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The relation of potato leaf roll virus net necrosis in potato tubers to the interval between planting and inoculation
C'ropl'r,mw,,mVol
16. No 6. pp. S-53'). 1497 6) 1997 Elsevier Science Ltd All nphts rewrvrd Prmted in Freal Britain 0261-2194197 $l7.cn+ll.llo
PII: SO261-2194(97)00032-X ELSEVIER
The relation of potato leaf roll virus net necrosis in potato tubers to the interval between planting and inoculation Jutta Roosen**, Ray G. Huffaker+, Raymond J. Folwell+, Thomas L. Marsh+ and Ronald C. Mittelhammer+ “Department of Economics, Iowa State University, Ames, IA 50071-1070, USA and +Department of Agricultural Economics, Washington State University, Pullman, WA 99164-6210, USA
The green peach aphid, Myzus persicae, is a vector of potato leaf roll virus. Inoculated potato plants may develop tubers expressing net necrosis at harvest or in storage, which can significantly reduce the crop’s commercial value. Insecticides have been traditionally used in a prophylactic manner to suppress the aphid population in the field thereby preventing inoculation and the advent of net necrosis. To analyze the rationale of such an insecticide application decision, data generated by two field experiments were used to establish an empirical relationship between the probability that a tuber will express net necrosis (NN probability) and the time after planting that inoculation occurs (inoculation interval). In contrast to past studies, the data analyzed here allow for the investigation of the impact of inoculation dates occurring over the entire growing season. This uncovers the previously unknown empirical result that NN probabilities may peak before monotonically declining in the second half of the growing season. It implies that insecticide spraying might profitably be concentrated on inoculation intervals generating peak probabilities, to ‘flatten’ the peaks to acceptable probability levels. The data also permitted a limited analysis of the systematic ways that increasing storage periods may alter the empirical relationship between NN probabilities and inoculation intervals. 0 1997 Elsevier Science Ltd Keywords: green peach aphid; potatoes; potato leaf roll virus; net necrosis
Introduction Potato leaf roll virus (PLRV) causes significant economic losses in US potato production, and has been identified as the single most important problem the industry faces (Folwell et al., 1981). The greatest loss owing to PLRV is the development of speckling or netting of discolored tissue in tubers, called net necrosis (NN), which leads to quality and price reductions. Not all tubers from an infected plant of a susceptible cultivar develop NN, and the time at which NN is expressed varies. Potato tubers that are not necrotic at harvest can become so in storage. Transmission of PLRV occurs when healthy potato plants are infected by viruliferous aphid vectors, predominantly the green peach aphid (GPA), Myzus persicae . One common management practice is to control aphid vectors in the field with insecticides in a prophylactic manner (Starch and Manzer, 1985). The recent reintroduction of aldicarb (Temik) into the pesticide market gives potato growers the choice of a *To whom correspondence
should be addressed
single pre- or post-emergent soil pesticide apphcation, or multiple applications of a sprayed foliar insecticide over the growing season. The objective of this research is to shed light on the application decision by using field-experiment data from the central Washington production region to establish an empirical relationship between the probability that a tuber expresses NN (for various fixed storage periods), and the time after planting that the associated cultivar is inoculated (inoculation interval). Identifying inoculation intervals of peak NN probability is an important first step toward establishing an optimized timing schedule that applies pesticides when they are the most effective, and foregoes their use when they are ineffective. Such fine-tuning will allow potato growers to minimize the use of pesticides with an acceptable level of production risk. Two previous studies have established the empirical relevance of PLRV-inoculation dates in other applications and geographic regions. Manzer, Merriam, Starch and Simpson (1982) conducted field experiments in Maine in 1958 and 1976. In 1958, the
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Potato leaf roll virus, planting and inoculation:
