease intensity, and then for F. graminearum and F. culmorum (and

F. poae for NIV) at GS77 and then at GS92 (Fig. 3.3; Tables 3.4 and 3.5). The largest correlations covered the period from around the time of anthesis to approximately 25 days after anthesis. Moreover, based on the global test, air temperature was negatively

86 correlated with DON and NIV concentrations (Tables 3.4 and 3.5) for one or more window lengths after adjustments for disease, and disease and fungal biomasses at GS77.

The correlation with AT was either significant or close to significant (Pg = 0.059) when an adjustment was made for all the biological variables (including fungal biomass at

GS92). The highest individual semi-partial correlations with AT were at time windows around 15 to 20 days post-anthesis for DON and around 15 to 25 days post-anthesis for

NIV.

Discussion

A window-pane analysis (6) based on the use of the nonparametric Spearman correlation coefficient was used in the current investigation to identify environmental variables that were associated with disease intensity, fungal biomass of FHB-causing pathogens, and the mycotoxins DON and NIV across three European countries. All disease, pathogen, and mycotoxin variables were significantly associated with at least one evaluated environmental variable. Significant correlations and semi-partial correlations with environmental variables were found for multiple windows that ranged from approximately a month before anthesis through to harvest. This was a generalization of the original work of Xu et al. (41), as they limited their analysis to two windows, one from anthesis to 7 days post-anthesis and the other from anthesis to harvest.

The current work extends a window-pane analysis conducted for four states in the

US (17) to Western Europe, and the work reported here also builds on the past analysis in several ways. New moisture-temperature-duration variables were considered that give 87 differential weight to high-moisture hours based on closeness of temperature to the optimum (e.g., LTRH80). When these variables were correlated with the biological response variables, the correlations were higher than found for the cruder moisture- temperature variables based on (in effect) a 0/1 weighting (e.g., THRH80). The US analysis was based solely on disease intensity, but here we considered environmental effects on disease intensity, fungal biomass, and DON and NIV mycotoxin concentrations. Semi-partial Spearman rank correlation coefficients were used to quantify the association between the mycotoxin concentrations and environment after adjusting for the influence of disease intensity and toxigenic pathogen density on DON and NIV. This allowed a more direct appraisal of environmental effects on mycotoxins, rather than an indirect effect of environment (through the influence of environment on the other variables). The current analysis also exclusively used in-field measurements of environmental data rather than measurements from nearby regional stations that were used in the US analysis. Thus, the environmental measurements should be more representative of the microenvironment in and around the wheat fields. Moreover, because the date of anthesis was known for the European location-years (unlike with the

US data sets), we were able to explicitly connect the windows to the time-distance from this important phenological stage known to be important for FHB infection (18,27).

Several moisture and/or wetness-related variables (e.g., ARH, HRH90, LHRH90) were significantly correlated with the biological response variables in the present analysis, which is consistent with the window-pane analysis for the US analysis (17).

Average daily relative humidity (ARH) and disease intensity in the US and in Europe had significant correlations around or slightly before anthesis. Precipitation and disease

88 intensity had a positive relationship around 3 weeks post-anthesis in the US data, and similar results for this time period were found between several moisture-related variables and disease intensity in the Europe data. Biomass of F. graminearum, and concentration of DON and NIV, was also correlated with moisture variables for various window start times during the 4 weeks after anthesis. Others also have shown the positive influence of moisture and wetness duration on this disease and related biological variables (9,24). De

Wolf et al. (9) found that the number of hours that temperature was between 15 and 30°C and relative humidity was greater than or equal to 90% (THRH90) was related to disease in the US, where F. graminearum is the most prevalent FHB-causing pathogen. THRH90 and LTRH90 also had some of the highest correlations with late-season F. graminearum

(GS92) in the Europe data for different windows. However, this was the only case where the two moisture-temperature-duration variables had similar estimated correlations. In other cases, the new variables exhibited the higher estimated correlations for DON and disease intensity. In addition, when the moisture-temperature-duration variables were significantly correlated with the biological variables, the highest correlations were at the same general times as found for the moisture-duration variables that did not include temperature (HRH80 and HRH90). The correlations for the moisture-duration variables that incorporated temperature also were not of greater magnitude than found for the duration variables that did not include temperature, indicating the dominating effect of moisture in the relationships. For disease intensity, DON, and NIV, correlations with

HRH80 were generally higher in magnitude than correlations with HRH90, but for the biomass of the Fusarium species (when significant), correlations with HRH90 were generally higher in magnitude than correlations with HRH80.

For the data from the US states (17), there was no evidence of a relationship between FHB intensity and any of the temperature variables that did not involve moisture

(e.g., AT) for any time window. However, for the European data, significant negative correlations were found between AT and disease, pathogen [F. graminearum (GS77) and

F. culmorum (GS92)], and mycotoxin (DON and NIV) variables for several window lengths and starting times. However, the temperature effect is complex and uncertain.

The result could be influenced by the common negative relation between ambient temperature and RH in a particular location (over short time spans), although this relation would not necessarily transfer across locations and years. Moreover, based on standard temperature-response relations (20), high ambient temperatures (above the optimum) can result in a negative relationship with a biological response, but daily temperatures in the

European data set were seldom very high (relative to the optimum for the fungi). There could also be confounding effects of other nonmeasured variables on the temperature- biological variable relations, where regional temperature was decreasing as some unknown regional variable favorable for the disease was increasing. Interestingly, when temperature was combined with moisture in an environmental variable (e.g., LTRH80), the correlations were positive, in part due to the strong effect of moisture on the biological variables.

Our results identified several of the environmental variables that have been implicated in other research as having a relationship with disease, mycotoxin, or fungal biomass (15,36,41) but we were able to give more accurate definitions of when these associations were occurring. Interestingly, the environmental variables most associated with disease intensity, fungal biomass of the Fusarium species (not including F. poae),

90 and the mycotoxins were similar, but in general, the length of significant windows and/or the window start times differed somewhat. For disease intensity, windows with the highest correlations were for moisture variables (e.g., ARH, HRH80), were relatively short in duration (e.g., 5-days), and started somewhere around 15 days before the beginning of anthesis.

For F. graminearum, Xu et al. (41) suggested that a longer duration of wetness was required for infection relative to the requirements for fungal colonization within the wheat spike. Some support for this suggestion is found in the current investigation by focusing on F. graminearum at GS77 and GS92. The highest correlations with F. graminearum at GS77 were for wetness variables (AP, AW), corresponding to windows with start times between 20 days to 10 days before anthesis. In contrast, the correlations for these wetness variables with F. graminearum at GS92 were considerably lower; rather, other moisture (but not wetness) variables had the highest correlations, and these were for several windows after anthesis (from about 5 days after anthesis to 40 days after anthesis). Therefore, our results suggest that F. graminearum is favored by moisture throughout the anthesis and post-anthesis time window, but that the importance of surface wetness declines over time after infection, during the later colonization of the spikes (and production of the mycotoxins).

Fusarium culmorum biomass did not have many significant correlations with environmental variables; in general, it was most associated with cooler conditions, and with high relative humidity before anthesis. Although generally not significant, the negative correlations with temperature and positive correlations with moisture/humidity remained during the time between anthesis and maturity. This is similar to the results of

Xu et al. (41) and Turner and Jennings (35). In contrast, F. poae at both GS77 and GS92 was associated with drier conditions for all window lengths and most window start times, and the highest of these negative correlations were around 10 to 20 days post anthesis.

Similarly, Turner and Jennings (35) found that wheat spikes inoculated with F. poae were less infected under high humidity than medium humidity. However, there is variability across studies, as others (40) have suggested there is a positive relationship between F. poae and moisture.

Most statistical models for FHB (or the mycotoxins) use environmental data around anthesis, since this is the time when wheat is most susceptible to infection and is about the latest time that a fungicide can be applied for effective FHB control (9,18).

However, predictions closer to crop maturity can be of benefit for estimating the magnitude of yield loss or contamination by mycotoxins before the crop is harvested or sold at grain elevators. As we found here with the nonparametric correlations, environmental conditions prior to anthesis were of little value in predicting mycotoxin concentration or late-season fungal biomass. Thus, for situations similar to those investigated here, we conclude that risk predictions for mycotoxins will need to be based on post-anthesis environmental conditions or forecasts of the environment for the period after anthesis (and possibly other factors not considered by us). Published studies so far are inconsistent in terms of the effects of moisture variables (including rainfall) late in the growing season on DON production and accumulation in grain (7,8). Here we show that moisture variables post-anthesis were positively correlated with DON and NIV levels in harvested grain. Unlike in the case with moisture, rainfall variables were not significantly associated with mycotoxin levels. The highest correlations for DON and NIV were with

ARH and HRH80, and these corresponded to 2 to 5 days post-anthesis. The 15-day averages of ARH during these periods ranged from 54% to 95% relative humidity, with overall averages around 77%. The averages of HRH80 ranged from 4 to 23 hours, with averages of 12 hours.

Using the same data set, Xu et al. (41) showed that the probability of DON being present was significantly associated with F. graminearum, and the presence of NIV was mainly associated with F. culmorum. Other researchers have also found relationships between mycotoxins and fungal biomass, and especially between DON and disease intensity (10,22,25). This, and the significant correlations found here between environment and disease and fungal biomass, suggests that the significant (regular

Spearman) correlations between the mycotoxins and environmental variables could be due just to the effects of the environment on the biomass of the fungal pathogens (which would then be affecting mycotoxin concentration), rather than to direct effects of environment on the mycotoxins. Through the use of semi-partial Spearman correlations, we showed that there were still significant associations between mycotoxins and several environmental variables (e.g., ARH, HRH80) after adjusting for monotonic effects of confounding biological variables. More complex (nonmonotonic [e.g., certain polynomial]) relations involving the confounding variables would not be removed by the semi-partial adjustment method; however, based on graphs of the data and of the residuals from fitting models to the ranked data, we saw no evidence of nonmonotonic relations (Kriss, unpublished). In general, the decrease in the semi-partial correlation

(relative to the usual unadjusted correlations) was rather small, and the highest correlations continued to be found for windows about 5 days before anthesis to 20 days

93 post-anthesis. No pre-anthesis time windows were found with large semi-partial correlations, demonstrating the difficulty in predicting mycotoxin risk based on conditions before anthesis.

Although several environmental variables were found to be associated with disease, fungal biomass, and mycotoxins, the magnitude of the correlations was not high.

Thus, there remains a substantial amount of unexplained variability. This is not surprising, given the heterogeneity found in other studies or among studies (7,8,24).

There are several factors not directly considered in the present analysis, which also have been shown to affect both FHB and mycotoxin levels. Some of these factors are use of fungicides, tillage method, soil type, cropping history in the field or nearby fields. All cultivars used were susceptible to FHB, but their level of resistance to mycotoxin production and movement within the wheat spike is generally unknown. Moreover, inoculum density, diversity of fungal species, and diversity of strains (biotypes) of each species in the region within the location-years could vary greatly, and independently of the environmental variables during a fairly narrow time span. Differential effects of environment on fungal species and biotypes could ultimately result in differences in disease and mycotoxins. Given the magnitude of the correlations, no single environmental variable for a single window length and start time will be sufficient for prediction purposes. However, the window-pane results show the variables and windows that will likely be most useful in the development of risk models with multiple predictor variables. Future research will focus on the use of logistic modeling, regression tree, and recently developed machine learning methods for developing predictions of disease or mycotoxins based on the environment from the identified time windows.

Table 3.1. Description of environmental variables, with units in parentheses, used in window-pane analysis of Fusarium head blight and associated mycotoxins in Europe Weather Description variables AT Average mean daily temperature (°C) ARH Average mean daily relative humidity (%) AP Average mean daily precipitation (mm) IP Number of hours with measurable precipitation AW Average mean daily surface wetness IW Number of hours with surface wetness > 612a HRH90 Number of hours with relative humidity >90% THRH90 Number of hours with relative humidity >90% and temperature between 15 and 30°C LTRH90 Sum of b for each hour with relative humidity >90% HRH80 Number of hours with relative humidity >80% THRH80 Number of hours with relative humidity >80% and

temperature between 15 and 30°C LTRH80 Sum of for each hour with relative humidity >80% a Surface wetness ranged from 0 to 1023. Threshold of 612 indicated wet or dry. b

where is temperature for each hour

Table 3.2. Global significance levels based on Simes‟ method and the highest Spearman rank correlation coefficients between each of the listed environmental variables and Fusarium head blight (FHB) intensity, biomass of Fusarium graminearum, F. culmorum, and F. poae, for data collected at growth stage 77 (milky ripe)a Significance level for window length (days) FHB intensity F. graminearum (GS77) F. culmorum (GS77) F. poae (GS77) Variableb 5 15 30 5 15 30 5 15 30 5 15 30 Pg AT 0.012 0.090 0.005 0.003 0.001 <0.001 0.032 0.077 0.359 0.161 0.285 0.331 ARH <0.001 <0.001 0.002 0.002 <0.001 <0.001 0.881 0.767 0.604 0.962 0.869 0.548 AP 0.018 0.011 <0.001 0.002 0.004 0.035 0.499 0.049 0.639 0.005 0.002 0.001 IP 0.006 0.049 0.015 0.002 0.001 0.002 0.803 0.695 0.954 <0.001 <0.001 <0.001 AW <0.001 0.046 0.002 0.003 0.004 0.006 0.920 0.919 0.868 0.100 0.153 0.478 IW <0.001 0.196 0.010 <0.001 <0.001 0.002 0.611 0.796 0.873 0.220 0.181 0.147 HRH90 <0.001 <0.001 <0.001 0.001 0.009 0.031 0.945 0.997 0.970 0.306 0.471 0.505

96 THRH90 0.189 0.134 0.139 0.146 0.037 0.002 0.194 0.175 0.231 0.670 0.514 0.025

LTRH90 <0.001 <0.001 <0.001 0.144 0.097 0.953 0.538 0.738 0.872 0.118 0.299 0.999 HRH80 <0.001 <0.001 <0.001 0.013 0.003 0.020 0.746 0.845 0.866 0.941 0.986 0.987 THRH80 <0.001 0.003 0.036 0.208 0.025 <0.001 0.163 0.135 0.530 0.199 0.914 0.190 LTRH80 <0.001 <0.001 <0.001 0.461 0.155 0.940 0.167 0.233 0.674 0.079 0.588 0.693 Spearmanc AT -0.455 -0.364 -0.469 -0.514 -0.493 -0.536 -0.268 -0.238 -0.201 0.391 0.402 0.402 ARH 0.593 0.583 0.482 0.385 0.450 0.438 0.215 0.113 0.161 -0.179 -0.218 -0.291 AP 0.425 0.370 0.529 0.431 0.394 0.345 0.246 0.252 0.176 -0.355 -0.325 -0.370 IP 0.437 0.346 0.433 0.491 0.398 0.449 0.183 0.175 0.093 -0.378 -0.356 -0.469 AW 0.515 0.343 0.460 0.593 0.552 0.534 -0.176 -0.202 -0.184 -0.299 -0.282 -0.217 IW 0.472 0.339 0.358 0.631 0.630 0.591 0.202 0.123 0.138 -0.249 -0.278 -0.298 HRH90 0.555 0.483 0.390 0.380 0.390 0.330 0.204 -0.117 -0.112 0.278 0.201 0.170 THRH90 0.233 0.222 -0.321 -0.260 -0.230 -0.324 0.417 -0.229 -0.246 0.189 0.197 0.448 LTRH90 0.471 0.482 0.407 0.245 0.305 0.143 0.302 0.245 -0.135 -0.280 -0.290 0.143 HRH80 0.585 0.546 0.475 0.325 0.394 0.354 0.315 0.108 0.122 0.176 0.117 -0.139 THRH80 0.370 0.329 -0.332 -0.214 -0.249 -0.372 0.329 0.288 0.237 -0.230 0.166 0.291 LTRH80 0.551 0.571 0.431 -0.229 0.289 -0.107 0.360 0.336 0.262 -0.295 -0.218 -0.238 Continued

Table 3.2: Continued

Table 3.3. Global significance levels based on Simes‟ method and the highest Spearman rank correlation coefficients between each of the listed environmental variables and biomass of Fusarium graminearum, F. culmorum, and F. poae, for data collected at growth stage 92 (harvest)a

Significance level for window length (days) F. graminearum (GS92) F. culmorum (GS92) F. poae (GS92) Variableb 5 15 30 5 15 30 5 15 30 Pg AT 0.598 0.636 0.350 0.021 0.013 0.012 0.041 0.611 0.382 ARH 0.006 0.011 0.009 0.014 0.057 0.066 0.365 0.618 0.643 AP 0.222 0.118 0.064 0.403 0.323 0.199 0.002 <0.001 <0.001 IP 0.210 0.059 0.167 0.054 0.195 0.160 0.003 <0.001 <0.001 AW 0.105 0.574 0.616 0.062 0.060 0.067 0.017 0.001 0.005 IW 0.348 0.527 0.441 0.111 0.104 0.035 0.039 0.013 0.024 HRH90 0.013 0.013 0.003 0.032 0.008 0.007 0.080 0.124 0.411 THRH90 <0.001 0.003 0.013 0.119 0.370 0.506 <0.001 <0.001 0.005 LTRH90 0.002 0.004 <0.001 0.311 0.272 0.081 0.012 0.175 0.158 HRH80 0.055 0.053 0.024 0.008 0.009 0.132 0.416 0.854 0.845 THRH80 0.006 0.011 0.029 0.298 0.954 0.242 <0.001 <0.001 0.070 LTRH80 0.012 0.055 0.007 0.345 0.202 0.109 0.003 0.132 0.056 Spearmanc AT -0.234 -0.273 -0.398 -0.499 -0.505 -0.485 0.464 0.409 0.388 ARH 0.380 0.321 0.355 0.400 0.358 0.386 0.241 -0.249 -0.312 AP 0.351 0.271 0.283 0.311 0.258 0.372 -0.406 -0.397 -0.442 IP 0.400 0.342 0.277 0.369 0.352 0.418 -0.383 -0.352 -0.471 AW 0.334 0.227 0.222 0.419 0.426 0.489 0.347 0.406 0.486 IW 0.292 0.297 0.250 0.458 0.443 0.488 -0.306 -0.383 -0.407 HRH90 0.381 0.311 0.397 0.375 0.421 0.399 0.280 0.265 0.215 THRH90 0.454 0.386 0.357 -0.282 -0.410 -0.475 -0.614 -0.601 -0.475 LTRH90 0.419 0.398 0.441 -0.280 0.262 0.313 -0.464 -0.317 -0.285 HRH80 0.322 0.278 0.298 0.396 0.405 0.342 0.238 0.173 -0.179 THRH80 0.389 0.357 0.335 -0.240 0.189 -0.318 -0.573 -0.584 -0.384 LTRH80 0.359 0.337 0.379 -0.274 0.254 0.262 -0.499 -0.387 -0.292 a Adjustment for multiple correlated test statistics. Single adjusted global P value (Pg) for the collection of time windows, each with different starting and ending dates, of the listed window lengths. Values of Pg < 0.05 (αg) are considered significant. b Variables are defined in Table 1. c Highest spearman correlation coefficient; italic font indicates individually significant correlations at P ≤ 0.005. Bold indicates there is at least one cluster of five contiguous correlation coefficients with individual P values ≤ 0.005.

