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© 2007 Plant Management Network.
Accepted for publication 26 April 2007. Published 26 July 2007.

An Application of Space-Time Analysis to Improve the Epidemiological Understanding of the Papaya-Papaya Yellow Crinkle Pathosystem

Paul D. Esker, Former Graduate Research Fellow, Department of Plant Pathology, Iowa State University, Ames 50011; Karen S. Gibb, Associate Professor, School of Science, Charles Darwin University, Darwin NT 0909, Australia; and Philip M. Dixon, Professor, Department of Statistics, and Forrest W. Nutter, Jr., Professor, Department of Plant Pathology, Iowa State University, Ames 50011

Corresponding authors: Paul D. Esker.

Esker, P. D., Gibb, K. S., Dixon, P. M., and Nutter, Jr., F. W. 2007. An application of space-time analysis to improve the epidemiological understanding of the papaya-papaya yellow crinkle pathosystem. Online. Plant Health Progress doi:10.1094/PHP-2007-0726-02-RS.


Yellow crinkle disease of papaya is a serious threat to papaya production in Australia.  Space-time point pattern analysis was used to study the spatial and temporal dependence of two phytoplasma strains that cause yellow crinkle: tomato big bud (TBB) and sweet potato little leaf V4 (SPLL-V4).  Incidence data for both phytoplasma strains were obtained from a field study conducted in Katherine, NT, Australia, between January 1996 and May 1999.  The primary ecological and epidemiological question of interest was to elucidate the scale of spatial or spatio-temporal aggregation of phytoplasma-infected papaya plants.  The hypothesis was that there would be a contagion process, where TBB- and SPLL-V4-infected papaya would be aggregated and not random.  To test this hypothesis, a point pattern spatial analysis using Monte Carlo simulation was initially applied to the incidence data.  Results of this analysis suggested that SPLL-V4 infected papaya plants displayed aggregation with spatial dependence up to 30 m (10 to 15 plants along or across rows), whereas there was not strong evidence to suggest that TBB-infected papaya plants were aggregated.  However, when a space-time point pattern analysis was subsequently used to simultaneously test for the interaction between space and time, there was strong evidence (P < 0.01 for SPLL-V4 and P < 0.10 for TBB) to suggest a space-time interaction for both SPLL-V4 and TBB.  For SPLL-V4, a space-time risk window of approximately 10 months and 20 m was detected, whereas for TBB, this risk window was 5 months and 10 m.  The results of these studies support the hypothesis that papaya infection by both phytoplasma strains appears to be the result of a contagion process, providing support for the contention that insect vectors are the most likely mechanism for acquisition, dispersal, and transmission.


Phytoplasma diseases affecting papaya (Carica papaya L.) have been responsible for severe epidemics in papaya plantations in the Northern Territory, Australia (3,9,12). The three major diseases of papaya caused by phytoplasmas in Australia are papaya dieback, papaya yellow crinkle, and papaya mosaic (3). Padovan and Gibb (12) reported that there were two predominant phytoplasma strains causing papaya yellow crinkle in the Northern Territories, based on the use of restriction fragment length polymorphism. The two strains were identified as either the tomato big bud strain (TBB) or the sweet potato little leaf strain V4 (SPLL-V4). These two strains have since been placed into the faba bean phyllody strain cluster based on 16s rRNA sequences (14).

An increased understanding of the epidemiological factors and processes that influence the development of papaya yellow crinkle epidemics should lead to the development and integration of management tactics that will reduce the risk of papaya plantations being affected by yellow crinkle disease. Esker et al. (6) have reported that once a phytoplasma-infected papaya plant was symptomatic and tested positive for either TBB or SPLL-V4, this plant would survive for approximately another 4 to 5 months before plant death occurred. Furthermore, no significant seasonal effects (season in which a plant was first found symptomatic), or the age of papaya plants was found to have influenced survival time. It was on the basis of these results that Esker et al. (6) questioned the use of ratooning of the infected papaya stems (the current disease management tactic) an effective management tactic. These results supported similar findings by Guthrie et al. (11), who suggested that new papaya shoots originating from the base of yellow crinkle-infected papaya plants that had been ratooned were (in fact) not always pathogen-free (11). 

From an epidemiological and ecological perspective, knowledge that the median time-to-death was 4 to 5 months for TBB and SPLL-V4 infected papaya once plants were symptomatic provides important epidemiological information concerning the potential risk window (in both space and time) where neighboring papaya plants are at increased disease risk to become infected by TBB or SPLL-V4. This hypothesis assumes that the infection process is a contagion process, which would be expected if an insect vector was responsible for the acquisition, dispersal, and transmission of TBB and SPLL-V4. Therefore, the objective of this study was to elucidate and quantify the spatial, and spatio-temporal pattern of TBB and SPLL-V4-infected papaya plants.