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Green Mountain cultivar was planted on six dates and inoculated on four dates over the first half of the growing season. Harvested tubers were examined for NN after approximately 4 months of storage at 10°C. A quadratic relationship was estimated between the percentage of tubers with NN and the number of days between planting and inoculation (Manzer et al., 1982, Fig. 2). The minimum of the function occurred increased 40 days after planting, and thereafter monotonically until the last inoculation date (80 days after planting). The 1976 experiment consisted of four plantings and six inoculations. NN frequencies (plotted in a bar diagram) monotonically increased at an increasing rate with later inoculation dates (Manzer et al., 1982, Fig. 3). Alternatively, Starch and Manzer (1985) set up field experiments in Maine over a 3 year period (1974-1976) to estimate the impact of the infection period over the latter half of the growing season (the time from inoculation date to harvest) on the of plants developing PLRV. The percentage incidence of NN in tubers was not of interest. Specifically, they planted on a single date, began inoculations in 3 day intervals over the latter part of 20 August to the growing season (from mid-September), harvested all tubers from each plant five times for each inoculation date (3, 6, 9, 12 and 15 days after each inoculation), stored tubers at 3°C until they were planted the following spring, and, finally, examined the produced plants for presence of PLRV. Although the percentage of plants developing PLRV increased with the infection period, there was no trend of increasing or decreasing numbers of leaf roll infected tubers from early to late inoculation. Similar to Manzer et al. (1982) and in contrast to Starch and Manzer, this research focuses on the statistical relationship between the probability that a tuber will express NN and the time interval between planting and inoculation. In contrast to the limited inoculation periods analyzed in the above studies, this research analyzes data generated by two US Department of Agriculture-Economic Research Service (USDA-ERS) field experiments that measured the impacts of inoculation over the entire potato growing season (from early July until mid-September). The concealed present analysis reveals a previously empirical result: NN probabilities peak at inoculation dates between the two time intervals examined in the prior studies, and later inoculation dates lead to monotonically declining NN probabilities for the remainder of the growing season. In other words, NN probabilities over the last half of the growing season do not monotonically increase as a continuation of the curve of Manzer et al. (1982) fitted for the first half. This result has important farm-management implications that are addressed in the discussion section of the paper. The USDA-ERS field experiments underlying this study were designed to measure the impact of inoculation date on the expression of NN, and this is the paper’s emphasis in analyzing them. However, the experiments also provided limited information on the combined effect of inoculation interval and storage time on the expression of NN, as harvested potatoes
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were examined after varying storage periods. The results imply potential gains from coordinating the timing of pest-control and marketing activities that can be validated in future studies focusing on the impact of storage time to a greater extent. A final contribution is that the regression model used here has more reliable statistical properties. The two prior studies apply probability models that fail to restrict estimated NN probabilities to the O-l range. The failure to impose this restriction on the regression can produce inefficient parameter estimates and biased variance estimates. Consequently, hypothesis tests can lead to incorrect inferences. Alternatively, the research reported herein uses a logistic regression model restricting the estimated probabilities to the proper O-l range.