Table 3.4. Global significance levels based on Simes‟ method and the highest Spearman rank correlation coefficient or semi-partial Spearman rank correlation coefficient between each of the listed environmental variables and DONa

Adjustment for: DON FHB intensity, FHB intensity, FHB intensity Fungal biomass (GS77)d Fungal biomass (GS77,GS92)e Variableb 5 15 30 5 15 30 5 15 30 5 15 30

Pg AT <0.001 0.003 0.043 0.002 0.035 0.261 0.004 0.081 0.794 0.003 0.059 0.205 ARH <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 0.001 0.003 0.002 0.003 0.010 AP 0.648 0.915 0.767 0.977 0.991 0.929 0.974 0.986 0.933 0.805 0.491 0.524 IP 0.176 0.696 0.765 0.560 0.963 0.900 0.788 0.990 0.853 0.612 0.658 0.368 AW 0.030 0.024 0.040 0.052 0.040 0.074 0.045 0.026 0.061 0.044 0.041 0.044 IW 0.047 0.198 0.291 0.146 0.200 0.226 0.966 0.998 0.994 0.160 0.307 0.262 HRH90 0.002 0.004 0.016 0.023 0.034 0.064 0.033 0.066 0.077 0.051 0.133 0.116

99 THRH90 0.149 0.342 0.721 0.394 0.441 0.810 0.274 0.290 0.872 0.287 0.304 0.867

LTRH90 0.018 0.026 0.020 0.093 0.114 0.125 0.056 0.073 0.079 0.065 0.115 0.176 HRH80 <0.001 <0.001 <0.001 0.001 <0.001 <0.001 0.003 0.002 0.002 0.003 0.004 0.002

THRH80 0.335 0.415 0.363 0.359 0.407 0.716 0.273 0.245 0.420 0.195 0.219 0.755 LTRH80 0.030 0.014 0.002 0.163 0.104 0.052 0.095 0.062 0.020 0.095 0.111 0.050 Spearmanc -0.423 -0.392 -0.368 -0.361 -0.302 -0.349 -0.287 -0.354 -0.297 AT -0.242 -0.165 -0.182 (25) (20) (-8) (24) (20) (24) (20) (24) (20) 0.424 0.438 0.411 0.385 0.364 0.389 0.368 0.345 0.349 0.361 0.333 0.318 ARH (9) (9) (3) (27) (9) (-5) (27) (9) (-6) (9) (5) (-6) AP 0.241 0.242 0.166 0.243 0.202 -0.142 0.245 0.219 -0.169 0.210 -0.263 -0.237 0.252 IP 0.202 0.224 0.216 -0.152 -0.154 0.209 -0.175 -0.186 0.204 -0.232 -0.234 (22) 0.314 0.291 0.289 0.280 0.291 0.275 0.285 0.303 0.278 0.285 0.298 0.298 AW (46) (19) (-6) (6) (22) (4) (6) (22) (5) (26) (20) (4)

Continued

Table 3.4: Continued

Adjustment for: DON FHB intensity, FHB intensity, FHB intensity Fungal biomass (GS77)d Fungal biomass (GS77,GS92)e

5 15 30 5 15 30 5 15 30 5 15 30

0.280 0.256 0.280 IW 0.209 0.207 0.254 0.244 0.215 0.151 0.157 0.250 0.239 (8) (29) (29) 0.336 0.308 0.286 0.294 0.274 0.280 0.256 0.273 0.251 HRH90 0.249 0.238 0.223 (7) (-2) (-11) (7) (-2) (7) (-2) (7) (-2) -0.399 THRH90 -0.337 0.261 -0.295 -0.391 0.237 -0.336 -0.382 0.226 -0.351 -0.399 0.245 (-17) 0.287 0.276 0.332 0.263 0.281 0.263 0.301 0.277 LTRH90 0.255 0.293 0.265 0.268 (7) (2) (-12) (7) (9) (3) (-12) (9) 0.380 0.405 0.421 0.367 0.365 0.364 0.349 0.345 0.342 0.344 0.337 0.333

100 HRH80 (9) (2) (-6) (24) (2) (-4) (24) (3) (-4) (24) (3) (-5)

THRH80 -0.250 -0.264 0.243 -0.234 -0.260 0.229 -0.288 -0.298 0.238 -0.306 -0.336 0.221

0.286 0.295 0.379 0.274 0.281 0.321 0.275 0.285 0.327 0.288 0.305 LTRH80 0.261 (9) (5) (-11) (30) (24) (-11) (30) (24) (-11) (30) (-11)

a Adjustment for multiple correlated test statistics. Single adjusted global P value (Pg) for the collection of time windows, each with different starting and ending dates, of the listed window lengths. Values of Pg < 0.05 (αg) are considered significant. b Variables are defined in Table 1. c Highest semi-partial Spearman correlation coefficient; italic font indicates individually significant semi-partial correlation at P ≤ 0.005. Bold indicates there is at least one cluster of five contiguous partial correlation coefficients with individual P values ≤ 0.005. Number in parenthesis is the start day of the window. d Adjustments made for the fungal biomass of Fusarium graminearum and F. culmorum at growth stage (GS) 77 – milky ripe. e Adjustments made for the fungal biomass of F. graminearum and F. culmorum at GS77 and GS92 (harvest).

Table 3.5. Global significance levels based on Simes‟ method and the highest Spearman rank correlation coefficient or semi-partial Spearman rank correlation coefficient between each of the listed environmental variables and NIVa

Adjustment for: NIV FHB intensity, FHB intensity, FHB intensity d e Fungal biomass (GS77) Fungal biomass (GS77,GS92) b Variable 5 15 30 5 15 30 5 15 30 5 15 30 Pg AT <0.001 <0.001 0.004 <0.001 0.002 0.009 <0.001 0.001 0.032 <0.001 0.002 0.033 ARH 0.001 <0.001 <0.001 0.005 0.003 0.005 0.006 0.002 0.004 0.015 0.006 0.010

AP 0.917 0.993 0.887 0.725 0.988 0.955 0.914 0.869 0.870 0.979 0.699 0.531 IP 0.928 0.635 0.959 0.656 0.814 0.903 0.885 0.968 0.555 0.955 0.822 0.344 AW 0.089 0.175 0.085 0.022 0.081 0.034 0.020 0.048 0.042 0.023 0.049 0.023 IW 0.139 0.264 0.227 0.026 0.016 0.006 0.033 0.027 0.004 0.046 0.036 0.005 HRH90 0.070 0.050 0.054 0.101 0.110 0.102 0.084 0.067 0.066 0.118 0.090 0.074

101 THRH90 0.131 0.071 0.220 0.092 0.082 0.293 0.088 0.084 0.524 0.276 0.381 0.693 LTRH90 0.206 0.541 0.327 0.516 0.844 0.979 0.595 0.796 0.782 0.936 0.930 0.994 HRH80 0.011 <0.001 <0.001 0.014 0.003 0.005 0.018 0.004 0.004 0.049 0.011 0.007 THRH80 0.094 0.028 0.123 0.070 0.035 0.230 0.061 0.041 0.403 0.132 0.092 0.557 LTRH80 0.352 0.394 0.058 0.520 0.485 0.444 0.561 0.592 0.303 0.732 0.818 0.781 c Spearman -0.433 -0.380 -0.333 -0.431 -0.370 -0.345 -0.437 -0.367 -0.285 -0.403 -0.355 -0.281 AT (27) (20) (-8) (27) (20) (-8) (27) (21) (3) (28) (23) (-10) 0.330 0.374 0.379 0.338 0.346 0.342 0.339 0.353 0.352 0.321 0.331 0.325 ARH (12) (4) (3) (26) (4) (3) (26) (4) (3) (26) (4) (3) AP -0.296 -0.328 -0.205 -0.276 -0.305 -0.155 -0.256 -0.210 -0.247 -0.248 -0.234 -0.255 IP -0.270 -0.286 -0.302 -0.322 -0.295 -0.154 -0.240 -0.229 -0.198 -0.255 -0.232 -0.229 0.255 0.317 0.280 0.290 0.316 0.303 0.281 0.322 0.299 0.304 AW 0.273 0.263 (24) (22) (22) (4) (22) (22) (2) (22) (22) (4)

Continued

Table 3.5: Continued

Adjustment for: NIV FHB intensity, FHB intensity, FHB intensity Fungal biomass (GS77)d Fungal biomass (GS77,GS92)e

5 15 30 5 15 30 5 15 30 5 15 30

0.254 0.305 0.322 0.344 0.292 0.309 0.356 0.293 0.286 0.350 IW 0.264 0.229 (8) (22) (15) (6) (22) (14) (6) (22) (14) (6) 0.277 0.249 0.253 0.286 0.262 0.264 0.284 0.274 HRH90 0.226 0.253 0.253 0.239 (25) (16) (-11) (25) (22) (25) (22) (22) 0.304 -0.260 THRH90 0.258 0.298 -0.298 0.229 0.292 -0.304 -0.205 0.283 -0.302 -0.201 (41) (18) 0.295 LTRH90 0.234 0.231 0.275 0.196 0.189 0.271 0.199 0.202 0.219 0.155 0.161 (41) 0.309 0.347 0.377 0.320 0.331 0.319 0.314 0.335 0.323 0.291 0.303 0.315

102 HRH80 (12) (2) (-10) (28) (2) (-5) (28) (2) (-5) (26) (2) (-5)

0.288 -0.307 -0.305 -0.274 THRH80 0.321 0.327 0.347 0.289 0.367 0.215 0.353 0.200 (42) (18) (18) (19)

0.308 LTRH80 0.284 0.249 0.309 0.244 0.260 0.291 0.263 0.272 0.287 0.252 0.232 (-11)

a Adjustment for multiple correlated test statistics. Single adjusted global P value (Pg) for the collection of time windows, each with different starting dates, of the listed window lengths. Values of Pg < 0.05 (αg) are considered significant. b Variables are defined in Table 1. c Highest semi-partial Spearman correlation coefficient; italic font indicates individually significant semi-partial correlation at P ≤ 0.005. Bold indicates there is at least one cluster of five contiguous partial correlation coefficients with individual P values ≤ 0.005. Number in parenthesis is the start day of the window. d Adjustments made for the fungal biomass of Fusarium graminearum, F. culmorum, and F. poae at growth stage (GS) 77 – milky ripe. e Adjustments made for the fungal biomass of F. graminearum, F. culmorum, and F. poae at GS77 and GS92 (harvest).

A Disease Intensity (GS77) 0.2 AT 0.6 ARH 0.6 AP 0.0 0.4 0.4 -0.2 0.2 0.2 -0.4 0.0 0.0 -0.6 -0.2 -0.2 0.6 AW 0.6 HRH80 0.6 LTRH80 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -20 -10 0 10 20 -20 -10 0 10 20 -20 -10 0 10 20 B Fusarium graminearum (GS77) 0.2 AT 0.6 ARH 0.6 AP 0.0 0.4 0.4 -0.2 0.2 0.2 -0.4 0.0 0.0 -0.6 -0.2 -0.2 0.6 AW 0.6 HRH80 0.6 LTRH80 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -20 -10 0 10 20 -20 -10 0 10 20 -20 -10 0 10 20

C Fusarium culmorum (GS77)

Spearman Correlation Coefficient 0.4 AT 0.4 ARH 0.4 AP 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -0.4 -0.4 -0.4 -20 -10 0 10 20 -20 -10 0 10 20 -20 -10 0 10 20

D Fusarium poae (GS77) 0.4 AT 0.4 ARH 0.4 AP 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -0.4 -0.4 -0.4 -20 -10 0 10 20 -20 -10 0 10 20 -20 -10 0 10 20

Time in days (anthesis = 0) Figure 3.1. Spearman rank correlation coefficients at 15-day windows for the association between environmental variables (graph titles, Table 1) and A, Disease intensity; B, Fusarium graminearum biomass; C, F. culmorum biomass; and D, F. poae biomass quantified at GS77 (milky ripe) across three European countries. Horizontal axis represents the starting time of the 15-day window, with day 0 representing the beginning of anthesis. Negative numbers represent days before anthesis began and positive numbers represent days after anthesis began. Bold vertical bars represent correlation coefficients for individual significance at α = 0.005.

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A Fusarium graminearum (GS92) 0.2 AT 0.6 ARH 0.6 AP 0.0 0.4 0.4 -0.2 0.2 0.2 -0.4 0.0 0.0 -0.6 -0.2 -0.2 0.6 AW 0.6 HRH90 0.6 LTRH90 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 B Fusarium culmorum (GS92) 0.2 AT 0.6 ARH 0.4 AP 0.0 0.4 0.2 -0.2 0.2 0.0 -0.4 0.0 -0.2 -0.6 -0.2 -0.4 0.6 AW 0.6 HRH90 0.4 LTRH90 0.4 0.4 0.2 0.2 0.2 0.0

Spearman Correlation Coefficient Correlation Spearman 0.0 0.0 -0.2 -0.2 -0.2 -0.4 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 C Fusarium poae (GS92) 0.2 AP 0.6 AT 0.4 ARH 0.0 0.4 0.2 -0.2 0.2 0.0 -0.4 0.0 -0.2 -0.4 -0.6 -0.2 0.4 AW 0.6 HRH90 0.4 LTRH90 0.2 0.4 0.2 0.0 0.2 0.0 -0.2 0.0 -0.2 -0.4 -0.2 -0.4 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60

Time in days (anthesis = 0) Figure 3.2. Spearman rank correlation coefficients at 15-day windows for the association between environmental variables (graph titles, Table 1) and A, Fusarium graminearum biomass; B, F. culmorum biomass; and C, F. poae biomass quantified at GS92 (harvest) across three European countries. Horizontal axis represents the starting time of the 15-day window, with day 0 representing the beginning of anthesis. Negative numbers represent days before anthesis began and positive numbers represent days after anthesis began. Bold vertical bars represent correlation coefficients for individual significance at α = 0.005.

104

105

A DON 0.4 AT 0.6 ARH 0.4 AP 0.2 0.4 0.2 0.0 0.2 0.0 -0.2 0.0 -0.2 -0.4 -0.2 -0.4 0.6 AW 0.6 HRH80 0.6 LTRH80 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 B DON: semi-partial correlations 0.4 AT 0.6 ARH 0.4 AP 0.2 0.4 0.2 0.0 0.2 0.0 -0.2 0.0 -0.2 -0.4 -0.2 -0.4 0.6 AW 0.6 HRH80 0.6 LTRH80 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 C NIV 0.4 AT 0.6 ARH 0.4 AP 0.2 0.4 0.2 0.0 0.2 0.0 -0.2 0.0 -0.2 Spearman Correlation Coefficient Correlation Spearman -0.4 -0.2 -0.4 0.6 AW 0.6 HRH80 0.6 LTRH80 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60

D NIV: semi-partial correlations 0.4 AT 0.6 ARH 0.4 AP 0.2 0.4 0.2 0.0 0.2 0.0 -0.2 0.0 -0.2 -0.4 -0.2 -0.4

0.6 AW 0.6 HRH80 0.6 LTRH80 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 -0.2 -0.2 -0.2 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 -20-10 0 10 20 30 40 50 60 Time in days (anthesis = 0)

Figure 3.3

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Summary

Measurements of local environmental conditions, intensity of Fusarium head blight (FHB) in wheat spikes, biomass of Fusarium graminearum, F. culmorum, and F. poae (pathogens causing FHB) and concentration of the mycotoxins deoxynivalenol

(DON) and nivalenol (NIV) in harvested wheat grain were obtained in a total of 150 location-years, originating in three European countries (Hungary, Ireland, United

Kingdom) from 2001 to 2004. Through window-pane methodology, the length and starting time of temporal windows where the environmental variables were significantly associated with the biological variables were identified. Window lengths of 5 to 30 days were evaluated, with starting times from 18 days before anthesis to harvest. Associations were quantified with nonparametric Spearman correlation coefficients. All biological variables were significantly associated with at least one evaluated environmental variable

(P < 0.05). Moisture-related variables (e.g., average relative humidity, hours of relative humidity above 80%) had the highest positive correlations with the biological variables, but there also was a significant negative correlation between average temperature and several biological variables. When significant correlations were found, they were generally for all window lengths, but for a limited number of window start times

(generally before anthesis for disease index and after anthesis for the toxins and late- season fungal biomasses). Semi-partial Spearman correlation coefficients were used to evaluate the relationship between the environmental variables and the concentration of

DON and NIV after the effects of FHB intensity and fungal biomass on the mycotoxins were removed. Significant semi-partial correlations were found between relative

107

humidity variables and DON, and between temperature and relative humidity variables and NIV for time windows that started after anthesis (and not for any earlier time windows). Results confirm that the environment influences disease, fungal biomass, and mycotoxin production, and help refine the time windows where the association is greatest. However, variability in the relationships was high, indicating that no single environmental variable is sufficient for prediction of disease or mycotoxin contamination.

108

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Chapter 4

Variability in Fusarium Head Blight Epidemics in Relation to Global Climatic

Fluctuations as Represented by the El Niño-Southern Oscillation and Other

Atmospheric Patterns

Introduction

The intensity of Fusarium head blight (FHB) of wheat (Triticum aestivum L.), a disease caused predominantly by the Fusarium graminearum species complex (35), is greatly influenced by meteorological factors (9,39), giving rise to high variability in disease from year-to-year and from location-to-location (29). In Chapter 2, it was found that annual variability in FHB over decades in four states in the US was related to environmental conditions at both shorter and longer time scales. In particular, FHB intensity ratings were shown to be significantly correlated with summary environmental variables, especially those based on atmospheric moisture and precipitation, for shorter (<

30 day) and longer (> 30 day) length time windows. The time windows giving rise to the highest correlations were typically during the last 2 months of the growing season, but earlier time windows (during the winter and early spring months) also gave rise to high correlations in some cases.

114 In Chapter 2, it was hypothesized that the relationship between FHB and the environment for the longer time scales (i.e., time windows of 30 days or longer) could be studied using climatic patterns. Climatic conditions can be serving a dual role in this context, both directly affecting components of the FHB disease cycle, or by influencing

(short-term) weather conditions (e.g., atmospheric moisture over a few days at critical times during the year) which can, in turn, be affecting components of the FHB disease cycle.

Variation in the climate of a geographical region can be the result of several different environmental phenomena, including teleconnections (51). Teleconnections refer to simultaneous variations in climate patterns in different regions of the globe (i.e. one region may be cooler and drier than average, while another is warmer and wetter).

