Rice Science, 2005, 12(3): 207－212 207 http://www.ricescience.org

Geostatistical Analysis on the Temporal Patterns of the Yellow Rice Borer, Tryporyza incertulas

1 2 1 YUAN Zhe-ming , WANG Zhi , HU Xiang-yue (1Bio-safety Science and Technology College, Agricultural University, 410128, China; 2Department of Life Science, Hunan Arts and Science University, 415000, China)

Abstract: In order to comprehend temporal pattern of the larvae population of the yellow rice borer, Tryporyza incertulas, and provide valuable information for its forecast model, the data series of the population for each generation and the over-wintered larvae from 1960 to 1990 in Dingcheng , Changde City, Hunan Province, were analyzed with geostatistics. The data series of total number, the 1st generation, the 3rd generation and the over-wintered larvae year to year displayed rather better autocorrelation and prediction. The data series of generation to generation, the 2nd generation and the 4th generation year to year, however, demonstrated poor autocorrelation, especially for the 4th generation, whose autocorrelation degree was zero. The population dynamics of the yellow rice borer was obviously intermittent. A remarkable cycle of four generations, one year, was observed in the population of generation to generation. Omitting the certain generation or interposing the over-wintered larvae only resulted in a less or slight change of autocorrelation of the whole data series generation to generation. Crop system, food, climate and natural enemies, therefore, played more important roles in regulating the population dynamics than base number of the larvae. The basic techniques of geostatistics applied in analyzing temporal population dynamics were outlined. Key words: Tryporyza incertulas; geostatistics; temporal patterns; population; forecast

Generally, population dynamics is durative. successive observations were obtained at different Based on the relativities among successive time intervals. Therefore, these data should be observations obtained at uniform time intervals, time processed with mathematic interpolation before using series analysis seeks after the rule of population for further analysis. Krigle estimates, which uses the dynamic and hereby carries through forecast [1]. semivariogram in calculating estimates of the surface Geostatistics is a branch of applied statistics at the grid nodes, is considered to be the optimum developed by George Matheron. A unique aspect of method among several mathematic interpolation geostatistics is the use of regionalized variables which methods because of its minimum variance and linear are variables that fall between random variables and unbiased estimates[9]. Secondly, auto-regression (AR) completely deterministic variables. As one of the most model in time series analysis usually presumes that important elements of regionalized variable theory, the current observation yt is the linear combination of semivariance expresses degree of spatial dependence itself last p observations, yt－1, yt－2,…, yt－i, …, and between samples. Geostatistics has been applied to yt－p (i＝1, 2, …, p). The upper limit of p value can be spatial patterns analysis of insect populations widely. conducted from the aftereffect time range given by

However, it seldom involved in the temporal patterns semivariance model and the weight of yt－i can be analysis [2–9]. Its potential applications in temporal given by Kriging[1, 9]. So, geostatistics can be used for patterns analysis can be summarized as follows at AR modeling. Thirdly, geostatistics can determine least. Firstly, the systemic data for forecasting should whether the time series data is stochastic or be intact and sampled at uniform time intervals. The deterministic, and if the data is deterministic, how certain year or generation data, unfortunately, were strong the autocorrelation degree is [10]? Obviously, omitted in some systemic data. Similarly, some not all successive observations are fit for time series analysis and forecast, if and only if the time series Received: 22 June 2005; Accepted: 28 August 2005 data display considerable autocorrelation forecast Corresponding author: YUAN Zhe-ming ([email protected]) values given by AR model based on Kriging are 208 Rice Science, Vol. 12, No. 3, 2005 reasonable. Thus, geostatistics can make the points minus time lag. suggestion that whether the year to year data or the Semivariance curve usually can be simulated by generation to generation data should be adopted for spherical model, exponential model or linear model. AR modeling. Fourthly, geostatistics can determine To spherical model A: whether the time series data is seasonal or not? If yes, how long is the cycle? [9] And the last, geostatistics can help to comprehend the effect of every generation Where c0 is nuggets, c is sills, a is aftereffect larvae and the over-wintered larvae on the time range. In practice, a better simulation usually can autocorrelation degree of the whole data series from be resulted from spherical model B: generation to generation by the omitting or interposing 2 3 r(h)=c0+c1h+c2h +c3h . analysis. In this study, semivariances were calculated with Temporal pattern is essentially different from a Visual Basic procedure programmed by ourselves spatial pattern for its one-dimension and uniaxial and the parameters of spherical model B were given orientation. Therefore, geostatistics need to be by Data Process System (DPS) with Marquart method. developed in theory and technique while it is used for Based on the given parameters, the partial maximum temporal patterns analysis. Furthermore, temporal value c of r(h) and its corresponding h (i.e. aftereffect pattern is more flexible in dividing up time series data, time range a) were also calculated by another Visual and both natural interval (e.g. year to year) and Basic program [3–6]. physiological & ecological interval (e.g. generation to Typical time series data usually contains generation) are permissible. The results of temporal long-term trend, periodicity and random element. The patterns analysis of the yellow rice borer, Tryporyza former two characteristics are just the deterministic incertulas, were reported and the geostatistics element of geostatistics model. The semivargram methods for temporal patterns analysis were displays a beeline with positive slope when the data established in the current paper. contains long-term trend mainly, or a seasonal fluctuation when the data contains periodicity mainly, MATERIALS AND METHODS especially for the h exceeding aftereffect time range [9]. Only 31 years data were involved in this research and Data resources the upper limit of h should be the half-length of time T. incertulas occurs four generations every year series, 15 years. Based on the period analysis in Dingcheng District, Changde, Hunan Province. The computed by DPS, their cycles of these data from year peak values of each generation larvae and to year were all beyond 8 years and no semivargram over-wintered larvae from 1960 to 1990 in Dingcheng displayed upwards of two intact cycles in the research. district were provided by Station of Plant Protection Therefore, only the data from generation to generation [1] and Quarantine of Hunan Province. was carried through period analysis in the research .