Materials and methods The data were generated from two field experiments conducted by USDA-ERS-Yakima from 1982 to 1983. The site of the 1982 experiment was the Moxee farm in the Yakima valley. Four test plots were arranged in a single-block design with a 10 ft buffer around th.e block’s perimeter. E,ach plot (measuring 70 ft long and 3 ft wide) contained five plants spaced 14 ft apart. The Russet Burbank variety was planted on 25 May, and each plant was inoculated with PLRV once on one of four dates: 2 July, 28 July, 16 August and 7 September. There were five replications on each inoculation date, and also five replications of an uninoculated control plant throughout the growing season. On the specific inoculation date, the selected potato plants were inoculated with PLRV by placing five apterous, viruliferous GPAs on each of the selected plants and allowing them to feed for 2 days. Afterwards, the entire test plot was sprayed with the insecticide ethylene dibromide (Dibrome). The plants were protected by cages to prevent uncontrolled infection, and periodically inspected visually for indications of other diseases that might cause NN or other physiological disorders. The potatoes were harvested on 1 October and put in storage under commercial potato storage conditions. In 2 month intervals, from November 1982 to May 1983, potato samples, randomly selected for each inoculation date, were taken out of storage and visually examined for NN. The sample consisted of 281 examined potato tubers of which 39 expressed NN. The 1983 experiment also was conducted at the Moxee farm, and was designed similarly to the 1982 effort. The potatoes were planted on 29 April 1983, inoculated on 10 June, 5 July, 1 August and 6 September, and harvested on 5 October. Out-ofstorage tests were carried out on 7 November, 9 January, 7 March and 30 April. The sample consisted of 318 examined potato tubers of which 63 expressed NN. Tables I and 2 summarize the basic field data used to statistically estimate the NN probability curves for the experiments in 1982 and 1983, respectively. The right-most columns of each table show the total number of examined tubers (N) and the proportions
Potato leaf roll virus, planting and inoculation: J. Roosen et al. Table 1. Number of observations
and proportions
of infected tubers for each inoculation
and storage interval, 1982
Time in storage 48 days
i 68days
1118days
22X days
Time between planting and inoculation (days)
N
I’
N
I’
N
I’
3x 64 X3 10s Total
IO IO 10 IO 40
0.20 0 0.10 0. IO 0. IO
IO IO IO 10 40
0.10 0 0 0 0.03
24 34 2X 20 I06
0.13 0.M 0.25 0.05 0. I2
tubers (p) for each inoculation interval (time elaDsed between planting and inoculation). The interior dolumns of each table sort these figures by the number of days that the tubers were in storage before examination. of necrotic
Statistical model The purpose of our statistical analysis is to explain the probability that PLRV is expressed in a potato tuber, given that the tuber comes from an infected plant. As mentioned above, past work estimated such probabilities using linear regression equations that fail to restrict probabilities within the theoretically proper O-1 interval [see Manzer et al. (1982), p. 3423. This section introduces the well-known logistic transformation of the linear regression model that statisticians employ to restrict probabilities within the proper interval (see Amemiya, 1981; Hosmer and Lemeshow, 1989; Mead et al., 1993). Let us consider a generalized version of the linear regression model used in previous studies. Let yj = 1 indicate the presence of necrotic tissue in the ith tuber sampled, and y; = 0 indicate the absence of necrotic tissue, where I = 1, . . . , N tubers in the sample. The linear regression model attempts to explain the presence of necrotic tissue with a linear combination of explanatory variables including, for example, the time interval between planting and inoculation, The linear regression model for the ith sampled tuber can be written as ?‘,= h;, x,, +b;zX;2+.
+b;kX,k+u,
and proportions
2s 30 21 I9 9s
I’
N
I’
0.12 0.23 0.3x 0. I6 0.22
69 x4 69 59 2x1
0. I3 0. I I 0.23 0.08 0.14
between planting and inoculation of the potato plant from which the ith sampled tuber was harvested. The his represent regression coefficients statistically tying measurements on the explanatory variables to whether necrotic tissue appears in the ith sampled tuber. Finally, ui is an error term needed because the linear model generally does not account for all the reasons that NN can occur in the ith sampled tuber. Linear regression models typically assume the error term to be an independently and identically distributed random variable. Using matrix notation, the linear regression model in equation (1) can be rewritten more compactly as y;=Xib+~l,,i=l,__.,
N