The El Niño-Southern Oscillation (ENSO) is one such teleconnection, and is one of the most important factors driving interannual global climate variability (42). The ENSO refers to the variation in sea-surface temperatures (SST) across the Pacific Ocean. On average, there is an ENSO warm event (El Niño) about every 4 years. However, this is highly variable, as sometimes there are only 2 years between events and sometimes there are several years (51). One of the principal measures used to monitor the ENSO is the

Oceanic Niño Index (ONI) (28). The ONI is the 3-month mean SST anomaly for the El

Niño 3.4 region (i.e., 5oN-5oS, 120o-170oW) (50). There are two phases of the ONI, a positive phase and a negative phase. Large positive values (> 0.5) of the ONI coincide with El Niño episodes, while large negative values (< -0.5) coincide with La Niña episodes. El Niño events are known to be associated with increased precipitation in the central (5) and southeastern US and in the southern Rocky Mountain region (42), and La

115

Niña events have been found to be associated with warmer and drier conditions in the US cornbelt than neutral years (40). Although the ENSO is centered in the equatorial Pacific

Ocean, there is an ―atmospheric bridge‖ that spans from the equatorial Pacific to the other oceans by way of alterations of the atmospheric teleconnections in regions remote from the ENSO. Therefore, ENSO-related SST anomalies in remote locations tend to peak after a peak in the ENSO, which can ultimately affect the air temperature, humidity, and wind around the world (1).

Whereas the ENSO affects climate variability—and ultimately weather— worldwide (42), other teleconnection anomalies such as the North Atlantic Oscillation

(NAO) and the Pacific-North American (PNA) pattern have strong influences in the

Northern Hemisphere, especially in the winter months (24,52). The NAO has its greatest influence on North America during the cold-season months (November–April) when the atmosphere is most dynamically active. There are also two phases of the NAO and PNA, a positive phase and a negative phase. Positive values of the NAO during winter-time relate to higher air pressure in eastern North America, which can lead to fewer cold-air outbreaks and decreased storminess. Negative values tend to result in lower air pressure, which can produce more storms and strong cold-air outbreaks (34). The PNA describes the atmospheric circulation patterns over the Pacific Ocean and North America (30).

During a positive PNA pattern, above average temperature and below average precipitation tend to be observed throughout the Ohio Valley and the Northeast US. The negative phase of the PNA is nearly the reverse pattern of the positive phase, with cooler temperatures and above average precipitation (34). The PNA has significant variability even in the absence of the ENSO, but it has been shown to be generally associated with

116 the ENSO (30). The positive phase of the PNA tends to be associated with El Niño conditions, and the negative phase tends to be associated with La Niña conditions.

The teleconnection series have well-defined, naturally occurring, oscillations

(cycles) as represented by the positive and negative phases. To specifically account for this cyclical structure in the investigated time series, a spectral analysis technique was utilized. Quantification of the relationship between climate variability, as determined from large-scale climate indices, and plant diseases has been attempted in the past. For instance, Scherm and Yang (45,46) used cross-spectral analysis to investigate the relationship between the ENSO and other teleconnection patterns and wheat rust in China and the US. Del Ponte et al. (12) showed the ENSO may be used to determine the predicted risk of soybean rust epidemics in Brazil.

The objective of this study was to determine the relationship between the ONI,

NAO, and PNA, and the annual variation of FHB intensity in two US states. We utilized spectral-analytical techniques (3,18) to relate climate patterns over multiple time (year) scales to FHB because the methodology provides for a temporal decomposition of one or a pair of (possibly correlated) time series of observations into multiple frequencies (or periods). Results for different frequencies can be related to different scales of temporal associations. Analysis was based on yearly observations of FHB intensity from Ohio (46 years) and Indiana (36 years). Other datasets used in the window-pane analysis in

Chapter 2 could not be used here because of insufficient number of years for the spectral analysis.

117

Materials and Methods

Disease data. In Ohio, FHB intensity in the state (broadly defined to include estimated yield impact) was rated from 0 to 9 at the end of each wheat season for 46 years (1965 to 2010) (Fig. 4.1). Details are given in Chapter 2. The total time span in

Ohio includes data from 2009 and 2010, which were not available when the study in

Chapter 2 was conducted. In Indiana, disease was assessed for 36 years (1973 to 2008) in variety nurseries by Purdue University researchers (Fig. 4.1). Observations used here were obtained from the susceptible ―check‖ cultivars. For all years, FHB disease index

(field severity) was estimated as the mean percentage of spike area with symptoms

(including the spikes with no symptoms). The square-root of the disease intensity observations were calculated to obtain a more symmetrical distribution of values and more linear relation with environmental variables (unpublished). More details on disease assessment are given in Chapter 2.

Climate indices. Monthly values of the NAO and PNA and 3-month averaged values of the ONI were obtained from the Climate Prediction Center, part of the National

Oceanic and Atmospheric Administration (http://www.cpc.ncep.noaa.gov/data/indices).

Two additional teleconnection indices, the Southern Oscillation Index (SOI; a measure of the ENSO) and Arctic Oscillation (AO), were also used in the analyses, but these indices are closely linked to the ONI and NAO, respectively (32,50), and the spectral-analytical results were very similar to that found for the ONI and NAO (unpublished). Two sets of

3-month averages of the indices were evaluated in the analysis (Fig. 4.2). Boreal winter

(December to February) and boreal spring (March to May) index values were used

118 because winter conditions are important for F. graminearum survival and spring conditions are important for disease development (sporulation, dispersal, infection, and colonization) (9,14,21,38,39). Moreover, winter or spring teleconnections could affect shorter-term concurrent weather, or later climate or weather conditions (1,36).

Spectral analysis. Spectral and cross-spectral analyses were used to characterize the disease and climate time series. Spectral analysis utilizes the Fourier transform to approximate a function (i.e., a Fourier series) by a sum of sine and cosine waves of different amplitudes and frequencies. The temporal-domain series (i.e., the time-series of observations) is effectively then transformed into a frequency-domain signal. This allows the total variance of a series of observations over time, such as FHB intensity or climate teleconnection index, to be partitioned into simpler individual frequency (or period

[=1/frequency]) scales, which helps determine which scales contribute most of the variability over time. The SPECTRA procedure in SAS (SAS, Inc., Cary, NC), which utilizes the fast Fourier transform developed by Cooley and Tukey (7), was used to conduct the spectral analysis. Based on the length of the disease time series (46 years in Ohio, 36 in Indiana), periods > 23 years and > 18 years, respectively, were not considered in the modeling because there would only be one complete cycle per series

(and thus insufficient data for model fitting).

The Fourier transform decomposition of a series is given by:

M k , where is the observation number or time in this case ; is the response variable at time , is the number of Fourier frequencies in the decomposition and is the

smallest integer greater than or equal to ( for Ohio and for Indiana),

119

and are coefficients of the cosine and sine functions, respectively; and is

the Fourier frequency (in radians) for (18, 27). For ease of the reading,

frequencies were converted to periods using the inverse function (i.e., period = ) (27).

The estimates for and form the basis of the spectral density at each period

[ . The spectral density is a standardized and smoothed version of the partial sum of squares resulting from the estimates of the two coefficients. Peaks (periods with high amplitude values) in the spectral density designate which periods are associated with a high amount of variance of the time series.

Cross-spectral analysis. For each pair of disease-climate time series (denoted Xt and Yt), a cross-spectral analysis was conducted as described by Brocklebank (3), also using the SPECTRA procedure in SAS. In cross-spectral analysis, the cross-spectral density is found, which is analogous to a cross-covariance function of two temporal series, showing how two (possibly) correlated series co-vary over time. Similarly to the univariate spectral density, the amplitude of the cross-spectral density at each period

[ is a measure of the variance accounted for between the two time series. Peaks in the amplitude spectrum (a plot of the amplitude, , at each period) indicate periods where there are possible strong associations between the two series.

The squared coherency spectrum provides estimates of the proportion of the variance in one series that is predictable from the other series for each period, and is analogous to a coefficient of determination in regression analysis. We call the squared coherency simply ―coherency‖ for ease of presentation. Large values of coherency indicate a strong relationship at the particular period. The coherency at period is given by: 120

where is the squared amplitude of the cross-spectral density, and and

are the univariate spectral density estimates at each period. The coherency spectrum was determined for each pair of FHB and climate-teleconnection-index time- series data. Interpretation of coherency estimates depend on the univariate spectral density of each time series; that is, if one or both univariate spectral densities have a negligible amount of variance [i.e. a small amplitude in or ] at a period of interest, then the coherency at that period is not especially important (47,53).

Because the cross-spectral density is generally a complex-valued function (27), a temporal difference (lead or lag) between each pair of time-series, the so-called phase shift, may result. The phase shift can only be reliably estimated for periods with a high coherency because sampling errors of the shifts are large at low coherency values

(47,53).

All phase differences displayed in the SPECTRA procedure output have been scaled from –π to +π radians. A phase difference of 0 means that the two series (predicted from the spectral model fitted to the data) are in perfect phase at a particular period

(peaks or valleys of the cyclical series occur at the same times for the two series). Phase differences of exactly π and -π radians are indistinguishable from each other, and indicate the two (predicted) series have a negative relationship at that period; that is, a peak in one series occurs at the same time as a valley (low) in the other series. Either series can be considered to lead or lag the other series (53) for other phase differences (e.g., series Xt leading Yt by less than π radians is the same as Yt leading Xt by more than π radians). For

121 ease of presentation, all phase shifts are calculated in terms of the climate index leading the FHB series and are given as positive numbers.

The phase shift (at a given period) for the lead of the climate series (from peak to peak or valley to valley) is given by PS(+). One can also determine (at a given period) the phase shift from a peak of the climate series to the next valley of the FHB series, or from a valley of the climate series to the next peak in the FHB series, this is given as PS(-

). The smaller of PS(+) and PS(-) for a given period indicates the most apparent relation between the two series (positive or negative). The phase can be rewritten in terms of years for ease of understanding phase in years phase in radians period π . Full details on this analysis are given in Appendix A.

Nonparametric significance testing of coherency. The coherency at each period was identified and tested for significance by a permutation procedure (37). Although there are test statistics based on distributional assumptions for normally distributed series that had been smoothed with a uniform filter, they may be biased for non-normally distributed data (27,47). Because of the non-normal data used in this study, a permutation-based approach is preferred. The procedure involved creating 1,000 randomly permuted versions of the FHB data sets (for Ohio and Indiana, separately).

Coherency estimates with the teleconnection time series were obtained from each permuted data set by the SPECTRA procedure in SAS and used to create a sampling distribution of coherency values under the null hypothesis of no coherency. That is, at each period, 1,000 values of the coherency were determined and used to find the 90-th percentile, which corresponds to the critical value for hypothesis test at significance level

(α) of 0. 0. That is, if the estimated coherency value for the observed time series was

122 greater than the 90-th percentile for the randomly permuted series, then the observed coherency was declared significantly greater than 0 (α 0. 0).

Results

Univariate statistics. As described previously in Chapter 2, there was a wide inter-annual variation in FHB intensity in Ohio and Indiana (Fig. 4.1A), and the covariation in the two disease series was not great over time (highs and lows in intensity did not necessarily occur in the same years). Univariate spectral densities for disease time series at both locations (Ohio FHB, Indiana FHB) and the three climate indices (ONI,

NAO, PNA) during winter and spring were analyzed first to find periods (or frequencies) that were associated with a larger proportion of the variation of each individual series.

This was to help ensure that results from the cross-spectral analysis and the coherency analysis (see below) were meaningful biologically or physically, and not artifacts. In other words, both individual series in the pair being analyzed must show a reasonable proportion of explained variation (peaks in the spectral density) at one or more periods in order to use the coherency estimates (47,53). The univariate spectral density for Ohio

FHB (Fig. 4.1B) showed a high proportion of the variance explained (peak) at periods between 4.6 and 7.7 years and had a small peak around a period of 3 years. A period of 5, for example, indicates that when there is a high amount of disease in a given year, then approximately 5 years later, there will be another high disease year. The univariate spectral density for Indiana FHB showed high peaks around periods of 3, 6, and 9+ years

123

(Fig. 4.1B). The relatively flat spectrum at 9+ years indicates these periods account for equal amounts of variance.

The winter ONI had larger amplitudes overall than the spring ONI. However, for both winter and spring ONI, positive values (those related to the El Niño) in general were of stronger amplitude than negative values (those related to the La Niña). The ENSO is known to have a cycle of 2 to 7 years (33). In this analysis of 3-month ONI index values for the ENSO, the winter and spring spectra had peaks around similar periods (e.g., 3.5 to

5.8 years) (Fig. 4.2).

Long-term variations were apparent in the historical record of the NAO. For about

20 years prior to 1965 (data not shown) the NAO was in a decreasing trend. However, since that time, it has been in an upward trend, which resulted in the NAO index being mostly positive since the early 1980s (49), although there is considerable inter-annual variation. One main exception is the 2009/10 winter where the NAO had a strong negative index. These patterns are most pronounced in the Winter NAO index (Fig. 4.2).

However, the spring NAO index is similar in that it tended to be mostly negative until the early 1980s and then in a positive trend until the early 1990s, but it appears to be fairly neutral since then. For the spectral density of the winter NAO teleconnection index, there was a slight maximum peak in amplitude around periods of 2 to 3 years. Then, beginning at periods of about 4 years, the spectral density of the winter NAO index also generally increased as the period increased (32), with the largest peaks around periods of 7 to 8 years (Fig. 4.2). The amplitude peaks at the longer periods in the spectral density reflects the long-term trends (49) in the index (Fig. 4.2), with extended years below or above 0

(on average); in contrast, the peaks at short periods reflect the smaller variations in the

124 index over short time spans. Similar trends in the winter NAO spectrum and detailed discussion can be found in Marshall et al. (32), although our results are based on data through 2010, whereas their analysis was based on the index values up to 1998. The spring NAO spectrum had one peak in amplitude around periods of 2 to 3 years, and no evidence of strong peaks at the longer time scales (Fig. 4.2).

The PNA is similar to the NAO in that both patterns have been in a general upward trend over the time of our study and their largest amplitudes occur during the winter months. The winter PNA has also been mostly positive since the early 1980s. The winter PNA spectrum had a large peak in amplitude around periods of 2.5 to 4 years, with a smaller peak around periods of 3.5 to 5.8 years. The spring PNA spectrum had a peak around 2.2 to 2.6 years, with a smaller peak around periods of 3.5 to 5.8 years and declining amplitude after these periods. Therefore, the PNA had mostly dominant temporal patterns over shorter periods.

Oceanic Niño Index and FHB. Coherency values and the amplitude of the cross- spectral densities varied greatly with period for FHB in the two states and the different teleconnection indices. The largest significant coherency values for each pair of time series (FHB and teleconnection index) are shown in Table 4.1. For instance, 71% of the variation in Ohio FHB could be explained by variation in the winter ONI at a period of about 5.1 years [i.e., ] (Fig. 4.3, Table 4.1). For the spring ONI, similar results were found, with the largest coherency peak at a period of 5.1 years, but with an even higher percentage of explained variation [ ; Table 4.1]; the coherency values were also significant for nearby peaks at periods of 4.6 and 5.8 years

(Fig. 4.3). The large significant coherency values for the relationship between Ohio FHB

125 and the ONI were at or around the periods that showed a high percentage of the variance explained in each univariate time series (Figs. 4.1 and 4.2).

Because the phase shift for periods with the highest coherency was not 0, π or –π, different shifts were calculated from the output of the SPECTRA procedure. These are demonstrated in Figure 4.4, which correspond to the predicted FHB and winter ONI temporal patterns for a period of 5.1 years (Table 4.1) over an arbitrary 10-year time span. FHB led the winter ONI series (from peak to peak or valley to valley) by an estimated 0.65π radians (equal to .66 years). This is equivalent to the winter ONI leading the FHB series by PS(+) = π – 0.65π .35π radians (3.45 years) (Fig. 4.4).

Thus, for the dominant period of 5.1 years, when the winter ONI is high/low, FHB intensity in Ohio is high/low approximately 3.5 years later. Moreover, the estimated negative relation between the series is PS(-) 0.35π radians (0.9 years) (Fig. 4.4). That is, when winter ONI is at a peak, FHB is in a valley ≈1 year later. Similar results were found for spring ONI and FHB (Table 4.1).

As with the results from Ohio, the amplitude of the cross-spectral density and coherency graphs for the Indiana FHB data and winter ONI showed clear peaks for selected periods of 4 years or less, as well as for 12 years (Fig. 4.5). The coherency, however, was significant only at a period around 2.8 years (Table 4.1), which is shorter than the periods identified for Ohio. However, the univariate spectral densities at this period were fairly low compared to the other periods (i.e., they were not at peaks); therefore, the coherency found may be an artifact.

North Atlantic Oscillation Index and FHB. There were several peaks in the coherency graph and cross-spectral density for FHB intensity in Ohio and the winter

126

NAO teleconnection index (Fig. 4.3). Coherency values were significant at periods of 4.2 to 5.1 years (Fig. 4.3), and about 75% of the variation in FHB was explained by variation in winter NAO [ ; Table 4.1]. The amplitude spectra and univariate spectral densities for FHB and winter NAO also had peaks with fairly large amplitudes at similar periods (Figs. 4.1 and 4.2), but there were even larger peaks in the univariate spectral density at periods of 6 or more years for winter NAO (Fig. 4.2). The positive phase difference, PS(+), indicates, for periods around 4.2 to 5.1 years, that there was a peak in the FHB series about 1.1 to 1.7 years after a peak in winter NAO (or a valley in

FHB 1.1 to 1.7 years after a valley for winter NAO) (Table 4.1).

The spring NAO and Ohio FHB had significant coherencies at shorter periods

(2.2 years) than found for the winter NAO. Because the Ohio FHB univariate series only had a small peak around these periods, the coherencies found may be artifacts.

Results for the relationship between FHB in Indiana and winter NAO were similar to those found in Ohio, except that the highest coherencies were for longer periods of 6 and 7.2 years (Fig. 4.5, Table 4.1). Univariate spectral densities were high for these periods. For the periods of 6 and 7.2 years, the small PS(-) values of 0.4 and 0.2 years, respectively, indicated there was a negative relationship between winter NAO and FHB intensity in Indiana in the same year; that is, a peak in winter NAO was followed about an estimated 5 and 2.5 months later with a predicted valley in FHB. Phase shifts less than

6 months indicate that the peaks in NAO are estimated to occur in the same year as the valleys in FHB.

Pacific-North American Pattern and FHB. Winter PNA was related to FHB intensity in Ohio at periods of 2.1 to 2.9 years and 5.1 to 5.8 years, with the highest

127 coherencies at the shorter periods (Fig. 4.3; Table 4.1). However, the coherencies at the shorter periods should be examined with caution, as the Ohio FHB univariate spectral density series had only a small peak around a period of 3 years (Fig. 4.1). With PS(-) =

1.4 years at the 5.1-year period, a low in the FHB series was estimated to follow a high in the PNA series by about 1.5 years, showing the general negative relation between the series. The spring PNA time series was significantly coherent with FHB in Ohio at periods around 3 years (Table 4.1). However, the univariate spectral density for the spring PNA did not have peaks at these periods, so these may be artifacts.