Geostatistics analysis Krigle interpolation Suppose Z(X ) is the value to be estimated. There Considering regular time series data interval (h) 0 are n known points X (i=1, 2, … , n), which apart, the semivariance r(h) can be estimated for i corresponding observation value is Z(X ), in the intervals that are multiple of (h): i neighborhood of X0 within the range. Li is the weight

of Xi. Then,

Z(X0)=∑Li(Xi)(i=1, 2, 3, …, n),

Where Z(Xi) is the measurement of a regionalized To make the expectation variance minimum in X0 variable taken in time Xi, Z(Xi+h) is another and to be satisfied with ∑Li＝1, Li can be calculated measurement taken h intervals away, and N(h) is the by semivariance model. The interpolation interval was number of separating time, expresses as number of half generation in the research [8].

YUAN Zhe-ming, et al. Geostatistical Analysis on Temporal Patterns of Yellow Rice Borer, Tryporyza incertulas 209

16.1%. Here would rather explore for research RESULTS methods than interpolate for application.

Semivariance analysis for total larvae, every Semivariance analysis and Krigle interpolation for generation larvae and the over-wintered larvae T. incertulas larvae population from generation to among years generation Total larvae, the sum of every generation except The peak values of every generation larvae of the over-wintered larvae, express the rampancy degree T. incertulas (total 124 generations) from 1960 to all-year. According to Table 1 and Fig. 2, the total 1990 in Dingcheng district, their semivariagram curve larvae, the 1st generation, the 3rd generation and the and the parameters for semivariance model were over-wintered larvae displayed rather better demonstrated or listed in Fig. 1, Fig. 2 and Table 1, autocorrelation. The ratios of deterministic elements respectively. The series data from generation to generation presented more stochastic than to total variances were 57.5%, 60.0%, 77.1% and deterministic and the ratios of stochastic elements to 75.0% respectively, and the aftereffect time range total variances were 83.9% and 16.1%, respectively. were 4.7, 2.9, 5.9 and 4.1 years respectively. Taken the Its aftereffect time range was 16.7 generations. Taken analysis results of data from generation to generation whether the deterministic element exceeds half of total and data from year to year together, the same variance or not as a criterion, the reliability will be generation larvae of the last 5, 3, 6 and 5 years should poor for forecasting the next generation population be mainly responsible for forecasting the next total with the last several generations only. A remarkable larvae, the 1st generation, the 3rd generation and the cycle of four generations, one year, was observed in over-wintered larvae, respectively. Contrarily, the base the semivariagram. It’s consistent with the result of numbers of the over-wintered larvae maybe play a the period analysis computed by DPS, and the feeblish role for forecasting. It suggests that the confidence coefficient was 0.9993 [1]. occurrence of T. incertulas depends on crop system, Based on the deterministic element of the data food, climate and natural enemies more [11-16]. The 2nd and the simulated semivariance model, the population generation larvae displayed poor autocorrelation, the individuals in every time within the research period ratio of deterministic element to total variance was could be estimated (Fig.1). The interpolation, however, 46.0% and the aftereffect time range was 4.1 years. As was not reliable because the ratio of deterministic for the 4th generation larvae, the ratio of deterministic element to total variance was less than 50%, only element to total variance was 0% and the data was

14000 ● True value ○ Krigle value 12000

10000

8000

6000 (×15 larvae/ha) 4000 No. of larvae populations 2000

0 1 21 41 61 81 101 121 Generation

Fig. 1. Dynamics and interpolated value of larvae population for the yellow rice borer over 124 generations in Dingcheng District, Changde City, Hunan Province. 210 Rice Science, Vol. 12, No. 3, 2005

Base number of over-wintered larvae year to year 8 10 9 The 3nd generation year to year 8 The 2nd generation year to year 6 7 ) )

h 6 h ( ( r r 4 5 × × 6 4 4

The 1st generation 10 10 3 2 The 1st generation year to year 2 year to year 1 0 0 024681012 0246810121416

Year Year

50 The 4th generation 12 45 year to year The 2nd-3rd-4th generation,1st generation omitted Total number of 11 The 1st-3rd-4th generation,2nd generation omitted 40 The 1st-2nd-4th generation,3rd generation omitted larvae year to year 10 35 The 1st-2nd-3rd generation,4th generation omitted 9

) Base number of over-wintered larvae + generation to generation

30 ) h h ( Generation to generation ( 8 r r

× 25 × 6

6 7 10

20 10 6 15 5 10 4 5 3 0 2 4 6 8 10 12 14 16 0 1020304050607080 Year Generation

Fig. 2. Semivariograms of temporal data series of the yellow rice borer.