(2) In equation (2), Xi = (Xl, XI, . . . , Xk) is the (1 x k) vector of measurements on the explanatory variables associated with the ith sampled tuber, b= T‘ is the (k x 1) coefficient vector, and (ht,h2, . . ..hk) the superscript T denotes the transpose operator. The compact form of the linear regression model in equation (2) is much more convenient to use in the derivations that follow than the expanded form in equation (1). As mentioned above, statisticians use a logistic transformation of the linear model to ensure that predicted levels of the y,s fall within the O-l interval required for statistically reasoqfble probabilities. The logistic transformation convertmg the linear model into a probability model is Pr[yi = l( Xi] = F(Xib) =
(1)
for the I = 1, . . ., N tubers in the sample. The X,s represent the measurements on the explanatory variables for the ith sampled tuber, and there are j=l 5 .-., k of them. For example, the first explanatory variable, X;,, could measure the time interval
Table 2 Number of observations
N
Total
exp(Xib)
(3)
1 + exp(Xb)
In equation (3), Pr[yi = llXj] denotes the probability that the ith sampled tuber exhibits NN (i.e. that yi = 1) given the corresponding measurements on the explanatory variables Xi, and F(Xib) is the logistic
of infected tubers for each inoculaGon and storage interval, 1983 Time in storage
36 days
99 days
200 days
146 days
Total
Time hctween planting and inoculation (days)
N
P
N
P
N
P
N
I’
N
P
42 67 94 I30 Total
20 20 20 20 80
0.21) 0.30 0.20 0.10 0.20
20 20 20 I9 79
0.10 0.30 0.25 0.2 I 0.22
20 20 20 20 X0
0.10 0.35 0.10 0.10 0.12
20 I9 20 20 79
0.15 0.40 0.20 0. IO 0.22
80 79 80 79 31X
0.14 0.34 0.14 0. IO 0.20
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Potato leaf roll virus, planting and inoculation: J. Roosen et al. cumulative distribution function (cdf) that forces the values associated with the linear model &b onto the O-l interval. It has the desired properties of a cdf: and F(Xib) is monotonically F(-co)=O, F(cc)=l, increasing in i&b. As F(Xib) is a nonlinear transformation of the linear regression function, the associated parameters b cannot be used as in the linear model Xib to directly translate a change in an explanatory variable into the change of the probability Pv[yi = l]Xi], Generally, the elasticity at means is calculated to interpret the effect of the explanatory variables on the probability that a tuber expresses NN. It gives the percentage change in NN probability if the kth explanatory variable (X,) changes by 1%. The elasticity at means is calculated as
(4) where Xk is the arithmetic mean of the kth explanatory variable, and all variables are evaluated at their means. In equation (4),
measures the change in NN probability owing to an incremental change in the kth explanatory variable, where f(B) is the logistic probability density function
To measure the goodness of fit of the logistic model, White (1993) suggested several conventional R2 statistics. Although the R* statistics are different in magnitude, each statistic can provide consistent comparisons of the relative goodness of fit across various estimated functional forms of the explanatory variables. Here the Cragg-Uhler R2 is reported, which is computed as R2 = l-exp{2[L(O)-L(~)]/N} 1 -exp[2L(O)/fVj where L(0) denotes the likelihood function estimated with the constant term only, and t(h) denotes the likelihood function estimated with all the variables included. The Cragg-Uhler R2 is not an absolute measure for the goodness of fit in a logistic regression as the R2 statistic is in an ordinary least-squares regression, and as a result it is not bounded within the O-l interval. Another measure for the goodness of fit is the percent of right predictions. It calculates the ratio of the correctly predicted observations at y; = 0 and y, = 1 to the total number of observations in the sample. We used both statistics to compare various functional forms of the explanatory variables specified in X. In our empirical model, we propose that the probability of y, = 1 (which indicates the presence of necrotic tissue in a tuber) and the probability y; = 0