Peaks in coherency were found for disease intensity in Indiana and winter PNA at short periods around 2.6 years (Fig. 4.5; Table 4.1). The univariate spectral densities also had peaks in amplitude at these periods (Figs. 4.1 and 4.2), although there were larger peaks at other periods. For these short periods, a peak in winter PNA was followed by a peak in FHB in an estimated 2 months [PS(+) = 0.16-0.19 years]; that is, the phase shifts showed a positive relation, because the peaks (or valleys) occurred in the same years.

There were several peaks in the coherency graph for the Indiana FHB and spring

PNA series for periods between 3 and 6 years (Fig. 4.5). However, the coherencies for the middle of this range (periods between 4 and 5 years) likely are artifacts because of the low amplitude of the univariate spectral density for the FHB series at these periods (Fig.

4.1). The largest coherency between Indiana FHB and spring PNA was at a period of 3 years (Table 4.1). The phase shift at this period [PS(-) = 0.8 years] indicates there was a negative relationship between the spring PNA and FHB intensity because peaks in one series were estimated to occur near the same years as valleys in the other series. The

128 other significant coherencies all also indicated negative relationships [i.e., PS(-) <

PS(+)].

Discussion

Several authors have shown significant relationships between generally short-term environmental conditions near flowering or during the later part of the growing season and FHB intensity (8,39). Forecasting models have been developed that use local weather conditions around these times to predict the risk of disease or high toxin contamination

(9,10,23,44). In Chapter 2 it was found that FHB was significantly associated with longer-term environmental variables (30 days or longer) and with environmental variables for different times during the growing season. These results suggested that large-scale climatic patterns may provide information for determining the risk of FHB on a regional scale, and possibly lead to earlier predictions of high (or low) risk years, than the current forecasters. However, whether large-scale climate variables can be incorporated into forecasts for this disease in the US to enhance their skill has been unknown, given the importance of environmental conditions near anthesis for spore production and infection. With the long-term goal of discovering (small- and large-scale) environmental effects on FHB and the possibility of ultimately improving disease forecasting, we attempted here to determine if the ENSO and various climatic teleconnections around North America were associated with FHB in two US states, Ohio and Indiana.

129

We followed the work of Scherm and Yang (45,46) and Workneh and Rush (54) and utilized cross-spectral analysis to characterize the relationship between teleconnection indices and inter-annual variation in FHB. We further extended the approach by using a nonparametric method for testing of coherency of the series. Clear amplitude peaks were found in univariate spectral densities for FHB and the teleconnection indices, which justifies the characterization of relationships using cross- spectral densities and coherencies (2,27,53). We primarily discuss coherency and phase- shift results for situations with peaks in the univariate spectra. Indices for the ENSO

(such as the ONI) are probably the most commonly considered when relating biological variables to climate patterns (17,22,26,48), possibly because of the well-known strong effect of the ENSO on temperature (43) and precipitation (42) patterns. Results for the cross-spectral analysis in our study showed that winter and spring ONI were significantly coherent with FHB intensity in Ohio, with a period of about 5.1 years. Coherency can be interpreted as the estimated proportion of variance that is shared between the two time series within that period. Therefore, FHB intensity in Ohio and the ONI share a significant proportion of variance when they are both modeled by cycles that repeat about every 5.1 years. Moreover, for spring ONI, periods neighboring 5.1 years were also significantly coherent. In general, the phase differences at the significant coherencies indicate that the ONI series and FHB series were negatively related because the estimated negative phase shift [PS(-)] was smaller than the estimated positive phase shift [PS(+)]

(Table 4. ), with phase shifts of 0.47π to 0.35π radians. This indicates that the peak in

FHB disease intensity is estimated to occur about a year after a low in the winter ONI series, and with a dominant period of ~5 years for the series, FHB is close to its peak

130 when ONI is at its low. Thus, for a La Niña year, when ONI is at a low, there tends to be more disease in Ohio. This can be seen also with the observed series: two years with the highest amounts of FHB (1986 and 1996) both followed persistent La Niña episodes. The

La Niña winter has been associated with an increase in heavy rainfall frequency south of the Great Lakes (Ohio-Mississippi River valley) compared with the El Niño (20) winter, with the heaviest precipitation west of the Appalachian mountains (15). The spectral analytical results are also consistent with the well-known result that the ENSO has a cycle of 2 to 7 years (33).

In addition to the winter and spring ONI coherency for Ohio, there were significant coherencies between FHB intensity and one or more of the other evaluated teleconnection indices for Ohio or Indiana. Although there was a significant coherency for winter ONI in Indiana, this could be an artifact (46,52). In Ohio, the highest coherencies for NAO and PNA were for similar periods as found for ONI (from about 2 to 5.8 years; Table 4.1), but in Indiana, the highest coherencies for NAO and PNA could be for periods as high as 7.2 years. For Indiana, the winter NAO had, in general, a negative relationship with the FHB series based on the estimated PS(-) values being less than 6 months [and because PS(-) was much lower than PS(+)]. Positive values of the

NAO during the winter are correlated with fewer cold-air outbreaks and decreased storminess and negative values tend to produce more storms and stronger cold-air outbreaks (34). The NAO is the dominant pattern of winter climate variability over the

North Atlantic (25), but it only explained a fraction of the total variance of the FHB series in Indiana. Interestingly, there was also a positive relation between winter NAO and FHB in Ohio, but with peak values of FHB occurring an estimated 1.1-1.8 years after

131 peaks in NAO. This indicates FHB in Ohio and Indiana does not respond similarly to variation in the NAO.

The winter and spring PNA index had significant coherencies with FHB in the two states. A negative relationship was found between the winter PNA index and FHB intensity in Ohio at a period of 5.1 years, and between the spring PNA index and FHB intensity in Indiana for several periods. That is, a peak in the PNA series was followed, in an estimated 10 to 16 months, by a valley in the FHB series. Coleman and Rogers (6) showed that the PNA index was inversely related to winter precipitation in the Ohio

River Valley region, with the strongest relationship found in southern Indiana. Notaro et al. (34) reached the same conclusions for Ohio as Coleman and Rogers did for Indiana, and they showed that there was a negative relationship between maximum temperature and the PNA. Ge et al. (19) showed that the PNA is associated with snow pack in several parts of the US, and recent work (13,41) has begun to investigate the effect of winter/spring snow mass anomalies on the spring/summer season. One would expect increased precipitation (low PNA value) to lead to an increase in disease, and the winter and spring PNA and FHB should have a negative relationship. However, a negative relation was not found at the shorter significant periods for winter PNA and FHB in

Indiana.

Even though there was a clear coherency of the teleconnection indices and FHB in two different states, the temporal pattern to the coherency was different in terms of the periods with the largest coherencies and the direction of the phase shifts. This was expected because the inter-annual variation in FHB was clearly different for Ohio and

Indiana (Fig. 4.1), where the highest disease intensities occurred in different years for the

132 two locations. Interestingly, work in Chapter 2 showed that the correlations of FHB with local weather variables for a range of time windows during the season were quite similar for the two locations, demonstrating a generally consistent biological response to local environment. The results in our current study suggest that the weather in Indiana and

Ohio respond differently to changes in the teleconnection patterns. Although this has not been investigated specifically, it is consistent with other results showing differences among regions for a given change in a teleconnection index (43). All three climate patterns investigated had some significant relationships with FHB intensity in Indiana or

Ohio. The ONI appeared to have a significant relationship with FHB in Ohio, but not on disease intensity in Indiana. The NAO had significant coherencies at more periods with the Ohio series than the Indiana series, but the univariate spectral densities were not at their largest amplitudes at these periods. The winter or spring PNA was significantly coherent with the FHB intensity series in both Ohio and Indiana at several periods, but the smallest estimated phase shift could be positive or negative. All of the climate patterns should be investigated further and possibly combined in a future multivariate analysis to identify how they jointly affect FHB.

The tendency that more of the evaluated climate patterns for the boreal winter had significant relationships with FHB than did the spring patterns was expected. It is well researched in the climatology literature that the amplitude (in absolute value) of the climate patterns are strongest during the winter season (32), which corresponds to most of the variability in the climate pattern occurring during this part of the year. Interestingly, even though there were fewer significant coherencies found for the relationship between

133

FHB and spring climate indices than winter climate indices, the coherency values with spring indices in some cases were of stronger magnitude than their winter counterparts.

The possible link between global climate patterns and FHB has been investigated in other countries. Zhao and Yao (55) studied relationships between Pacific sea-surface temperatures and FHB outbreaks in eastern China, and Del Ponte et al. (11) found that the frequency of the predicted risk of FHB in southern Brazil was higher during El Niño and ‗neutral‘ years than during La Niña years. In this region of the Western Hemisphere, rainfall in the spring months is usually higher during El Niño years. In an expansion of past work with this wheat disease, we were able to show long-term periodic trends in the

FHB-climate relationships through the spectral analyses. Del Ponte et al. (11) also suggested that there is a possible decadal variability of FHB seasonal risk in their data from southern Brazil. With this methodology, we could not only determine if yearly changes in the climate correlate with yearly changes in FHB, but also if changes in the climate lead to changes in FHB at some later point in time. We found that often there was not necessarily a concurrent (one-to-one, same year) correspondence between a particular climate index and disease. Instead, the phase differences showed the time series investigated had lead-lag relationships. This is usually due to the understanding that a certain state of the climate pattern can persist for several consecutive years (4). This is also consistent with the results from Scherm and Yang (45,46) as they found coherent relationships at periods of greater than one year with various phase differences.

Epidemics of FHB depend, in part, on local environmental variables because the local conditions affect survival, sporulation, dispersal, infection, and spike colonization in a given area (14,16,21,38). The teleconnection patterns can be linked to FHB intensity

134 because the climate patterns can influence the local environment where epidemics occur.

However, certain parts of the disease cycle, primarily infection, take place over a narrow time window, with increased atmospheric moisture around anthesis leading to increased risk of epidemics (9,39). In other words, the environmental conditions around anthesis can have a disproportionally large influence on epidemics. In addition, wheat across a state tends to reach the critical anthesis stage over a few weeks. Thus, the large-scale climate patterns discussed here can only account for a portion of the inter-annual variability in disease in a state or region that is attributable to environment. Even with a very high coherency between teleconnection indices and local weather, monthly or 3- month averaged climate indices (as used here) are not capable of capturing this short- term variability in weather. For instance, a very short-term dry spell at the ―right‖ time in an otherwise wet spring could negate the overall impact of the wet climate (in contrast to weather) on the epidemic (31). This means that there is an upper limit to the predictive ability of any teleconnection index, or any local measure of overall climate (―wet spring‖,

―dry June‖, etc.), for risk of FHB. In addition, the observed dynamics of the FHB series in Ohio and Indiana are not strictly dependent on climate and weather in the region. Over such a large number of years, changes in cultivars grown, cultural practices used, and population dynamics of the pathogens have implications to the disease series that are not specifically accounted for. Despite these qualifications, cross-spectral analysis was useful for showing significant coherencies between FHB and climate patterns, and as found by

Scherm and Yang (45,46) for other pathosystems, this type of analysis helped to discern some of the complex relationships between large-scale climate patterns and disease.

Although the coherencies clearly suggest that teleconnection indices can be used to

135 improve disease forecasts, direct utilization of the indices in real-time predictive models will be challenging. This is because the form of the climate-disease relationship depended on location, the effects of climate indices were ―spread out‖ over years, and because of the phase shifts that vary with index. For the latter situation, results showed that the coupling may involve changes in disease that are shifted by years from the changes in the teleconnection index. Nevertheless, we suggest that further studies of climate variability on FHB are important as they will continue to increase our understanding of these climate-disease relationships and the best statistical methods for finding them.

136

Variable (Index)a coherency (1/frequency) PS(+) PS(-) coherency (1/frequency) PS(+) PS(-) radians (yearsc) radians (years) radians (years) radians (years) Winter ONI 0.706 5. †d .35π (3.45 ) 0.35π (0.900) 0.539 2.769 0. 8π (0. 5 ) . 8π ( .637) 0.556 5.75† .4 π (4.060) 0.4 π ( . 85)

NAO 0.753 4.6† 0.59π ( .347) .59π (3.647) 0.701 6† . 4π (3.405) 0. 4π (0.405) 0.665 5. † 0.68π ( .745) .68π (4.300) 0.502 7. † .05π (3.787) 0.05π (0. 87) 0.523 4. 8 † 0.54π ( . 38) .54π (3. 9)

137 PNA 0.930 2.191 0.39π (0.4 9) .39π ( .5 4) 0.541 .57 † 0. 4π (0. 85) . 4π ( .47 ) 0.870 2.3 0.4 π (0.47 ) .4 π ( .6 ) 0.522 .769† 0. π (0. 57) . π ( .54 ) 0.779 5. † .54 π (3.937) 0.54π ( .38 )

Spring ONI 0.914 5. † .44π (3.687) 0.44π ( . 3 ) NSe 0.813 4.6† .47π (3.37 ) 0.47π ( .07 ) 0.715 5.75† .46π (4. 94) 0.46π ( .3 9)

NAO 0.754 2.191 . 4π ( .355) 0. 4π (0. 59) NS 0.546 2.3 . 4π ( .4 7) 0. 4π (0. 77)

PNA 0.658 2.875 .68π ( .409) 0.68π (0.97 ) 0.734 3† .55π ( .3 5) 0.55π (0.8 5) 0.649 3.067 .53π ( .348) 0.53π (0.8 4) 0.695 5.143 . 9π (3.3 8) 0. 9π (0.757) 0.678 6† .40π (4. ) 0.40π ( . )

Continued

Table 4.1: Continued

a Climate variables are the Oceanic Niño Index (ONI), North Atlantic Oscillation (NAO), and Pacific-North American Pattern(PNA). Winter climate index values represent the mean of December to February values. Spring climate index values represent the mean of March to May values. b Phase shifts were always put in terms of positive numbers with the climate series leading the FHB series. PS(+) is used to quantify the positive phase shift between the series, and PS(-) is used to quantify the negative phase shift between the series. c Phase in years (Phase in radians) · period ( π) d The symbol † is used to indicate that there was a noticeable peak (although there could be larger peaks elsewhere) in the univariate spectral density at the identified period. e NS – not significant

138

A Ohio Indiana 3 6 A A 5

2 4 3

1 2

Scaled FHB Index FHB Scaled

Scaled FHB rating FHB Scaled 0 0

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Year

B 0.4 0.6

0.5 0.3 B B 0.4 0.2 0.3

0.2 0.1

Spectral Density Spectral 0.1

0.0 0.0 2 4 6 8 10 12 14 16 18 20 22 24

Ohio Period (year) Indiana

Figure 4.1. A, Scaled (transformed) Fusarium head blight intensity for Ohio (1965 - 2010) and Indiana (1973 - 2008). B, Spectral density of yearly values of FHB intensity in Ohio and Indiana. The square-root of disease intensity was used for all analyses. Interior tick lines on the lower Period axis are the Fourier frequencies (converted to periods) for Ohio and on the upper Period axis are the Fourier frequencies (converted to periods) for Indiana. The scaled disease data points overlap completely in 1986 and only one point can be seen.

139

Winter Spring

2.5 2.5 0.35 2.0 2.0 1.5 1.5 0.30 1.0 1.0 0.25 0.5 0.5 0.20

ONI 0.0 0.0 0.15 -0.5 -0.5 -1.0 -1.0 0.10

-1.5 -1.5 Density Spectral 0.05 -2.0 -2.0 0.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 2 4 6 8 10 12 14 16 18 20 22 24 2.0 2.0 0.35 1.5 1.5 0.30 1.0 1.0 0.25 0.5 0.5 0.20 0.0 0.0 0.15

NAO -0.5 -0.5 -1.0 -1.0 0.10 -1.5 -1.5 0.05 -2.0 -2.0 Density Spectral 0.00 -2.5 -2.5 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 2 4 6 8 10 12 14 16 18 20 22 24 2.0 2.0 0.35 1.5 1.5 0.30 1.0 1.0 0.25 0.5 0.5 0.0 0.0 0.20

PNA -0.5 -0.5 0.15 -1.0 -1.0 0.10 -1.5 -1.5 -2.0 -2.0 Density Spectral 0.05 -2.5 -2.5 0.00 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 2 4 6 8 10 12 14 16 18 20 22 24 Year Year Period (year)

140

Winter ONI Spring ONI 1.0 0.3 1.0 0.3 0.8 0.2 0.8 0.2 0.1 0.1 0.6 0.0 0.6 0.0 3 5 7 9 11131517192123 3 5 7 9 11131517192123 0.4 0.4

Coherency 0.2 0.2 0.0 ** 0.0 *** 3 5 7 9 11 13 15 17 19 21 23 3 5 7 9 11 13 15 17 19 21 23 Winter NAO Spring NAO 1.0 1.0 0.15 0.15 0.8 0.10 0.8 0.10 0.05 0.05 0.6 0.00 0.6 0.00 3 5 7 9 11131517192123 3 5 7 9 11131517192123 0.4 0.4

Coherency 0.2 0.2 0.0 *** 0.0 * 3 5 7 9 11 13 15 17 19 21 23 3 5 7 9 11 13 15 17 19 21 23 Winter PNA Spring PNA 1.0 0.15 1.0 0.15 0.8 0.10 0.8 0.10 0.05 0.05 0.6 0.00 0.6 0.00 3 5 7 9 11131517192123 3 5 7 9 11131517192123 0.4 0.4

Coherency 0.2 0.2 0.0 ****** ** 0.0 ** 3 5 7 9 11 13 15 17 19 21 23 3 5 7 9 11 13 15 17 19 21 23

Period (year) Period (year)

Figure 4.3. Coherency relationships among time series of annual FHB intensity values in Ohio and the Oceanic Niño Index (ONI), North American Oscillation (NAO), and Pacific/North American Pattern (PNA) from 1965 to 2010. Insert graphs are the amplitude of the cross-spectral density for each pair of time series. Interior vertical lines on the Period axis are the Fourier frequencies (converted to periods). Asterisks denote periods where the coherency is significant as determined by the permutation procedure (α 0. 0).