Table 1. Parameters, nuggets, sills and ranges for different temporal data series of the yellow rice borer.

2 Data series c0 c1 c2 c3 c a 1－c0/c R

Generation to generation 5184436 134685 －5408 55 6181688 16.7 0.161 0.16 Total number of larvae year to year 14234901 9416168 －1379190 53058 33533224 4.7 0.575 0.58 The 1st generation year to year 28237 32734 －7551 452 70679 2.9 0.600 0.89 The 2nd generation year to year 2575479 1217880 －201016 8454 4772377 4.1 0.460 0.68 The 3rd generation year to year 1597369 2074453 －238887 7090 6977157 5.9 0.771 0.65 The 4th generation year to year 10149536 Plane beeline almost Number of larvae over-wintered year to － year 415313 740737 137116 7522 1665870 4.1 0.750 0.75

Generation over-wintered + generation to － generation 4483339 95451 3074 25 5366595 20.9 0.164 0.13

The 2nd-3rd-4th generation, the 1st － generation omitted 5690741 334130 17210 229 7628348 13.2 0.254 0.36

The 1st-3rd-4th generation, the 2nd generation omitted 6065188 Plane beeline almost

The 1st-2nd-4th generation, the 3rd generation omitted 5615274 Plane beeline almost

The 1st-2nd-3rd generation, the 4th － generation omitted 2915269 196924 9925 128 4079902 13.4 0.285 0.28

YUAN Zhe-ming, et al. Geostatistical Analysis on Temporal Patterns of Yellow Rice Borer, Tryporyza incertulas 211 completely stochastic. No semivariagram displayed a periodicity of temporal pattern is usually more clear beeline with positive slope. It meant that the and important than that of spatial pattern. A occurrence of the pest was intermittent markedly and remarkable cycle of four generations, one year, was no long term trend [14]. observed in the semivariagram of the data generation to generation. For the first time, the effect of every Effect of every generation larvae and the generation larvae and the over-wintered larvae on the over-wintered larvae on the temporal pattern of autocorrelation degree of the whole data series from the whole series data from generation to generation generation to generation was analyzed by the omitting If the certain generation or the over-wintered or interposing methods. The results indicated that the larvae plays an important role on the temporal pattern deterministic of the whole series data from generation of the whole series data from generation to generation, to generation was affected to a certain extent by the omitting the certain generation or interposing the 2nd and the 3rd generation larvae but not by the other over-wintered larvae would decrease the ratio of generations and the over-wintered larvae. Crop system, deterministic element to total variance remarkably. food, climate and natural enemies, therefore, played According to Table 1 and Fig. 2, the ratio displayed a more important roles in regulating the population [11 16] slight change with increment from 0.161 to 0.164, dynamics than base number of the larvae – . after interpolated the over-wintered larvae. The ratios As for forecast, the Krigle estimated value even rose to 0.254 and 0.285 if the 1st and 4th usually depends on the previous observed value generation larvae were omitted, respectively. The mainly for the one-dimension and uniaxial orientation ratios, however, all reduced to zero if the 2nd and 3rd of the time series. Its precision, therefore, is inferior to generation larvae were omitted. It suggested that the that of spatial estimate. However, it is feasible as the deterministic of the whole series data from generation ratio of deterministic element to total variance is big to generation was affected to a certain extent by the enough [9, 10]. As for interpolation, the estimate value 2nd and the 3rd generation larvae but not by the other depends on known values both the previous and the generations and the over-wintered larvae. after. The methods used in Kriging allow it to have an advantage over other estimation procedures in that the DISCUSSION estimated values have a minimum error associated with them and this error is quantifiable. Kriging, Population dynamic usually presents durative or therefore, can be used for interpolation of the time aftereffect, so it may be a one-dimension regionalized series data when the data is fit for the model variable and can be analyzed with geostatistics. An remarkably and the ratio of deterministic element to introduction to geostatistics methods for temporal total variance is big enough at the same time [8]. patterns analysis was presented in the current paper. Especially for the data generation to generation, the According to geostatistics, the data series of total interpolated values associated with the estimation number, the 1st generation, the 3rd generation and the errors can be used to calculate the historical over-wintered larvae year to year displayed rather coincidence rate when the interpolation interval is a better autocorrelation and predictability, and the same generation. generation larvae of the last 5, 3, 6 and 5 years should The static pest population model such as be main response for forecasting, respectively. 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