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(which indicates no necrotic damage in the tuber) can be significantly influenced by two important variables. These variables are the number of days between planting and inoculation, hereafter the ‘inoculation interval’, which is denoted as Xi,, and the number of days the potatoes are in storage, hereafter the ‘storage interval’, which is denoted as XZz. The importance of the inoculation interval was established in the literature review discussed above. Studies by Rich (1951) and Powell and Mondor (1972) suggest that the probability that PLRV infected tubers express NN is contingent upon the storage interval. Once an empirical relationship is reliably established, potato growers can control these variables to decrease the probability that net necrosis will be expressed at harvest or in storage. A priori, it was expected that the number of tubers with net necrosis either increases with the storage interval or remains constant once all infected tubers have developed visual symptoms. The inoculation interval should play an important part in determining the impact of the storage interval, with potato plants inoculated early (late) in the season probably yielding necrotic tubers after relatively short (long) storage intervals. To model this effect an interaction term (X1X2) was included in the regression equation. As the inoculation and storage intervals change simultaneously, the interaction term allows the effect of storage to vary directly with the inoculation date. To arrive at the final functional forms of the linear structure xb for the 1982 and 1983 samples, combinations of transformations of the explanatory variables cubic, interaction, etc.) were (1inear, squared, included. Then, non-significant terms were gradually dropped out, based on standard t-statistics, likelihood ratio test, Cragg-Uhler R2, and prediction success tables. The standard t-statistics were used to test whether each estimated coefficient was significantly different from zero. They can be calculated as the absolute value of the ratio of an estimated coefficient to its standard error. The likelihood ratio statistics were used to test whether a set of estimated coefficients were significantly different from zero. The likelihood ratio test procedure compares the maximum value of the likelihood function under the assumption that each coefficient in the set is zero L(bo) to the maximum value of the unrestricted likelihood function L(b). Under the null hypothesis, the asymptotic likelihood ratio statistic is calculated as which is distributed as a x2 2{ln[L(b)J-ln[L(bo)]}, random variable with degrees of freedom q equal to the number of coefficient restrictions. The equations were estimated using a maximum likelihood estimation procedure in the statistics package Shazam by White (1993) which automatically computes the various measures of fit. The functional forms resulting in the best fits for the 1982 and 1983 data, respectively, were
X%3 =hx3,t,+&,,Xr
+bK0,*X:+b83,3X,X2+bX3,~~
where bx2.o and bH3,,)are intercept and 1983 regressions, respectively.
(gb)
terms for the 1982
Potato leaf roll virus, planting and inoculation: J. Roosen et al. Table 3. Estimation
Table 4. Marginal effects
results 1982
Variable
I983
h X’,,, = 14.361’ (1.86, 7.7105) hxz., = -0.84847’ (2.28, 0.37204) h XL,>= 1.277E- 02” (2.33, 5.4808E-03) hxr..q= -6.139E-OS (2.41. 2538E-OS) h x2,4= 1.4E-04”’ (2.82, 4.9661E-OS)
Constant XI (XI )’ (XI ).? XJZ
h X3,(,= - 3.9587’ ’ (3.19, 1.2427) h xz,, = 7.388-01” (24. 3.0483E ~ 02) h Hi,Z= -4.4E-04” (2.6. 1.6921E-04)
h nq.?= - 2.hShE -OS (0.38, 6.9309E -OS) h xx,? = 9.4SE -06 (0.38, 2.4508E - OS)
(X,1’
16.533 (4 d.f.)’ 0. IO3 77.7%
Likelihood ratio test Cragg-Uhler R’ Percent of right predictions Numbers
,
in parentheses
8.49767 (4 d.f.)’ 0.042 69.1 r/r’
denotes signilicance
(r-statistic,
standard
error).
at the alpha = O.IO. 0.M.
0.01 level.
The estimated coefficients for equations (8a) and (8b), along with the summary statistics defined in the preceding section, appear in Table 3. The t-statistics reported in the table are used to test whether each estimated coefficient is significantly different from zero. They are calculated as the absolute value of the ratio of an estimated coefficient to its standard error. Figures I and 2 plot estimated NN probabilities 0.3s -
&
9
Il.30
-
I).?5 -
3.5 40
l
Stor=50
.
Stor=lOO
A
Stor=ISO
.50
45
Number
1983
0.69 0.12
-0.0612 -0.0012
71 163
83 120
against the time interval between planting and inoculation for fixed storage periods in the 1982 and 1983 experiments, respectively. The results are presented for each year separately. Results of 1982 experiment
represent
Results
+ 4
Elasticity at means (%) XI XZ Means (days) XI XZ
1982
5s
60
of days
65
70
between
Figure 1. Results of 1982 experiment.