141

0.65π .660 years .35π 3.45 years years

ONI

FHB 0.35π 0.900 years

0 1 2 3 4 5 6 7 8 9 10

Time (arbitrary starting year)

142

Winter ONI Spring ONI 1.0 1.0 0.2 0.2

0.8 0.1 0.8 0.1

0.6 0.0 0.6 0.0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 0.4 0.4

Coherency 0.2 0.2 0.0 * 0.0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 Winter NAO Spring NAO 1.0 0.2 1.0 0.2

0.8 0.1 0.8 0.1

0.6 0.0 0.6 0.0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 0.4 0.4

Coherency 0.2 0.2 0.0 * * 0.0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 Winter PNA Spring PNA 1.0 1.0 0.2 0.2

0.8 0.1 0.8 0.1

0.6 0.0 0.6 0.0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 0.4 0.4

Coherency 0.2 0.2 0.0 ** 0.0 ***** * * 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18

Period (year) Period (year)

143

Summary

Cross-spectral analysis was used to characterize the relationship between climate variability, represented by atmospheric patterns, and annual fluctuations of Fusarium head blight (FHB) disease intensity in wheat. Time series investigated were the Oceanic

Niño Index (ONI), which is a measure of the El Niño-Southern Oscillation (ENSO), the

Pacific/North American (PNA) pattern and the North Atlantic Oscillation (NAO), which are known to have strong influences on the Northern Hemisphere climate, and FHB disease intensity observations in Ohio from 1965 to 2010 and in Indiana from 1973 to

2008. For each climate variable, mean climate index values for the boreal winter

(December to February) and spring (March to May) were utilized. The spectral density of each time series and the (squared) coherency of each pair of FHB–climate-index series were estimated. Significance for coherency was determined by a nonparametric permutation procedure. Results showed that winter and spring ONI were significantly coherent with FHB in Ohio, with a period of about 5.1 years (as well as for some adjacent periods). The estimated phase-shift distribution indicated that there was a generally negative relation between the two series, with high values of FHB (an indication of a major epidemic) estimated to occur about 1 year following low values of ONI (indication of a La Niña); equivalently, low values of FHB were estimated to occur about 1 year after high values of ONI (El Niño). There was also limited evidence that winter ONI had significant coherency with FHB in Indiana. At periods between 2 and 7 years, the PNA and NAO indices were coherent with FHB in both Ohio and Indiana, although results for

144

phase shift and period depended on the specific location, climate index, and time span used in calculating the climate index. Differences in results for Ohio and Indiana were expected because the FHB disease series for the two states were not similar. Results suggest that global climate indices and models could be used to identify potential years with high (or low) risk for FHB development, although the most accurate risk predictions will need to be customized for a region and will also require use of local weather data during key time periods for sporulation and infection by the fungal pathogen.

145

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Chapter 5

Characterizing Heterogeneity of Disease Incidence in a Spatial Hierarchy: A Case

Study from a Decade of Fusarium Head Blight of Wheat in Ohio

Introduction

Heterogeneity of plant diseases occurs at multiple temporal and spatial scales

(21,45,81). Spatial variability at a given time can be at small scales, such as within or among sampling units (sites) within a field, or at larger scales, such as among fields, counties, or states and countries. Additionally, variability can be observed at different temporal scales, such as among assessment times within years, among years, or even among decades. Fusarium head blight (FHB) of wheat, caused by the fungus Fusarium graminearum Schwabe (teleomorph: Gibberella zeae (Schwein.) Petch), as well as other species, is a plant disease with high variability in space and time (53,87). The disease causes yield reduction resulting from the production of small, shriveled, light-weight kernels, and harvested grain are often contaminated with mammalian mycotoxins, especially deoxynivalenol (DON), produced by the pathogen (3).

It has been known for 80 years that FHB disease intensity in the field and mycotoxin accumulation in grain are highly variable, both spatially and temporally

(9,79). This variability has been attributed to variability in: environmental factors,

151 including weather and climate (12,40,41,44); agronomic practices such as crop rotation and tillage methods (8,14); other management practices, including resistance level of the cultivars and fungicide use (27,62); species and fungal strains causing the disease

(84,88); as well as unknown factors. A better understanding of the spatial and temporal variability in FHB can aid in the development of efficient sampling protocols (46) for risk assessment, elucidation of factors that influence epidemics, and development and refinement of prediction systems based on risk models.

Originally prompted by the need to evaluate a new risk model for FHB in the US

(12), a survey of wheat fields from the major wheat-growing areas of the state was initiated in 2002. Disease incidence data were obtained from multiple counties, fields within counties, and sites (sampling units) within fields. The survey has continued yearly since then in an effort to eventually characterize the spatial heterogeneity of FHB in

Ohio, obtain estimates of the intensity of disease in different regions (i.e., counties) of the state, and describe any temporal patterns to the heterogeneity.

Several authors have shown how to quantify and interpret the heterogeneity of disease incidence within fields or at higher scales (28,31,33,45,47,80). The use of discrete probability distributions for overdispersed binary data is especially useful, because a heterogeneity parameter can be estimated to quantify the magnitude of disease aggregation at the scale of the sampling unit or smaller. The beta-binomial distribution has been heavily used for this purpose, partially because one can directly re-express the heterogeneity parameter () as the intra-cluster correlation (), a measure of the agreement in disease status of individuals within sampling units (45). As an alternative,

Hughes and Samita (33) have proposed the use of the logistic-normal-binomial (LNB)

152 discrete distribution for the same purpose. The LNB can be considered a special case of the marginal distribution that arises when fitting a generalized linear mixed model

(GLMM) with a logit link, a single random-effect term for the effect of sampling units, and a binomial distribution for number of diseased individuals (Y) conditional on the random effect. Although the beta-binomial distribution is much more commonly used in epidemiology than the LNB, the former cannot be readily expanded to account for multiple sources of variation in a spatial hierarchy (2). In principle, GLMMs can be used for discrete data with any number of spatial scales of variation and be used to analyze experiments with a wide range of experimental designs (35, 49, 67). At present, however, there is little evidence regarding the effectiveness of GLMMs for characterizing the heterogeneity of disease incidence at multiple scales in a hierarchy.

Linear mixed models have been successfully used to represent the variability in the incidence of disease of plants or animals, or the counts of organisms, at multiple scales in a spatial hierarchy (25,57,85). Mixed models, in general, are also very useful for estimating (predicting) the mean for different so-called domains (e.g., counties) in a survey, even when the sample size per domain is small, a process often known as ―small area estimation‖ (34,65). Although use of linear mixed models can be effective, generalized linear mixed models offer several advantages for various data sets. The linear mixed modeling approach is based on the assumption that incidence is a continuous random variable. However, with GLMMs, nonnormal or discrete data are explicitly incorporated into the model through a link function. In addition, although one can estimate an intra-cluster correlation for the agreement of (possibly transformed) mean incidence of the sites within fields using linear mixed models, one cannot estimate the

153 intra-cluster correlation for disease status of individuals within sampling units, as is possible with GLMMs. Also with GLMMs, it is possible to predict probabilities of specific values of incidence (76), and to drop the assumption that the variance is not a function of the mean. Thus, there are clear advantages to the use of GLMMs over linear mixed models. Nevertheless, fitting of GLMMs to data is much more computationally demanding compared to the fitting of linear mixed models (5). Until recently, most model fitting methods for hierarchical GLMMs in commercial software were based on so-called quasi-likelihood or pseudo-likelihood methods (71). This approach, based on approximating the GLMM using a Taylor-series expansion, is prone to biased parameter estimates in some circumstances (64), although the methodology works in a wide range of experimental and survey conditions (35,49,67). More importantly, likelihood-based statistical inference is not generally possible with quasi- and pseudo-likelihood methods

(5) because the likelihood that is calculated is on an arbitrary (―pseudo-data‖) scale that changes with the random effects in the model. Consequences of this include the inability to directly compare goodness of fit of nested models or to directly determine confidence intervals for variances based on the likelihood (72), the latter being especially important when the objective is to characterize heterogeneity. Major recent advances in statistical computation now make it possible to use maximum likelihood (ML) methods instead of quasi- and pseudo-likelihood methods to fit hierarchical GLMMs directly to data (5,72).

Although there are still approximations used to numerically integrate the likelihood function, the full range of likelihood-based inference methods is available to the investigator with these ML methods.

154

The major objective of this study was to use GLMMs to assess the heterogeneity in FHB incidence in Ohio at three scales in a spatial hierarchy, county, field within county, and site within field and county, over a 10-year period. Through the discrete distribution modeling, an analytical protocol for characterizing variability of incidence of a disease at multiple levels is developed. Secondary objectives were to ―estimate‖ mean incidence of FHB at the county scale using empirical predictions of random effects in the fitted GLMMs for each year, and investigate whether this mean incidence was related to county-aggregated data on environment and cropping information.

MATERIALS AND METHODS

Data collection. Incidence of Fusarium head blight (FHB) on wheat spikes in

Ohio wheat fields was obtained through a survey conducted during the 2002 through

2011 growing seasons. Within the state, 12 to 32 counties each year were selected for the survey (Table 5.1), primarily from the northern and western parts of Ohio since most of the wheat is grown in these regions. Selection of each county in some years was also influenced by the availability of a county extension educator who was qualified and capable of assessing disease. Within each county, between one and fifteen fields were chosen indiscriminately from across the county (Table 5.1); field characteristics such as tillage method, cultivar, fungicide use (except for 2011), or other agronomic practices were not considered in field selection. In 2011, we attempted to survey some fields in each county that were sprayed with a fungicide for control of FHB, and some fields that were not sprayed with a fungicide. This was the first year with substantial use in Ohio of

155 some of the most effective fungicides labeled for FHB control (Paul, unpublished). Most importantly, prior information on FHB disease was not used in selecting fields. Within each field, ten sites (sampling units) were surveyed in the vast majority of the fields, counties, and years. Occasionally, less than ten sites per field were surveyed (in about 6% of the cases). The sites were approximately 30 m apart and along a main diagonal of the field. As described in Hughes et al. (29), this data collection within each field is known as a cluster sampling.

Each site consisted of 0.3 m of one wheat row. A measuring fork that was 0.3 m long and attached to a rod was used to isolate only the wheat plants within one row for observations. All wheat plants within the 0.3 m were counted to provide the number of spikes at each site (n) and each spike was individually inspected for visual symptoms of

FHB. The value of n varied within and among fields, with 80% of the values being between 31 and 62 spikes per site, with an average of 45. Each person doing the assessments was previously trained on how to recognize symptoms of FHB and how to effectively distinguish between symptoms of FHB and other diseases or injuries in the field. Disease incidence (Y/n) was calculated as the number of spikes with symptoms of

FHB (Y) out of the total number of spikes at each site (n). Over the 10 years, a total of

1,195 wheat fields and 11,515 sites were sampled; overall, 522,372 wheat spikes were evaluated for disease symptoms.

Data analysis—basic notation. The expected probability of a wheat spike being diseased in any cluster of spikes (such as in a sampling unit or site) is given by p.

Without consideration of random effects (see below), p = E(Y/n). With random effects, p is considered the expected probability of disease conditional on the random effects (66).

156

For generalized linear mixed models (GLMMs), one models a function of p, known as the link function, g(p), in relation to any (fixed or random) variables that may be affecting the expected probability. For notational convenience, the symbol  is equated to g(p), where  is known as the linear predictor. Several choices for the link function are possible, and the logit is the most common for proportion data. However, we used the complementary log-log link [CLL(∙)], given as CLL(p) = ln(-ln(1-p)). This link function was chosen because Paul et al. (61) previously showed that there was a linear relationship between the CLL transformation of FHB spike incidence and the CLL transformation of

FHB field severity (the proportion of wheat spikes with symptoms), known as disease index by many FHB researchers. Hughes et al. (30) also gave a more theoretical foundation for the relation between the CLL of incidence and CLL of severity. Based on the above definitions, one can write the equalities as:

g(p) = CLL(p) = ln(-ln(1-p)) = .

The inverse link function is used to determine p from a given value of ; the inverse link is given generically by g-1(). For the CLL link, one can then write:

p = g-1() = 1 – exp(-exp()).

With the hierarchical sampling design, we use the subscripts i, j, and k to label the county, field, and site, respectively. Yijk, nijk, and pijk represent, respectively, the number of the diseased spikes, number of assessed spikes, and the expected conditional probability of a spike being diseased for the k-th site of the j-th field of the i-th county.

The corresponding link function and linear predictor are given as g(pijk) and ijk, respectively.

157

Data analysis—model fitting. Spatial variability was characterized by fitting a

GLMM to the incidence data in the spatial hierarchy. In the model, Ci represents the effect of the i-th county, F(C)ij the effect of the j-th field within the i-th county, and

S(FC)ijk the effect of the k-th site within the j-th field within the i-th county on the linear predictor. County, field, and site were considered to have random effects on the linear predictor; variability was quantified through the variances of the random effects. The random effects were assumed to have normal distributions with means of 0, and constant

variances of , , and , respectively, for county, field within county, and site within field and county. The model for the linear predictor is written as:

g(pijk) = ηijk = μ + Ci + F(C)ij + S(FC)ijk (1) where μ is the overall expected value (mean) on the CLL link scale (―intercept‖), and other terms are as defined above.

Using the inverse link function, the expected probability of a spike being diseased conditional on the three random effects of county, field, and site is given (for a CLL link) by:

-1 pijk = g (ηijk) = 1-exp(-exp(ηijk)) (2)

One can also write

pijk = E[Yijk/nijk | Ci + F(C)ij + S(FC)ijk] to show that pijk is an expected value conditional on the ijk-th random effects. The number of diseased spikes in the model, Yijk, has a binomial distribution conditional on the random effects; this is equivalent to stating that Yijk has a conditional binomial distribution. That is, one can write: Yijk ~ Bin(pijk, nijk). The so-called marginal distribution of Yijk has no explicit mathematical form in a hierarchical GLMM (74), but will have a

158 variance larger than a marginal binomial distribution if any of the random-effect variances are larger than 0. The entire model can be written as:

g(pijk) = ηijk = μ + Ci + F(C)ij + S(FC)ijk

Ci ~

F(C)ij ~ (3)

S(FC)ijk ~

-1 pijk = g (ηijk)

Yijk ~ Bin(pijk, nijk)

As a special case, if there was only one field, there would be no C or F(C) terms, and the random effect would simply be Sk; if the link function was the logistic instead of the CLL, then equation 3 would correspond to the logistic-normal-binomial model in

Hughes and Samita (33).

Equation 3 was fitted to the FHB incidence data using maximum likelihood with the GLIMMIX procedure in SAS. The integral of the likelihood over the random effects

(required for ML estimation) is mathematically intractable for this type of GLMM (50), so it was numerically approximated with a Laplace function in the estimation procedure

(using the method=laplace option in GLIMMIX) (64,69). Fitting equation 3 to data from a single year can take up to several hours of computer time, depending the speed and memory of the computer, and options regarding the tests for the random effects. From the fitted model, one obtains estimates of  and the three variances, estimated asymptotic standard errors of these terms, and the solutions of the effects of each county ( ), field

within county ( ), and site within field and county ( ). Because county, field, and site are random effects, the solutions are known as predictors; specifically, the 159 predictors from the model fit are known as estimated best linear unbiased predictors

(estimated BLUPs or EBLUPs) (42). Because the expected values of the random effects are 0, by definition, is an estimate of the linear predictor at the means of the random effects, and

(4) is the estimated (overall) probability of disease at the means of the random effects.

The significance of the random effects was determined with a likelihood ratio test

(69), which consists of a difference in two log-likelihoods (for the model with and without the random-effect term). Under the null hypothesis of no effect, the test statistic has a sampling distribution involving a weighted mixture of chi-square distributions (69).

Moreover, likelihood ratio tests were performed to test the null hypothesis that ,

and the null hypothesis that . Profile confidence intervals were calculated for each of the random-effect variances. This is the most computationally demanding part of the analysis. All testing of the random effects and determination of the profile confidence intervals were done using the covtest statement in the GLIMMIX procedure (69). This procedure automatically determines the weighted combination of chi-square variables for hypothesis testing.

Because the fungicide usage was a criterion for selecting fields in 2011, the

GLMM was generalized to account for possible fungicide effect on the overall linear predictor (µ). In particular, a fixed-effect factor was defined, with two levels (µl; l = 1, 2), for the effects on the linear predictor of fungicide or no fungicide use. Using µl instead of

µ, equation 3 was fitted to the data using maximum likelihood. An F test was used to determine the effect of fungicide. 160

County (or field) level predictions. For each of the 10 years, the linear predictor for each county was determined as . This is the (estimated) linear predictor at the means (0) for the other random effects. Because is an EBLUP, is also an

EBLUP. In terms of inference, this expression for the linear predictor is for a broad inference space (52). Similarly, the broad-inference EBLUP for field within county is

given as . The EBLUP for the expected probability of disease for county i, conditional on the fields and sites within the county being at their expected values, is given for each county by

(5)

The expression after the last equals sign applies strictly for the CLL link function.

Estimated standard errors for EBLUPs obtained from the inverse link are determined using the delta method (58,69). From use of equation 5, the percent of counties with probabilities of disease greater than 0.05 (> 5% incidence) was also calculated for each year.

EBLUPs for specific fields can be obtained in an analogous manner. That is, the estimated probability of a spike being diseased in field j of county i is given by:

The GLMM outlined above can be used as one form of a so-called ―small area model‖ (65). When a domain (e.g., area on a map) is considered to be large in a sampling context, direct estimates of the variable of interest (such as a simple arithmetic averages of the proportion of diseased spikes) have adequate precision. When a domain is considered ―small‖, indirect or synthetic estimates of the variable of interest have greater

161 precision. Because EBLUP for a domain such as a county is based on all the data

(through the model fitting), and not just on the data from the single domain, county-level

(or field-level) EBLUPs are considered to be ―indirect estimators‖, ―synthetic estimators‖, or ―model-based estimators‖ (65). In one sense, the EBLUP county values are shrunken (less extreme) compared to sampling-design-based fixed-effects estimates of disease. This is analogous to the county random-effect values being regressed towards the overall mean based on the magnitude of the random-effect variances (42). For county

EBLUPs, the shrinkage increases with decreasing . This makes the EBLUPS more robust, stable, and precise than direct calculations of incidence. Based on the county

EBLUPs, the Spearman rank correlation (r) was calculated between pairs of adjacent years. When there is spatial autocorrelation, the usual (unadjusted) P values for significance of r will be lower than the true P value (16).

The possible effects of geographical location, corn and wheat acreage per county, and environmental conditions on the linear predictor for each county were also examined.

This analysis shows if the county-level variability is due, in part, to these covariables.

Geographical location was expressed as the latitude and longitude of the center of each county and was used as a possible effect to see if there were N-S or E-W trends in disease incidence within Ohio. Area of land within each county with corn and wheat, expressed in absolute area (hectares) or as a proportion of the total land in the county, were also considered. The previous year’s corn and wheat acreage was investigated since inoculum is produced on infected or infested corn and wheat (59), and increasing abundances of these crops may lead to higher amounts of crop residue and subsequent inoculum production in the region the following year (38). The current amount (present year) of

162 wheat in the county was considered because it could reflect the level of inoculum in the area. All acreage values were collected from the National Agricultural Statistics Service

(www.nass.usda.gov).

Environmental variables were calculated based on data collected from automated weather stations (maintained by the National Climatic Data Center or the Ohio

Agricultural Research and Development Center) in or very near each county. Based on availability of data and previous results (40), only two weather variables were calculated based on temperature and precipitation. Total daily precipitation (TotalP) over a 30-day window and total daily precipitation when average daily temperature was between 15 and

30°C (TempP) were considered. TotalP and TempP were found for each county for 30- day windows. The start and end time of the 30-day window, and the exact form of the covariable used in the analysis was derived in the following manner. Disease rating data for Wooster, Ohio (which was on a scale from 0 to 9) from Kriss et al. (40) over 46 years was used in a logistic regression procedure, where years with a rating of 0, 1, or 2 were considered to have low disease and all other years were considered to have high disease.