Study Area and Data Collection

A single papaya plantation located 350 km south of Darwin in the Northern Territory was selected for an on-farm study concerning the temporal and spatial dynamics of the two strains (TBB and SPLL-V4) that cause yellow crinkle disease of papaya (Fig. 1). Both Padovan and Gibb (12) and Esker et al. (6) have reported the details concerning the field design and sampling methods used in this study. Commercially-available papaya obtained by the grower (and not tested for presence of phytoplasmas) were planted in January 1996 within a plantation measuring 65 rows by 55 plants per row. Rows were spaced 2.5 m apart, while plants within rows were 2 m apart (total of ~ 3,500 papaya plants). Beginning in May 1996 (month = 5 following transplanting), a monthly census of all papaya plants was conducted to sample for the presence of symptomatic papaya plants having symptoms typical to those caused by phytoplasmas (dieback, yellow crinkle, and mosaic) (Fig. 2). These assessments continued monthly until April 1999 (month = 40). For a papaya plant that had symptoms of a phytoplasma, leaves were collected and a polymerase chain reaction (PCR) method was used to detect and differentiate papaya dieback from papaya yellow crinkle (12). More than 99% of the phytoplasma-infected papaya were found to be caused by just two phytoplasma strains causing yellow crinkle. Subsequently, RFLP was used to identify the specific phytoplasma strain (TBB or SPLL-V4) that caused symptoms of yellow crinkle (12). For each symptomatic and infected papaya plant that had tested positive, the month, row number, plant number within the row, and phytoplasma strain (TBB or SPLL-V4) were recorded. These data were subsequently used for spatial point pattern and spatio-temporal point pattern analyses.


Fig. 1. Epidemiological study site for papaya yellow crinkle on papaya plants in Katherine, Northern Territory, Australia.  Note chlorosis and necrosis on phytoplasma-infected trees.


  Fig. 2. Papaya plants showing (A) early and (B) late symptoms of papaya yellow crinkle disease in Australia.  

Space-Time Point Pattern Analysis of Sweet Potato Little Leaf V4 and Tomato Big Bud

Numerous methods have been developed to examine temporal data (1), as well as spatial data (2,5,7); however, time-space interactions in plant pathosystems have been less commonly used. The integration of space and time into analyses should increase the epidemiological and ecological understanding of the temporal and spatial dynamics of plant disease epidemics. With regards to yellow crinkle disease of papaya, the application of such analyses may provide critical insight into whether or not a contagion process is occurring, which would support the contention concerning the role of an insect vector (or vectors) in acquiring and disseminating TBB or SPLL-V4. The importance of this information for papaya yellow crinkle disease would be an increased understanding regarding the epidemiological importance of local inoculum sources (i.e., phytoplasma-infected neighboring plants) and the increased risk window for infection of neighboring plants. Because Guthrie et al. (11) and Esker et al. (6) have questioned the use of ratooning as an effective disease management tactic for papaya yellow crinkle, further information regarding the spatio-temporal dynamics of papaya yellow crinkle epidemics will help to support or refute this viewpoint.

Initially, temporal and spatial data were considered individually. For temporal data, the hypothesis for both phytoplasma strains was that the infection process was temporally uniform and that any papaya plant may be infected at any time following transplanting. However, for both SPLL-V4 and TBB, this was determined not to be the case, as there was a nonuniform distribution as to when papaya plants were found to be symptomatic (and infected) by either phytoplasma strain (Fig. 3).


Fig. 3. Distribution of (A) Tomato big bud-infected papaya plants (TBB) and (B) Sweet potato little leaf V4 (SPLL-V4) at Katherine, Northern Territory, Australia between May 1996 and April 1999.  Yellow crinkle disease was recorded each month and the bars represent the month in which a papaya plant was found to be symptomatic and infected with TBB.