A window-pane analysis (40) was used on the weather variables from one weather station in Wayne County, Ohio, to determine the ―best‖ 30-day window over the growing season. This is similar to the previous analysis in Kriss et al. (40), except that in the published article, nonparametric correlation analysis was used instead of logistic regression. The best-fit logistic model for both TotalP and TempP was the window from

May 17 to June 15, which covers the time of anthesis throughout the state. The resulting logit functions were logit = -5.57 + 0.04(TotalP), and logit = -4.15 + 0.04(TempP). The logit functions for risk based on environment (i.e., the left-hand side of these two logistic

163 equations) were used as the covariables in the GLMM for the spatial heterogeneity.

Adjustments to the starting dates of the 30-day window had to be made because anthesis time varies within the state, especially from south to north. The average anthesis date was approximated for each county, relative to anthesis in Wayne County, based on reports from the surveyors or from reports on nearby counties. In general, counties in the southern part of the state were given 30-day windows earlier in the season, and northern counties were given 30-day windows later in the season.

This covariance analysis was based on fitting an expansion of equation 3 to the data for each year using maximum likelihood. The intercept parameter  was expanded to

i, and expressed as i = Xi, where Xi is one the covariables for the i-th county.

Significance was determined using Student t statistics for each estimated  parameter.

Intra-cluster correlations. Measures of the relationship of mean disease incidence (on CLL scale) among sites within fields and counties, and the disease status of wheat spikes within sites (within fields and counties), were made through the use of different versions of the intra-cluster correlation coefficient (ICC). One first defines the total variance on the CLL-link scale as:

The ϕ ICC indicates the degree of similarity of the link function of expected conditional probability of disease (a continuous variable) of sites within fields and counties. This ICC is given by:

(6)

164

ϕ can also be thought of as the proportion of the total variance that comes from the differences between the fields and counties. When ϕ is near 1, sites within the same field and county tend to have a very similar level of CLL(pijk) (relative to the total variability over the multiple scales of data in the hierarchy). When ϕ is near 0, sites within the same field and county tend to have very different values of CLL(pijk). Estimates of the variance parameters are substituted for the theoretical values here.

With discrete distributions for disease incidence, interest is often on the intra-class correlation () of the disease status of individuals within sampling units such as sites, which depends on the variability of the number of diseased individuals among the sites

(6,18,82). With a (marginal) binomial distribution,  = 0, which indicates that the disease status of individuals is independent; with this situation, it is often stated that the disease is random. As the degree of heterogeneity among sites increases, the probability that the disease status of any two individuals is the same within a site increases; the increase is in direct proportion to  (68). The parameter  is greater than 0 when the beta-binomial distribution (with  > 0) or a GLMM with nonzero site variance describes the data (2,46).

With conditional modeling of discrete data with a non-identity link function, as done here using GLMMs (with the LNB distribution being a special case for a single field when the logit link is used), there is no exact expression for  because the modeling is on different scales. That is, the variance terms are for the variation in the linear predictor (), which is on the scale of a link function (in our case, the CLL link). In contrast,  is on the scale of the binary observations for disease status (diseased or healthy). As shown in equation 2, p

165 is a nonlinear function of , which means that the variance of pijk can only be approximated based on large-sample theory (37).

There are several different approaches taken to approximate the estimated  for hierarchical GLMMs (6,18,70,82). Most of the work has been focused on the two-scale problem, such as multiple sampling units in a single field (82), and we generalize one approach for multiple scales. One method ignores the nonlinear relation between p and , and also assumes that the binary observations within sites are a manifestation of an underlying ―latent‖ continuous random variable (22). The other general method explicitly accounts for the nonlinearity of the link function (82), and treats the within-site variable

(the individual spike, in our case) as being strictly Bernoulli (a special case of binomial with a sample size of 1) (70,83). We follow this second general approach.

If the variance of ijk is given by , then, based on the delta method (37), the

variance of the random variable pijk can be approximated by

, where is the inverse-link function [i.e., ], and is the first derivative of the inverse link function (82) with respect to . Note that the inverse- link and its first derivative are calculated here at the overall value of the linear predictor

(when all random effects are at their expected value of 0), which is the  term in equation

3 (i.e., when  = µ). This approximation, which is derived using a Taylor series expansion, is usually accurate unless the variance is very large. For the CLL link, the variance on the incidence scale is specifically

166

Here, p is determined from the inverse link of  in equation 3. Following Murray (55),

Goldstein et al. (22), and Browne et al. (6),  can be written as:

(7)

where p (no subscript) is the overall probability of disease, and p(1-p) is the theoretical variance for a Bernoulli distribution. Some authors prefer to call equation 7 a variance partition coefficient (VPC). For the specific case of the CLL link function, and three levels to the spatial hierarchy,  is approximated as:

(8)

One substitutes the estimate of the variances and p when estimating ρ from a fitted model.

RESULTS

Heterogeneity at multiple scales. The GLMM in equation 3 was successfully fitted to the FHB incidence data for each of the years using maximum likelihood. From the fitted model, the overall estimated mean on the complementary log-log (CLL) scale

( ), the variance parameter estimates for the three levels of the hierarchy ( , , ), and the estimated asymptotic standard errors of these parameters were obtained. Results were for years with as few as 12 counties or as many as 32 counties (Table 5.1); the average number of fields surveyed per county did not vary much over the decade of disease assessments. Across the 10 years investigated, there was a wide range in the estimated overall mean CLL; was lowest in 2005 (-5.81) and highest in 2010 (-1.92) 167

(Table 5.1). In 2011, the estimated mean of fields treated with a fungicide was significantly lower than the estimated mean of fields that were not treated. Based on the inverse link function (equation 4), estimated state-wide mean incidence (more explicitly: estimated overall probability of a spike being diseased times 100) ranged from <1% to about 14% (Table 5.1).

Even though the estimated state-wide mean was very different among the years, spatial heterogeneity at each level in the hierarchy (county, field within county, and site within field and county), as characterized by the three variances in equation 3, had similar values over all the years (Table 5.1). This can also be seen by the point estimates and the

95% profile-likelihood-based confidence intervals for the variances shown in Figure 5.1.

Across the years, the estimated variances at each level had the same order of magnitude, and the confidence intervals had a large degree of overlap for each variance. The width of the confidence intervals for the variances depended, in part, on the number of observations (e.g., number of counties), and generally increased with the magnitude of the point estimates of the variances. As expected, the confidence intervals were not symmetrical, because the sampling distributions of estimated variances are known to be skewed at finite sample sizes (54). There was no apparent trend in the magnitude of the variance estimates with year.

In all years, based on the likelihood-ratio test results, the variances for counties and fields within counties were significantly different from 0 (Table 5.1), which indicates that heterogeneity at these levels was greater than expected for a binomial (―random‖)

distribution. In 8 of the 10 years, the point estimate of the county variance ( ) was

similar to the point estimate of the field-within-county variance ( ). Only in 2007 and

168

2010 was the point estimate of the variance at the county level significantly higher than at the field-within-county level (Table 5.1). The magnitude of the point estimates of the variances at the two higher scales was considerably greater than the magnitude of the point estimates of the variances for sites within fields and counties (Fig. 5.1; Table 5.1).

In no year was the estimated variance for sites within fields and counties greater than the

other estimated variances (Table 5.1). Only in 2007 was close to , and this was a year in which the estimated county variance was much larger than other others. In 3 of the 10 years (2006, 2008, and 2009), the variance among sites within fields and counties was not significantly greater than 0. For these 3 years, conditional on the field and county, there was only binomial variation in disease incidence within the fields.

County-level predictions. Based on the solution from the fit of equation 3 to the

data, the predicted probability of disease on the CLL link scale ( ) was determined for each county of each year (Table 5.2). Over all years, county-level

EBLUPs on the CLL scale ranged from -7.42 to -0.44. Based on the inverse link

(equation 5), the predicted expected (conditional) probability of disease for the counties ranged from 0 to 0.47. The percent of counties with an estimated probability of disease greater than 0.05 ranged from 0 to 88%. The magnitude of the county EBLUPs within a

year (and, hence, the estimated probabilities of disease) depended on and  (the latter

determining ), and the range of EBLUPs within a year was a function of  (see Table

5.1). For instance, the range from the minimum to maximum county EBLUP was largest

for 2007 and 2010, which had the two largest values (1.53 and 0.83, respectively

[Table 5.2]), and was smallest for 2002, 2006, and 2008, which had the three smallest

values (0.37, 0.32, and 0.40 [Table 5.2]). Because of the nonlinear relation between 169 the conditional probability of disease and the EBLUP, the range in estimated diseaise

probabilities within years had a much more complex relation with the  values (Table

5.1).

In comparison, the field-level EBLUPs ( ) ranged from 0 to

0.71, and, as required with a nonzero variance for fields within counties, the range was wider in each year compared to the county-level EBLUPs (Table 5.2). The percent of fields with an estimated probability of disease greater 0.05 ranged from 0 to 86%, with the percentage proportional to (or ).

The county-level EBLUPs each year were mapped to investigate the spatial arrangement of predictions of FHB across the state for the different years (Fig. 5-2).

Results are shown on the CLL link scale because the model for heterogeneity was fitted on this scale; moreover, if the results were graphed on the incidence (probability) scale

(using the inverse link), a different scale of variation would be required on the map for each year (because the variability on a probability scale depends explicitly on the magnitude of the probability [45]). The EBLUPs were also centered at the estimated µ for each year in the maps (so that only is shown) in order to be able to directly compare the county-level heterogeneity (without confounding by the magnitude of CLL [or it’s inverse link]) across years in the same figure. For some years, there was some apparent clustering of counties with similar EBLUP values (or corresponding values of incidence).

For instance, in 2010, one can see a large group of counties with predominantly high

EBLUPs in the western region of the state, with groups of counties in the north and south with lower EBLUPs (Fig. 5-2). In most years, there also were situations where there were high ( ) and low ( ) EBLUPs in adjacent counties, or a low EBLUP 170 county surrounded by high EBLUP counties, or a high EBLUP county surrounded by low

EBLUP counties (Fig. 5.2). As an example, Defiance County in northwestern Ohio in

2011 had a very high EBLUP (blue) which was surrounded by low EBLUP counties

(red).

There was no consistent temporal pattern to the county EBLUPs, and the location of the highest or lowest EBLUPs changed from year to year. That is, a county with a large EBLUP in one year could have either a large or small EBLUP the following year

(Fig. 5.2). Consider Highland County, the southernmost county surveyed from 2007 through 2011. The EBLUP was very negative (i.e., the CLL link and corresponding disease incidence was considerably below the overall mean) in 2007 and 2008, but was moderately high in 2009, moderately low in 2010, and very high in 2011. The lack of consistency was confirmed by the Spearman rank correlation (r), which are given on the lower right corner of each map in Figure 5.2. The correlations were generally all low, and the point estimate could be either positive or negative. None of the estimated correlations were significantly different from 0 (P > 0.10).

Several covariables were investigated to determine if location or county-scale environmental or agronomic variables were associated with the among-county heterogeneity in the linear predictor. No covariable had a significant effect in the majority of years (Table 5.3). Latitude and longitude were significant in just two of the 10 years

(but not the same years), and the sign of the parameter estimate ( ) was different in the two years with significant results. Neither of the two considered environmental variables was ever significant. Corn acreage the previous year was not significant in any year, and wheat acreage the previous or present year was not significant in at least 70% of the

171 years. With wheat acreage per county, the sign of the estimated parameter was not consistent. Thus, given the variability of the linear predictor within counties (Table 5.2), the county-level covariables were likely to be at too coarse of a measurement scale to account for the variation among counties.

Intra-cluster correlations. The estimated intra-cluster correlations (ICC) for the similarity of disease incidence on the CLL link scale among sites within fields and counties ( ) were very high (Table 5.1) for all years. Most estimates were close to 1. As indicated by equation 6, this is because of the very small estimated site within field and

county variances ( ) relative to the county and field within county variances for each year. This shows that in each year, sites within the same field and county tended to have a very similar level of the CLL link of the expected probability of disease. That is, disease incidence for the sites, on a CLL scale, were very similar relative to the variability of disease across fields and counties.

The estimated intra-cluster correlation of disease status of individuals within the sampling units ( ) was generally small. This is partly because is positively related to the magnitude of the variation in expected values of incidence among the sampling units

(such as sites) (28,46,47). Because of the low values (Table 5.1) in most years,

(equation 8) was generally small. The values indicated that for most years, spikes within the same site were somewhat more likely to share the same disease status relative to spikes from other sites, fields, or counties. For all years except 2005 and 2007, was between 0.02 and 0.13. Although these values are not large, they do indicate that the disease status of spikes within sites is not random (as defined by the binomial distribution

[where = 0]). The magnitude of is also a complex function of p (see equation 7) (26), 172 but is low at values of p near 0 and 1 for any given value of total variance (on the link scale). In 2005 and 2007, because the estimated overall probability of disease ( ) was very low, the values of were very close to 0.

One can also estimate conditional on the individual field and county ( ). Then,

the total variance in equations 7 and 8 would simply be: . For this situation, the conditional intra-cluster correlation coefficient was very close to 0 whenever the site variance was at or near 0, such as in 2006.

DISCUSSION

There is great interest in several disciplines to assess the incidence and risk of disease in a spatial setting. For instance, disease mapping has been used to estimate incidence of human, animal, and plant diseases over different spatial scales (20,60,77).

The occurrence of disease and magnitude of disease incidence (or other variable of interest) at various locations is directly tied to the heterogeneity of the response variable

(26). This heterogeneity is the outcome of an array of biological and physical factors that operate over a range of spatial and temporal scales (23). Thus, multiscale methods have been given considerable attention in some disciplines in recent years (43). For the specific objective of investigating disease incidence within a spatial hierarchy, there are several approaches that can be taken (57), and our approach was built on the use of generalized linear mixed models (GLMMs) for representing variation in incidence at multiple levels.

173

Generalized linear models have been successfully used for characterizing heterogeneity of plant disease incidence when there was only one level to the variation

(among sampling units), plus the implicit (conditionally Bernoulli) variation of the binary observations within each sampling unit (32). Expansion to larger scales (multiple fields) has been done in a fixed-effects setting, without additional variance terms (33). Others have considered the variation at multiple hierarchical levels in single fields as random effects (49,63), but the interest was in the treatment effects on disease, and the variances were considered nuisance parameters in order to properly estimate the effects of the treatments. GLMMs with multiple random effects have also been successfully used in the analysis of animal disease incidence for several spatial scales (15,51). In these studies, and in the Piepho (63) and Madden et al. (49) reports, quasi- or pseudo-likelihood methods were employed in model fitting, precluding direct inference on the variances based on the magnitude of the likelihood. Here we were able to use new maximum likelihood computational methods (64,69), with the corresponding likelihood-based procedures for inference, to more directly characterize the variances at three different scales, a primary objective of our investigation. Laplacian approximations to the likelihood may still produce biased parameter estimates (64), but substantial bias typically only occurs when the number of observations at the lowest level in the hierarchy

(e.g., number of spikes per site) is very small, with n = 1 being the extreme [so that each cluster (e.g., site or sampling unit) can only take on one of two values] (36). Laplacian methods are often less biased than pseudo-likelihood methods, and the bias is typically very small with small-to-moderate variances and large number of observations per cluster at the lowest level in a hierarchy (e.g., number of spikes). With variances typically less

174 than 1 (Table 5.1) and n (more specifically nijk) typically being around 45, bias is not of concern.

Even though overall mean disease incidence varied substantially over the 10 years of observations (Table 5.1), heterogeneity was fairly consistent based on the estimates of the three variances (see Fig. 5.1), with a large degree of overlap of the confidence intervals for each variance across years. There was relatively large and highly significant spatial heterogeneity on the CLL-link scale among counties and fields within counties, and much lower heterogeneity among sites within fields and counties each year.

Moreover, point estimates of the county variances tended to be larger than the field- within-county variances in several years, although the county variance was only significantly larger in two of these. This ordering in the variance estimates in a spatial hierarchy has been found in other studies (78). However, the ranking of variances for the levels is not inevitable for spatial data; in fact, the opposite has also been found in the plant and animal sciences. For instance, based on a survey for the incidence of Phomopsis cane and leaf spot of grapes and the use of a linear mixed model (with transformed incidence), Nita et al. (57) found the largest variances were at the lowest spatial scale considered (shoots within vines), with variances decreasing as the scales increased

(shoots within vinesvines within fieldsfields within farmsfarms within regions). In addition, McDermott et al. (51) investigated the incidence of cows with antibodies to the bovine rhinotracheitis virus, and found the greatest variability at the lowest spatial scale evaluated (among farms within areas and districts).

The variability among higher-level domains — fields (and counties) — dominated in the partitioning of the total variance each year. Wilhelm and Jones (86) also indicated a

175 high variability in FHB incidence among fields in their study over 2 years in spring wheat fields in Minnesota. They were able to associate some of the variability to the previous crop grown in the fields, but also suggested, as we do here, that there are several field- level factors likely contributing to the heterogeneity between fields. These include planting date, anthesis date, variety, tillage, weed control, and fertilizer use. These field- scale variables were not available or known with our investigation, but we expect they vary broadly across the fields and counties. In contrast, we expect less variation in these variables among sites within fields, resulting in a lower among-site variance (relative to the others), as found here. Measures on the heterogeneity at the site level have been used to link disease incidence with type of dispersal (airborne or rain-splash) (13,32).

The variability among units or domains (sites, fields, counties) can be directly interpreted in terms of the similarity of the response variable within the units, as quantified by one of the intra-cluster correlations (ICCs) (10). Over each of the years, we found a very high similarity in the (estimated) expected probability of disease on a CLL- link scale for the sites within fields and counties, as measured by  (equation 6). This was because of the relatively low among-site variance relative to the variances for the higher levels (Table 5.1).  is based on the partitioning of the total variances on the scale of the linear predictor (), and shows the proportion of the higher-level variances relative to the total. This version of the ICC has frequently been estimated for multi-level spatial studies, and is applicable whether a linear mixed model for continuous data or GLMM for discrete or continuous data is used for analysis (18,83). However, only methods designed strictly for discrete data can be used to characterize the similarity of individuals within the lowest level of a hierarchy. Here we used the  ICC of equation 8, based on the 176 results of the fitted GLMM, to quantify the disease status of wheat spikes within sites within fields and counties. Estimates of  were small, but nonzero, which is consistent with a high . This is because for a fixed p, increasing similarity of expected values of disease among the sampling units (and, hence, decreasing site variance) leads to decreasing similarity of individuals within sampling units (31). Although  estimates were not large, their magnitude must be considered in the context of the size of the sites

( , mean number of spikes per sampling unit). For the general situation with discrete data, the observed variance of the number of diseased individuals, Y (suppressing subscripts for convenience), can be written as var(Y) = var(Y)bin∙deff, where var(Y)bin is the variance of Y if it had a binomial distribution, and deff is known as the so-called design effect (29,39), which reflects the overdispersion (extra-binomial variation) of the random variable. The design effect can be written as: . With a mean of 45 spikes per site, even small  values can have a large influence on deff, and hence, on the observed variation. For instance, deff = 2 is achieved with  ≈ 0.02, and deff

= 3 is achieved with  ≈ 0.05. Thus, the estimated  values in our investigation were sufficient to have a clear effect on the degree of overdispersion. It should be noted that others have found that  decreases as the size of the sampling unit (i.e., n) increases

(24,48). This is not surprising because as the size (i.e, n) of the sampling unit becomes larger, there is more ―room‖ for heterogeneity within the units such as sites.

The estimates of  in Table 5.1 are approximations because the variances used in equation 7 were on the CLL-link scale but the ICC is on the scale of the binary variable

(83). There is no agreed-upon preferred approximation method for  when GLMMs are

177 fitted to data, and limited comparison of approximations do not shed any light on which approach is best (most accurate). We compared several of the published approximations for  (11,55,70), and the estimates were of the same order of magnitude to those given in

Table 5.1 (Appendix B), which means that interpretation was not influenced by the use of equation 7. The estimated  for each year should also be considered a type of composite or ―average‖ correlation of disease status of spikes across the domains in the data set for two reasons. First,  depends on the value of p and the site variance (equation 7 or 8), and we estimated  only for the overall p for each year (based on the inverse link of the estimated  [Table 5.1]), which is the standard approach for calculating . Second, because the degree of heterogeneity among sites within fields likely depends on the field, the estimated site variance in equation 3 is also a type of composite variance for the linear predictor within fields. If our objective were to characterize the degree of overdispersion in individual fields, as is done often in epidemiology (13,17), we would have needed at least 20-30 sites (29) in order to obtain precise variance estimates for each field. In contrast, our objective was to determine the overall level of heterogeneity for each of the three levels in the hierarchy.

In addition to focusing on the spatial process at the lowest level in the hierarchy, through the ICC, one can use the GLMM-fitting results to focus on the higher-level domains through the empirical predictions (the EBLUPs) for county, field, or even individual site. As discussed in the Methods, these EBLUPs (―synthetic estimates‖,

―small area estimates‖) are often more precise (lower mean square error) than other

―estimators‖ of domain means (such as direct estimators [arithmetic averages]) because they ―borrow strength‖ from the other domains through the process of model fitting. 178

Small-area estimation techniques have been used extensively in many disciplines (34), and have even been used to predict the wheat and corn acreage in individual counties

(65), variables we considered in the covariance analysis. Because of their precision,

EBLUPs can also be used in ―hot spot‖ detection for unusually high values of a risk-type random variable (56) in a spatial setting. The EBLUPs for counties in Figure 5.2 show the considerable spatial heterogeneity in FHB incidence over the decade of observations, and hot spots could be identified each year by the EBLUPs larger than 1, for instance.

However, county EBLUPs were not generally related to geographic location in any given year (based on the analysis of covariance), or to the other county-level covariables in the large majority of years. Moreover, despite the temporal patterns to (or corresponding

) over the decade, the high hot spots (or the low ―cold spots‖), relative to were not found in the same counties over successive years. County borders are obviously based on political decisions, not on agronomic, landscape, or climate factors. However, for policy reasons, there is direct interest in the incidence or risk of disease for these political domains. Because of the high variability of FHB within counties, at about the same level as among counties, and the county-scale coarseness of the measurements of the covariables, it is not surprising that there was no clear factor that influenced the among- county heterogeneity. In a future investigation, field-scale measurements of the covariables (local weather, local density of wheat and corn, etc.) could be obtained to determine if use of these covariables in the model would have an effect on the estimated variances.

Knowledge of the variances at multiple levels in a hierarchy is of direct value in the development of sampling protocols (46). With linear mixed models, there are well-

179 developed methods for determining optimum number of observations at each level in the hierarchy (e.g., number of sites) to estimate (with a desired level of precision) the overall fixed effect parameter in the model for the linear predictor () (4,7). A similar approach could be taken, with little difficulty, with the use of a GLMM for estimating the overall fixed effect parameter, but the linear predictor would be on the scale of the link function.

The link is often chosen for strictly statistical reasons, not biological ones, so the variances of the linear predictor in a GLMM do not automatically have a direct physical interpretation (75). However, because of the previously shown empirical and theoretical linear relationship between disease severity and incidence on a CLL scale (30,61), there is a more direct interpretation of the magnitude of the different variance estimates that is of relevance for prediction and estimation of fixed effects. Thus, one could estimate sample sizes at each of the levels at the scale of the linear predictor in equation 3 using standard methods. The alternative is to approximate the variances on the inverse-link scale, but this would complicate the calculations because, in part, the variances are then functions of disease incidence. For both approaches, results depend on the size of the sampling site used in the original data collection (~45 spikes).

However, in terms of sample size calculations, the precise estimate of  for the entire state (or p from the inverse link function) is only of partial interest. Of greater interest for policy makers would be sample sizes for the EBLUPs (small-area estimates) of individual counties, or EBLUPs of fields. For instance, one could estimate the optimum number of fields and sites per field, of a given site size (n), to obtain county

EBLUPs with a desired precision (standard error). Because of the complex formulae for

EBLUPs (34), especially with unbalanced designs, such an approach would likely require 180 numerical rather than analytical solutions. This area merits further investigation for prediction of disease using EBLUPs in a spatial setting.

In conclusion, there was generally consistent heterogeneity of FHB incidence—on a CLL-link scale—at multiple spatial scales over the time frame of a decade, with the lowest level of heterogeneity at the lowest scale in the hierarchy. Our results were based on the use of frequentist statistical methodology founded on the fitting of the GLMM in equation 3 using maximum likelihood. Other approaches could be used for fitting this or similar GLMMs (34). For instance, explicit spatial correlation between counties or fields could be modeled by using a more complex variance-covariance structure for Ci or Fij based on spatial separation of the domains (73). Preliminary analysis revealed little evidence of spatial correlation of the county effects (unpublished). With a different statistical philosophy, fully Bayesian approaches (in contrast to empirical Bayesian approaches) are becoming quite popular to fit GLMMs (such as equation 3) to data, with either vague or informative prior distributions for the parameters. Although most

Bayesian analyses are now done using MCMC sampling of a posterior distribution, a computer intensive procedure, some approaches also use a Laplacian approximation to simplify calculations (19). With vague priors, Bayesian methods can result in similar point estimates of the parameters for linear models or GLMMs (5) as the frequentist approach, although the estimated standard errors typically are different. With informative priors, parameter estimates can be substantially different from those obtained with the frequentist approach, depending on the prior that is specified. In the current context, one could formulate a prior distribution for the variances based on the estimates in previous years, which could produce more precise estimates of these terms for the next year’s data

181

(assuming the prior is appropriate). Bayesian analysis has also been shown to be useful for calculating confidence intervals for ICCs (82). Future research will focus on spatial correlation modeling using GLMMs and Bayesian approaches, as well as use of statistical diagnostic tools (1) to evaluate the appropriateness of model assumptions, in order to gain a more complete understanding of the spatial heterogeneity of FHB.

182

Table 5.1. Structure of the data for 2002 to 2011 with estimated mean disease incidence (complementary log-log (CLL) scale ( ) and original

incidence scale ( ) with standard errors) and estimated variances (and standard errors) from the generalized linear mixed model for county ( ),

field within county ( , and site within field and county ( ) for incidence of Fusarium head blight in Ohio over 10 years with measures of the intra-site correlation Range (mean) χ2 χ2 Number of number of ( - ) ( - ) Year b c d e f g counties fields per county 2002 30 1 – 10 (5.3) -3.69 (0.14) 0.025 (0.003) 0.369 (0.145) 0.774 (0.125) 0.112 (0.023) 3.01 70.60* 0.911 0.030 2003 31 1 – 10 (4.8) -2.89 (0.16) 0.054 (0.008) 0.647 (0.207) 0.515 (0.081) 0.075 (0.012) 0.38 87.26* 0.940 0.063 2004 19 3 – 15 (6.1) -2.30 (0.17) 0.095 (0.015) 0.458 (0.173) 0.296 (0.052) 0.070 (0.012) 1.05 38.66* 0.914 0.073 2005 23 1 – 10 (5.2) -5.81 (0.21) 0.003 (0.001) 0.611 (0.300) 0.575 (0.173) 0.391 (0.129) 0.01 0.73 0.752 0.005 -7 -18 183 2006 17 4 – 11 (5.6) -3.26 (0.01) 0.038 (1∙10 ) 0.318 (0.142) 0.451 (0.086) 3∙10 (0.015) 0.51 82.59* > 0.999 0.028

2007 12 3 – 10 (5.6) -5.32 (0.39) 0.005 (0.002) 1.526 (0.895) 0.253 (0.117) 0.229 (0.105) 6.03* 0.02 0.886 0.010 2008 20 2 – 12 (5.1) -3.58 (0.16) 0.027 (0.004) 0.399 (0.154) 0.357 (0.076) 0.020 (0.020) 0.06 39.29* 0.975 0.021 2009 21 2 – 6 (4.6) -3.78 (0.21) 0.023 (0.005) 0.755 (0.281) 0.424 (0.090) 0.013 (0.017) 1.81 52.35* 0.989 0.026 2010 32 1 – 7 (4.5) -1.92 (0.17) 0.136 (0.021) 0.826 (0.227) 0.236 (0.037) 0.045 (0.006) 15.99* 76.43* 0.959 0.131 2011 27 2 - 10 (5.3) -2.59 (0.18)a 0.072 (0.012) 0.619 (0.202) 0.481 (0.075) 0.085 (0.012) 0.47 78.25* 0.929 0.060 a Results shown are for ―no fungicide‖ use for the control of Fusarium head blight. Results for ―fungicide‖ use are: , , and . b Standard error of the inverse CLL estimate was based on the delta method. c In all years, was significantly greater than zero (P < 0.005). d In all years, was significantly greater than zero (P < 0.005). e was significantly greater than zero (P < 0.01) in all years except 2006 (P > 0.999), 2008 (P =0.153), and 2009 (P = 0.203). f An intra-cluster correlation indicating the degree of similarity of the CLL link of expected probability of disease of sites within fields and counties as calculated from equation 6. g An intra-cluster correlation indicating the degree of similarity of the disease status of wheat spikes within sites as calculated from equation 8. * indicates significant at P < 0.05.

Table 5.2. Estimated best linear unbiased predictors (EBLUPs) at the county and field levelsa

County Field

Year CLL: proportion: 5%b CLL: proportion: 5%

2002 -4.87 ↔ -2.80 0.01 ↔ 0.06 13% -5.95 ↔ -0.54 0.00 ↔ 0.44 25%

2003 -4.55 ↔ -1.74 0.01 ↔ 0.16 58% -5.52 ↔ 0.21 0.00 ↔ 0.71 50%

2004 -3.62 ↔ -0.93 0.03 ↔ 0.33 84% -4.43 ↔ -0.10 0.01 ↔ 0.60 86% 2005 -6.84 ↔ -4.56 0.00 ↔ 0.01 0% -7.10 ↔ -2.80 0.00 ↔ 0.06 0%

2006 -3.83 ↔ -2.21 0.02 ↔ 0.10 29% -4.87 ↔ -1.16 0.01 ↔ 0.27 43%

18 2007 -7.42 ↔ -3.67 0.00 ↔ 0.03 0% -7.49 ↔ -3.26 0.00 ↔ 0.04 0%

2008 -4.42 ↔ -2.46 0.01 ↔ 0.08 15% -5.34 ↔ -1.87 0.00 ↔ 0.14 29%

2009 -5.30 ↔ -2.44 0.00 ↔ 0.08 14% -6.00 ↔ -1.16 0.00 ↔ 0.27 26% 2010 -4.11 ↔ -0.44 0.02 ↔ 0.47 88% -4.55 ↔ -0.04 0.01 ↔ 0.62 85%

c 2011 -3.89 ↔ -1.46 0.02 ↔ 0.21 70% -4.19 ↔ -0.35 0.01 ↔ 0.51 69% a Shown for the linear predictor ( or which is based on the CLL link function, and for the proportion scale for disease incidence

which is based on the use of the inverse link function . b The percent of counties with an estimated probability of disease greater than 5%. c Results shown are for ―no fungicide‖ use for the control of Fusarium head blight. Results for ―fungicide‖ use are: County [CLL: - 4.50 ↔ -2.07, proportion: 0.01 ↔ 0.12, 5%: 44%]; Field [CLL: -5.47 ↔ -1.17, proportion: 0.00 ↔ 0.27, 5%: 52%].

Table 5.3. Estimated parameters (β) with standard errors for a subset of the covariablesa evaluated geographical locationa corn and wheat acreage per countyb environmental conditionsc

Corn Corn and Wheat Wheat acreage wheat acreage Year Latitude Longitude acreage past TotalP TempP past acreage past present year/area year/area year/area year/area 2002 -0.04(0.20) -0.03(0.14) -1.64(1.45) -5.20(3.20) -1.57(1.10) -8.15(3.49)* 0.27(0.42) 0.38(0.53) 2003 -0.21(0.24) -0.41(0.15)* -1.78(1.75) -5.13(4.31) -1.57(1.35) -4.45(3.19) 0.44(0.55) 0.40(0.67) 2004 -0.41(0.26) -0.08(0.18) -0.48(2.05) -2.97(3.30) -0.76(1.42) -3.73(3.65) -0.43(0.75) -1.17(1.06) 2005 -0.23(0.28) 0.01(0.30) -3.54(2.72) 1.76(4.85) -1.66(2.04) 1.71(5.04) -15.86(10.12) -6.63(4.39) 2006 0.07(0.20) 0.53(0.17)* 2.94(1.58) 3.24(3.59) 2.32(1.25) 2.77(2.88) 0.18(0.55) 1.09(0.65) 2007 0.88(0.58) 0.64(0.54) 9.02(6.01) 9.14(7.01) 6.00(3.70) 20.35(13.24) -1.81(7.96) -3.74(4.35) * 2008 0.62(0.18) 0.37(0.22) 1.00(2.18) 12.46(4.27)* 2.14(1.71) 9.52(2.07)* -1.00(0.62) -0.72(0.70) 2009 0.13(0.28) 0.54(0.32) -1.18(3.17) 2.28(3.50) 0.30(2.13) 2.68(3.96) 0.54(1.33) 1.05(0.96) 185 2010 -0.44(0.24) 0.33(0.22) 4.22(2.23) 2.87(3.70) 2.93(1.66) 3.71(4.28) 0.90(0.54) 0.22(0.65)

2011 -0.70(0.22)* 0.24(0.23) -1.49(2.62) -8.20(3.89)* -2.55(1.88) -8.20(3.89)* -1.05(0.70) -1.07(0.64)

a Latitude and longitude of the center of the county. b Proportion of county area where corn or wheat was grown during the previous or present growing season. c TotalP and TempP are defined in the text. * indicates significant at P < 0.05.

A 6.0 County 5.0 2.0

1.5 Variance 1.0 0.5 0.0

B 2.0 Field (County) 1.5

1.0

Variance 0.5

0.0

C 2.0 Site (Field and County) 1.5

1.0

Variance 0.5

0.0 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Year

Figure 5.1. Point estimates and 95% confidence bounds for the variance parameters at the A, county; B, field within county; and C, site within field and county levels for each year. Estimates with standard errors are in Table 5.2.

186

Figure 5.2. Estimated best linear unbiased predictor (EBLUP) on the complementary log-log (CLL) scale for each county ( surveyed, based on the fit of equation 3 to the data for each year. Counties with EBLUPS below the estimated mean ( are in red and counties with EBLUPS greater than are in blue, with the darkest shades indicating very low or very high estimated incidence levels on the CLL scale. As an example, for the counties in dark red in 2002, = -3.69 - 1. The Spearman correlation (r) between county EBLUPs for pairs of adjacent years is next to each map. For instance, the correlation between county EBLUPS in 2002 and 2003 is next to the 2002 map. All correlations were not significant (P > 0.10). Because of nonsignificance, any spatial autocorrelation is not relevant.

187

2002 2003 2004

2005 2006 2007

2008 2009 2010

2011

EBLUP for each county surveyed (CLL link scale) < -1.0 -1.0 to -0.5 -0.5 to 0

0 to 0.5 0.5 to 1.0 > 1.0

Figure 5.2 188

Summary

A multi-level analysis of heterogeneity of disease incidence was conducted based on a survey for Fusarium head blight (caused by Fusarium graminearum) in Ohio during the 2002 through 2011 growing seasons. Sampling consisted of counting the number of diseased and healthy wheat spikes per 0.3 m of row at 10 sites (about 30 m apart) in a total of 67-159 sampled fields in 12-32 sampled counties per year. Incidence was then determined as the proportion of diseased spikes at each site. Spatial heterogeneity of incidence among counties, fields within counties, and sites within fields was characterized by fitting a generalized linear mixed model (GLMM) to the data, using a complementary log-log link function, with the assumption that the disease status of spikes was binomially distributed conditional on the effects of county, field and site. The marginal model for an individual field corresponds to an overdispersed discrete distribution. Based on the estimated variance terms, there was highly significant spatial heterogeneity among counties and among fields within counties each year; magnitude of the estimated variances was similar for counties and fields. The lowest level of heterogeneity was among sites within fields, and the site variance was not significantly greater than 0 in three of the ten years. Based on the among-site variances, the intra- cluster correlation of disease status of spikes within sites indicated that spikes from the same site are somewhat more likely to share the same disease status relative to spikes from other sites, fields, or counties. The estimated best linear unbiased predictor

(EBLUP) for each county was determined, showing large differences across the state in disease, but no consistency between years for the different counties. The effects of

189

geographical location, corn and wheat acreage per county and environmental conditions on the EBLUP for each county were not significant in the majority of years.

190

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Appendix A: Spectral Analysis and Cross-Spectral Analysis

This appendix provides details on spectral analysis and cross-spectral analysis as conducted in Chapter 4. Spectral analysis and cross-spectral analysis can be executed using the SPECTRA procedure in SAS or with other specialized software. A detailed explanation of the mathematical concepts involved and how to use the SPECTRA procedure and interpret the results is provided.

Spectral analysis. Spectral analysis utilizes the Fourier transform to approximate a function (i.e., a Fourier series) by a sum of sine and cosine waves of different amplitudes and frequencies. The temporal-domain series (i.e., the time-series of observations) is effectively then transformed into a frequency-domain signal. This allows the total variance of a series of observations over time to be partitioned into simpler individual frequency (or period [=1/frequency]) scales, which helps determine which scales contribute most of the variability over time.