For the spatial data (i.e., location of SPLL-V4- or TBB-infected papaya), statistical analyses were based on point pattern methods (2,5,7,8). Point-pattern methods have been used extensively in human epidemiology, but have only been used more recently in plant pathosystems (10). The hypothesis for the spatial pattern of SPLL-V4 and TBB-infected papaya plants was complete spatial randomness. The primary alternative hypothesis of interest was if phytoplasma-infected papaya were aggregated (using a one-sided test) (13). Analyses for these spatial patterns were conducted using the SPATSTAT library in R (The R Project for Statistical Computing, online). Two functions of importance in these analyses are the K- and L-functions. The K function was defined as:

     K(d) = πd2 [1]

where, d2 represents a squared-distance from each individual point (5). Distances from 0 m to 60 m away were examined for each SPLL-V4 and TBB-infected plant (at 1.5 m intervals). The L function is a 1-1 transformation of K. The utility of the L-function is that is provides a clearer representation of the data process. The L function was written as:

L(d) =


—   d                     [2]

where, K represents the spatial K function and d represents the distances with respect to each SPLL-V4 and TBB-infected papaya plant that were examined. A Monte Carlo simulation simulation-based approach was used to compare the observed K and L functions to simulated spatial pattern (based on 999 simulations). Quantile simulation envelopes (2.5, 5, 95, and 97.5% quantiles) were examined, thereby enabling the construction of 90 and 95% confidence intervals. In Fig. 4, the observed L function across the range of distances for SPLL-V4 and TBB-infected papaya plants indicated an aggregated spatial pattern for SPLL-V4 for distance of approximately 30 m from an infected papaya plant (meaning that the observed pattern fell outside the 97.5% quantile envelop). For TBB, there was not strong evidence to suggest an aggregated spatial pattern.


Fig. 4. Results for a spatial point pattern for (A) sweet potato little leaf V4 (SPLL-V4) and (B) tomato big bud-infected (TBB) papaya plants.  The hypothesis of complete spatial randomness was tested using K and L functions based on Ripley (19) and Diggle (6).  The black line indicates the L-value at each distance examined from a SPLL-V4 and TBB-infected papaya, while the different dotted lines indicated the 2.5, 5, 95, and 97.5% quantile envelopes obtained from n = 999 simulations of SPLL-V4 and TBB-infected papaya.  From this analysis, it appears that SPLL-V4 has an aggregated distribution of infected papaya, while there is not strong evidence to suggest that TBB-infected papaya are aggregated.


In spite of the observation of no spatial aggregation of TBB-infected papaya, this does not imply that there may not be a space and time interaction. Based on the nonuniform temporal pattern for TBB-infected papaya (Fig. 3), it is important to examine the dissemination and infection processes in terms of a coupled space-time interaction. This is important because it will help to determine if there are small space-time windows where the risk of infection by TBB (and also SPLL-V4) is higher. Furthermore, the presence of a space-time aggregation in this study would be suggestive of a contagion process, which would support our hypothesis that the primary dissemination process (acquisition, dispersal, and transmission) is most likely dependent upon insect vectors. Furthermore, a space-time interaction would also provide support that ratooning is not a viable management tactic, since the regrowth of new shoots can serve as a source for insect vectors to acquire and then transmit both phytoplasma strains for many months (median is 4 to 5 months) before the papaya plant fully succumbs to the disease and can no longer serve as an inoculum source. Thus, an increased risk in small space-time windows, when combined with knowledge that ratooning does not completely eliminate the infectious agent, explains epidemiologically how a yellow crinkle epidemic may continue to develop in ratooned papaya plantations. 

To determine if there was a space-time interaction for yellow crinkle disease of papaya the approach of Diggle et al. (4) was followed, in which the hypothesis tested was of complete spatio-temporal randomness.  Complete spatio-temporal randomness would be indicated by the independence between the spatial and temporal components, and would be represented by a space-time K function that is equal to the spatial K times the temporal K:

  K(d,t) = KD(d)KT(t) [3]

(4,8). Using the SPLANCS library in R, the following functions (along with descriptions of what each function does) were used to test the hypothesis of complete spatiotemporal randomness for SPLL-V4 and TBB-infected papaya: 

 1. stkhat = this function calculates the space-time K function and also provides estimates of the spatial K and temporal K.

2. stsecal = computes the estimate of the standard error for the space-time K function.

3. stmctest = performs a Monte Carlo test of the observed space-time process through the random sampling of the time variable to the fixed spatial locations of SPLL-V4 and TBB-infected papaya plants.

4. stdiagn = produces a summary plot (Figs. 5 and 6) that provides the location of the original TBB-infected papaya plants, a perspective plot that examines the difference between a space-time K-function and the product of the space and time K functions, a plot of standardized residuals against the product of the space and time K functions, and a histogram of the difference space-time test statistics, along with the location of the observed space-time test statistic (4,8).


Fig. 5. Summary plots for the space-time point pattern analysis for sweet potato little leaf V4 (SPLL-V4).  Time was defined as the month in which a plant was found to be symptomatic and infected by SPLL-V4.  The Data map (A) represents the observed locations of SPLL-V4-infected papaya within the papaya plantation.  The Dzero plot (B) is a perspective plot that examines the difference between the space-time K function and the product of the space and time K functions and is written as:

D0 =K(s,t) - K(s)K(t)              [4]

The Residual Plot (C) is a plot of standardized residuals against the product of the space and time K functions.  This plot is similar to a residual plot from regression analysis and values ±2 are indicative of a space-time interaction occurring.  Finally, the MC results (D) summarizes all of the test statistics from a Monte Carlo simulation, whereby, the time data for each SPLL-V4-infected location was randomly assigned to the fixed locations for SPLL-V4-infected papaya.