Spectral analysis utilizes the Fourier transform decomposition of a series , which is given by:

. where is the observation number or time in this case ; is the response variable at time , is the number of Fourier frequencies in the decomposition and is the

smallest integer greater than or equal to ( for Ohio and for Indiana),

217

and are coefficients of the cosine and sine functions, respectively; and is

the Fourier frequency (in radians) for (3,4).

Frequencies can be converted to periods using the inverse function (i.e., period = ).

Table A.1. Frequencies and periods for the 46 year time series in Ohio

period period period period 1 46.0 7 6.6 13 3.5 19 2.4

2 23.0 8 5.8 14 3.3 20 2.3

3 15.3 9 5.1 15 3.1 21 2.2

4 11.5 10 4.6 16 2.9 22 2.1

5 9.2 11 4.2 17 2.7 23 2.0

6 7.7 12 3.8 18 2.6

Notice that , and , and are directly from the time series under investigation. Therefore, at each , one simply needs to estimate and . This is equivalent to conducting a linear regression. The output from the SPECTRA procedure in

SAS will provide these estimates. For example, for FHB in Ohio at the 9th frequency (i.e. for ), the estimated coefficients are (Table A.1) and

The periodogram can be defined as the plot (i.e., spectrum) of the sum of each sine and cosine coefficient squared

the so-called amplitude, versus frequency across all frequencies in the time sequence. The total variance (or total sum of squares) of a time series can be partitioned into components of different frequencies, so the sum of squares at each frequency can be 218 considered as a partial variance of the series. To continue the example, for ,

The directly estimated amplitudes of the periodogram are known to be imprecise and erratic (4). Thus, spectral analysis is based on the smoothed periodogram. Smoothing refers to replacing each amplitude value with a weighted average of values from neighboring frequencies. There are several different choices for this smoothing, and we used a triangularly weighted function with a bandwidth (number of neighbors) of 5 to calculate the smoothed periodogram. This is completed in SAS with the weight statement.

The standardized smoothed periodogram, often termed the spectral density, was then calculated by standardizing the smoothed periodogram using an appropriate divisor (4π), so the area under the spectral density curve equals the total variance of the time series of observations. The spectral density at each frequency is given by:

(1)

where is a vector of weights ( for the triangular function. This standardization allows for estimation of the proportion of the variance accounted for by various frequencies in the series. For the example, .

Cross-spectral analysis. For each pair of time series (denoted and ), a cross- spectral analysis can be conducted (2). In cross-spectral analysis, the so-called cross- spectral density is found (a standardized smoothed cross-periodogram), which is analogous to a cross-covariance function of two temporal series, showing how two

(possibly) correlated series co-vary over time. Since the cross-covariance function in this

219 case is not required to be symmetric, the cross-spectral density is generally a complex- valued function. Therefore, it consists of a real part

, known as the cospectrum, and an imaginary part

, known as the quadrature spectrum. For example, for the relationship between FHB in

Ohio and the Winter ONI, the cross-spectral density at the 9th frequency (i.e., for ), which corresponds to a period of 5.1 (46/9) years, is defined (using estimates of the coefficients) by

, where . All of the following discussion on phase shift could come directly from the realized values of the cospectrum and quadrature spectrum (1). However, this may get very complicated, so the cross-spectral density is often presented in terms of its amplitude and phase rather than its cospectrum and quadrature spectrum. This is related similarly to the idea that both polar coordinates and Cartesian coordinates can represent a complex number. A simple conversion from the Cartesian form to polar form yields an amplitude of

(2) and phase of

(3)

220 at each frequency. The SAS output uses the symbol PH for phase shift and not PS as used here. Continuing the example, this is equivalent to the polar coordinates

(0.23 , 0.65π radians).

The squared coherency spectrum provides estimates of the proportion of the variance in one series that is predictable from the other series for each frequency, and is analogous to an (coefficient of determination) value in regression analysis. We call the squared coherency simply “coherency” for ease of presentation. Large values of coherency indicate a strong relationship at the particular frequency. The coherency at each frequency is given by:

(4)

where is the squared amplitude of the cross-spectral density (eq. 2) and

and are the univariate spectral density estimates at each frequency (eq.

1). The SAS output uses K for the squared coherency. For the example,

Interpreting the phase shift. The phase spectrum (a plot of the phase at each period) (eq. 3), indicates the temporal difference (lead or lag) between the pair of time- series. This shows the extent to which changes in one univariate spectral density occur at the same time as changes in the other univariate spectral density, or if there is a tendency for the changes in one series to lag behind or lead the other by some fixed amount of time.

All phase differences displayed in the SPECTRA procedure output have been scaled from –π to +π radians. The original output is in radians, but to loo at π radians

221 simply divide the output result for the phase shift by π. From above, the phase shift for

was 2.0406 (SAS output) or 0.65π. A phase difference of 0 means that the two series (predicted from the spectral model fitted to the data) are in perfect phase at a particular frequency (peaks or valleys of the cyclical series occur at the same times for the two series). Phase differences of exactly π and -π radians are indistinguishable from each other, and indicate the two (predicted) series have a negative relationship at that frequency; that is, a peak in one series occurs at the same time as a valley (low) in the other series. Other phase shifts indicate that the peaks and valleys are offset from one series relative to the other. For example, at 0.65π, the two series have a more negative relationship than a positive relationship, although the negative relationship is not exact.

With the SPECTRA procedure, consider the series listed first after the var statement as the Xt series and the value second as the Yt series. Then a positive phase difference (e.g., 0 to π) indicates the Xt series leads the Yt series at that frequency, and a negative number indicates that it lags (i.e., that the Yt series leads). However, any positive phase shift up to +π is equivalent to a negative phase shift of between -2π and -π.

Equivalently, a lead by one series of less than π (on an absolute scale) is the same as a lead by the other series by more than π radians (specifically, from π to 2π radians). For example, with 0 < c < 1, a lead of c for one series is the same as a lead of 2 - c for the other series. To continue our example, the Xt series (FHB in Ohio) leads the Yt series

(Winter ONI) by 0.65π radians and the Yt series leads the Xt series by 2 - 0.65 .35π radians.

The phase shift (at a given frequency) described above for the lead of the climate series (from peak to peak or valley to valley) is given by PS(+). For the example, PS(+) 222

.35π radians. PS(+), coupled with the coherency, is used to quantify the positive relationship between the series. One can also determine (at a given frequency) the phase shift from a peak of the climate series to the next valley of the FHB series, or from a valley of the climate series to the next peak in the FHB series. This is given as PS(-) =  - c when the FHB series leads the climate series and PS(-) =  + c when the climate series leads the FHB series. For the example, PS(-) =  - 0.65 0.35π. PS(-), together with the coherency, is used to quantify the negative relationship that can exist between the two series (the degree to which there is a negative relation between the climate index and FHB). The smaller of PS(+) and PS(-) for a given frequency indicates the most apparent relation between the two series. That is, if PS(-) is smaller than PS(+), then after a peak in the climate index, the next valley in the FHB series is estimated to occur before the next peak in FHB. Conversely, if PS(+) is smaller than PS(-), then after a peak in the climate index, the next peak in FHB is estimated occur before the next FHB valley.

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Table A.2. Simplified definitions and notations used

Amplitude Vertical distance between the extrema of the sinusoid curve and the mean value (usually zero). Frequency Number of times the sinusoid curve repeats itself within the frame of the time series. Period Duration of time it takes to complete one full cycle of the sinusoid curve; period is the reciprocal of the frequency. Measured value at each observation (t) in the series. The FHB intensity time series in the current analysis. Measured value at each observation (t) in the series. The climate time series in the current analysis. Observation number in a series. Length of the series (t , … , N). Number of Fourier frequencies used in the Fourier transform

decomposition. General count index for the Fourier frequencies; . Vector of weights for the weight function (e.g., triangular, boxcar). General count index for the weights function. For a bandwidth of 5, .

Estimated coefficient of the cosine function for the frequency. Provided in SAS output. is the estimated coefficient of the cosine function for the frequency (i.e., the frequency j units from k).

Estimated coefficient of the sine function for the frequency. Provided in SAS output. is the estimated coefficient of the sine function for the frequency (i.e., the frequency j units from k). Fourier frequency (in radians) for the frequency. is the

Fourier frequency for the frequency (i.e., the frequency j units from k). Periodogram Spectral density Cospectrum The estimated coefficient of the cosine and sine functions, respectively, for series at the frequency. The estimated coefficient of the cosine and sine functions, respectively, for series at the frequency. Quadrature spectrum Amplitude spectrum Phase spectrum

Squared coherency spectrum Spectral density for series and , respectively.

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References

1. Bloomfield, P. 2000. Fourier analysis of time series: an introduction, second ed. Wiley, New York, NY.

2. Brocklebank, J. C., and Dickey, D. A. 2003. SAS for forecasting time series, second ed. SAS Institute Inc., Cary, NC.

3. Fuller, W. A. 1996. Introduction to statistical time series, second ed. Wiley, New York, NY.

4. Koopmans, L. H. 1995. The spectral analysis of time series. Academic Press, San Diego, CA.

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Appendix B: Intra-cluster Correlations for Binary Data in Hierarchical Random

Effects Models

The intra-cluster correlation (ICC) is a value that quantifies the degree of similarity in the responses of individuals from the same cluster. The ICC can be estimated in several different ways depending on the structure of the data and the model chosen to explain the data. Here we focus on estimations of the ICC for clustered binary data in generalized linear mixed models (Chapter 5).

General definition of the intra-cluster correlation. The basic definition of ICCs assumes that any two responses from the same cluster are correlated, and the correlation is the same for all pairs of individual from the same cluster, but any two responses from different clusters are independent (4). This general definition assumes there is only one level of clustering, although generalizations to multiple levels are possible, and most easily defined with continuous data (4). We let i represent the i-th cluster, and l and m represent any two individuals within the cluster. If Y is the random variable of interest, then, for instance, Yil is the l-th individual within cluster i. Using the basic definition for correlation, we can define the ICC (ρ) for each cluster i as (4):

(1)

when l ≠ m. If one is willing to assume that the correlation is the same for all clusters

(also known as a common correlation), then the subscript i can be dropped from the

226 equation. Now, we are concerned here with binary data for Yil, that is, Yil equals 0

(healthy) or 1 (diseased), and Yi (no second subscript) represents the sum of the Yil in the i-th cluster. Then, Yil is a Bernoulli random variable, and Yi is a binomial random variable. For variables with the same distribution, , so:

(2)

The variance of a random variable with a Bernoulli distribution is

, where pi is the parameter of the distribution for cluster i, which represents the probability of occurrence (e.g., probability of a spike being diseased). The pi values here are parameters that are not observed (but can be estimated). Again assuming a common

Bernoulli distribution across the clusters, then . Substitution into equation 2 yields

According to Collet (2), “the effects of correlation between the binary responses and variation between the response probabilities cannot be distinguished.” In other words, variation and correlation are two sides of the same coin. If we allow the Bernoulli random variables Yil and Yim to have probability parameter pi, then

, where is the actual variance of the (unobserved) pi values among the clusters.

This equality holds since all of the pi‟s are identically and independently distributed random variables with variance . Substituting for , we have the generic expression for the ICC with binary data:

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When hierarchical models (such as generalized linear mixed models [GLMMs]) are used to describe clustered data, there is a specified distribution for each level of the hierarchy. With GLMMs, the distributions among units is normal, but with different variances for each level. From Chapter 5, the cluster-level distributions (i.e., the between- cluster variation) are on the complementary log-log (CLL) scale, while the total outcome variance is on the original incidence scale (10). Therefore, the variances are not compatible directly in calculations, and there is no closed form relationship for these two types of variances. There are several different approaches (including numerical integration, simulation, and approximation) that can be used to circumvent these problems (4). We discuss approximation methods below.

Linearization approach. In Chapter 5, we have a three-level hierarchy, with counties (i), fields within counties (j), and sites within fields within counties (k), so we are actually utilizing as the variance of this variable probability, which is the covariance between Yijkl and Yijkm, observations l and m in the ijk-th cluster. In this case,  can be written as (10):

(3)

where, as above, the denominator is for the common-distribution situation. One fundamental step (see below) is the approximation of based on the variances for the link function of pijk.

Note that is equation 3 in Chapter 5, the l (or m) subscript is only implied for the individual binary observations within the cluster, so that the model was written for Yijk

(with a binomial distribution conditional on random effects). For equation 3 in this

228 appendix, we explicitly deal with the Bernoulli random variables. In either case, the disease status of the wheat spike is conditional on the random effects of site, field, and county, so (7):

and

Now, one could also define ρ as:

(4)

Note that equation 4 takes a slightly different approach to define the total outcome variances compared with equation 3.

From the notation used in Chapter 5, we have the variance of ijk on the CLL-link scale is given as:

In order to use this value on the proportion scale, we need to find an adequate approximation for the variance. One approximation that is based on the delta method (9)

yields , where additional symbols are defined below. In basic terms, the delta method provides a technique for approximating the moments of functions of random variables. It uses a first-order Taylor series expansion centered at the mean of the random variable.

Again, using the notation in Chapter 5 with the CLL link, and suppressing subscripts for convenience,

and

229

Here, is the inverse of the link function, and is the first derivative of the inverse link function with respect to .

Therefore, an approximation for the variance is

which, from equation 3, leads to an approximation of ρ as:

(5)

and from equation 4, leads to an approximation of ρ as (1,5):

(6)

Although using a different link function, note that Goldstein et al. (5) arrives at the same basic expression for the ICC as in equation 6, as a form of a variance-partition coefficient, by directly approximating the model for the CLL link as a linear model for Y

(also determined through a Taylor series expansion), and applying the methods for linear models and continuous data. In contrast, we show the approach where the variance is determined for the GLMM, and then the “linear scale” variance is approximated.

Equations 5 and 6 can be rewritten in the following manner so they are only on the probability (proportion) scale. Note that:

since for the CLL link

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Therefore, equation 5 can be rewritten as (3):

(7)

and equation 6 can be rewritten as:

(8)

Equation 8 was used in Chapter 5 to measure the disease status of wheat spikes within sampling units (i.e. within sites that are also conditional on fields and counties).

Thus far, we have assumed that the within-cluster variance for the count is directly from a binomial distribution (based on the underlying Bernoulli distribution for the binary observations), but we could put in a value (δ) to account for any „extra- binomial dispersion‟ that exists. If δ > 1, there is overdispersion (i.e., the data exhibit more dispersion than expected under a binomial model with the specified effects), and if

δ < 1, there is underdispersion. This value can be calculated as the ratio of the Pearson statistic and its degrees of freedom when fitting a conditional binomial distribution to data using a maximum likelihood method (found under „Fit Statistics‟ in the output from use of the GLIMMIX procedure in SAS, with the Laplace estimation method).

Incorporating δ leads to an approximation for ρ as (6):

(9)

Higher order Taylor expansions may provide more accurate approximations of ρ than the first order Taylor expansion that has been utilized so far. However, higher order models can get very complicated and may not be worth the extra effort, given the

231 marginal improvement in accuracy. For instance, using a second-order Taylor expansion,

ρ can be approximated as (8):

(10)

Latent variable approach. Another approach is to assume there is an underlying unobservable continuous random variable (the latent response) that represents the propensity of an individual to have a positive outcome value. This latent response of underlying probabilities is the negative extreme value or log-Weibull distribution when the CLL link is used. The variance of this “inverse CLL distribution” is a constant , where . This constant, which is independent of the mean of each cluster, becomes the within-cluster variance. Similar equations to those shown above can be used in this context, derived from the ICC equations for continuous data. One such results is

(7):

(11)

Numerical calculations based on equations. We approximated ρ using equations 7, 8, 9, 10, and 11 for each of the 10 years of Fusarium head blight disease incidence data (Table B.1). We also used the basic definition of the correlation, equation

1, to estimate ρ. For this situation, one does not use the GLMM results, or any other model fits, but defines all-possible pairings of the binary (0/1) values within each cluster (where l ≠ m), and then calculates a Pearson product-moment correlation across the observations, where N is the number of clusters (number of counties times number of fields per county times number of sites per field).

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Table B.1. Approximations of the intra-cluster correlation with the data and model used in Chapter 5 Year Eq. 1 Eq. 7 Eq. 8 Eq. 9 Eq. 10 Eq. 11 2011 0.097 0.070 0.065 0.106 0.069 0.441 2010 0.159 0.151 0.131 0.193 0.148 0.403 2009 0.033 0.027 0.026 0.035 0.027 0.420

2008 0.025 0.021 0.021 0.026 0.021 0.320

2007 0.015 0.010 0.010 0.018 0.010 0.550 2006 0.049 0.029 0.028 0.033 0.029 0.319 2005 0.015 0.005 0.005 0.010 0.005 0.489 2004 0.129 0.081 0.075 0.114 0.080 0.342 2003 0.098 0.067 0.063 0.096 0.066 0.429 2002 0.063 0.031 0.030 0.046 0.031 0.433

As can be seen from the table, the ICC estimates are generally of the same order of magnitude, and similar to each other, except for equation 11 (which is based on very different assumptions). As stated by Browne et al. (1), the equation 11 results typically do not agree with others. We used equation 8 in Chapter 5, but one can see that the results are not substantially affected by the use of several other approximations. Agreement of these results will depend on the magnitude of the variances and on p.

233

References

1. Browne, W. J., Subramanian, S. V., Jones, K., and Goldstein, H. 2005. Variance partitioning in multilevel logistic models that exhibit overdispersion. J. R. Statist. Soc. A. 168:599-613.

2. Collet, D. 1991. Modelling Binary Data. Chapman and Hall, London.

3. Commenges, D., and Jacqmin, H. 1994. The intraclass correlation coefficient: distribution-free definition and test. Biometrics 50:517-526.

4. Eldridge, S. M., Ukoumunne, O. C., and Carlin, J. B. 2009. The intra-cluster correlation coefficient in cluster randomized trials: a review of definitions. Int. Stat. Rev. 77:378- 394.

5. Goldstein, H., Browne, W., and Rasbash, J. 2002. Partitioning variation in multilevel models. Understand. Statist. 1:223-231.

6. Murray, D. M. 1998. Design and Analysis of Group-Randomized Trials. Oxford University Press, New York.

7. Ren, S., Yang, S., and Lai, S. 2006. Intraclass correlation coefficients and bootstrap methods of hierarchical binary outcomes. Statist. Med. 25:3576-3588.

8. Sashegyi, A. I., Brown, K. S., and Farrell, P. J. 2001. On the correspondence between population-averaged models and a class of cluster-specific models for correlated binary data. Statist. Prob. Let. 52:135-144.

9. Turner, R. M., Omar, R. Z., and Thompson, S. G. 2001. Bayesian methods of analysis for cluster randomized trials with binary outcome data. Stat. Med. 20:453-472.

10. Turner, R. M., Omar, R. Z., and Thompson, S. G. 2006. Constructing intervals for the intracluster correlation coefficient using Bayesian modeling, and application in cluster randomized trials. Stat. Med. 25:1443-1456.

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