Fig. 6. Summary plots for the space-time point pattern analysis for tomato big bud (TBB).  Time was defined as the month in which a plant was found to be symptomatic and infected by TBB.  The Data map (A) represents the observed locations of TBB-infected papaya within the papaya plantation.  The Dzero plot (B) is a perspective plot that examines the difference between the space-time K function and the product of the space and time K functions and is written as:

D0 =K(s,t) - K(s)K(t)               [4]

The Residual Plot (C) is a plot of standardized residuals against the product of the space and time K functions.  This plot is similar to a residual plot from regression analysis and values ±2 are indicative of a space-time interaction occurring.  Finally, the MC results (D) summarize all of the test statistics from a Monte Carlo simulation, whereby, the time data for each TBB-infected location was randomly assigned to the fixed locations for TBB-infected papaya.


The combination of statistical approaches within this analysis allows for the determination of the presence of a space-time interaction if the following are found to occur: (i) peaks in disease risk within perspective plots, (ii) values of the standardized residual values ±2 from the expected value of zero, and (iii) the test statistic from the Monte Carlo simulation is significant (P < 0.10). For both SPLL-V4 and TBB-infected papaya plant data, 999 Monte Carlo simulations were used, where time (i.e., the month when a papaya plant was found to be infected and symptomatic) was randomly assigned to the fixed locations of the infected and symptomatic plants. 

For both SPLL-V4 (Fig. 5) and TBB (Fig. 6), there was evidence for a space-time interaction. For SPLL-V4, the D0 perspective plot (indicated as Dzero in Figs. 5 and 6) showed a well-defined peak at distances of less than 20 m (8 plants across rows and 10 plants within a row) and times of less than 10 months. For TBB, the perspective plot showed a defined peak at distances less than 10 m (4 plants across rows and 5 plants within a row) and times less than 5 months, indicating TBB has a shorter window of risk in time and space compared to SPLL-V4 phytoplasma strain. This difference in the windows of risk for the two phytoplasma strains may indicate the presence of strain-specific insect vectors, or differences between strains as to how long an insect remains infectious after it is has acquired one of the phytoplasma strains. Furthermore, in both situations, there were numerous instances where standardized residual values fell outside our ± 2 level, which provided additional evidence to more closely examine the existence of space-time interactions. Finally, the results of the Monte Carlo test resulted in a statistically significant test statistic for the observed space-time patterns (P = 0.004 for SPLL-V4 and P = 0.07 for TBB). When considering these approaches in concert, the results suggest that there is an increased risk for healthy papaya plants to become infected by SPLL-V4 and TBB if any of their neighboring plants are already infected. Moreover, the time windows for both SPLL-V4 and TBB closely matched the length of the post-symptomatic infectious periods (based on survival analysis), which provides additional evidence that the current disease management tactic of ratooning may not be most appropriate (6).


The results from this study indicated that the primary process for the pathogen dissemination mechanism (acquisition, dispersal, and transmission) of TBB and SPLL-V4 is a contagion process, most likely due to insect vectors. Previous research (12) has not revealed the presence of a predominant insect vector (or vectors) in this pathosystem; however, in the absence of strong observational evidence from the field, the integration of statistical methods to analyze the spatio-temporal distribution of papaya plants does support the insect vector(s) hypothesis. This new information also has importance with regards to what may be the most appropriate disease management tactics. Both Esker et al. (6) and Guthrie et al. (11) have questioned the efficacy of ratooning phytoplasma-infected papaya plants to reduce disease risk from either TBB or SPLL-V4 phytoplasma strains. The revelation of the occurrence of statistically-significant space-time windows for increased disease risk from spatio-temporal analyses used in this study provides further evidence to suggest that alternative disease management tactics (in lieu of rationing) need to be developed and evaluated for their efficacy to control papaya yellow crinkle in Australia.


 The first author was supported by a National Science Foundation/Iowa State University Vertical Integration of Graduate Research and Education (VIGRE) Fellowship, under NSF Grant DMS-0091953. Research for this project was funded by the Australian Research Council and by funds from the Iowa Agricultural and Home Economics Experiment Station while the fourth author was on Faculty Development Leave in Australia. We thank the reviewers for their constructive comments regarding this manuscript.

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