l
7s
80
planting
xs
90
95
100
105
and inoculation
NN, Net necrosis
Stor=50
. Stor=100 A Stor=150 x
Stor=200
Each estimated parameter in the 1982 regression is significant according to an individual t-statistic. As explained above, because these parameters do not directly translate a unit change in the associated explanatory variables into a change in NN probability, we calculated the elasticities at means reported in Table 4. The elasticities are evaluated at mean inoculation and storage intervals of 71 days and 163 days, respectively. They indicate that when inoculation and storage intervals increase from their means by l%, NN probability increases by the smaller-than-unit percentages of 0.69% and 0.12%, respectively. In other words, the response of NN probability to percentage changes in both variables away from their means is inelastic. The above elasticities characterize the behavior of NN probability at fixed levels of the explanatory variables. The estimated NN probability curves in Figure 1 provide a wider prospective by displaying behavior over the entire range of inoculation intervals over the growing season. Each probability curve is associated with a different fixed storage interval, and exhibits the same general behavior. The curves first decrease to a minimum at g-55 day inoculation intervals, then increase toward a maximum at about and finally monotonically 85-90 day intervals, decrease for longer intervals. The summary statistics reported at the bottom of Table 3 relate to the overall fit of the estimated 1982 equation. The likelihood ratio test measures the joint significance of the parameters by comparing the likelihood function of the equation estimated with constant term only with the likelihood function of the entire estimated equation. The test statistic of 16.533 is highly significant at the 0.01 level, and thus reflects a good fit. The percent of right predictions for the estimated equation is a very respectable 77.7%, given the likely existence of other variables influencing the expression of NN that were not controlled in the field experiment. Results of 1983 experiment
0
I
I
I
!
I
I
I
,I, 45 50 55 hO65 70 7s Number
of days
I
I
I
I
I
I
x0
x5
90
YS
100
105
between
Figure 2. Results of 1983 experiment.
planting
I I10
I 115
and inoculation
NN, Net necrosis
I
I 12011~1v
I
The estimated coefficients associated with the inoculation-date variables are individually highly significant, whereas those associated with storage times are
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Potato leaf roll virus, planting and inoculation:
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individually insignificantly different from zero. The elasticity at means is calculated to be -0.0612% with respect to the inoculation interval, and 0.0012% with respect to the storage interval. The mean inoculation interval is 83 days, and the mean storage interval is 120 days. The elasticity at means with respect to the inoculation interval is negative because the mean of 83 days lies on the decreasing portion of the NN probability curves. Similar to the 1982 results, the response of NN probability to each variable is highly inelastic at their means. FigL1~ 2 shows NN probability curves for each storage period as a function of inoculation intervals for the 1983 experiment. Similar to the 1982 curves in Figure I, the 1983 curves monotonically increase to maxima at approxiinoculation intervals, then 75-85 day mately monotonically decrease for longer intervals. Finally, the likelihood ratio test is significant at the 0.10 level, and the percent of right predictions is 69.1%. Both measures reflect a moderately good fit of the estimated equation to the 1983 data.
Discussion
The 1982 NN probability curves are identical in shape over a comparable period to the NN probability curve estimated by Manzer et al. (1982) for their 1958 experiment (see Manzer et al. (1982) Fig. 2). We recall that those workers looked at inoculation dates only over the first half of the growing season (about 80 days after planting) in that experiment, and stored the tubers for approximately 120 days after harvest. They estimated a curve monotonically decreasing toward a minimum at about 40 days from planting to inoculation, and then monotonically increasing at a steep rate for the remainder of the first half of the growing season. Although the minimum of our 1982 curve occurs approximately 10 days later for a similar fixed storage period, the shape and steepness of the curve are remarkably similar. In contrast, our 1983 curves do not initially monotonically decrease toward a minimum probability. The absence of this behavior was observed by Manzer et al. (1982) in the plotted NN frequencies resulting from their 1976 experiment. Interestingly, our 1982 and 1983 NN probability curves peak at inoculation dates after those studied by Manzer et al. (1982) and then monotonically decline. If NN probabilities were found instead to continue increasing for inoculation dates throughout the second half of the growing season, the grower might be well advised to undertake a continuously high spraying regimen to prevent these later inoculations. However, the existence of peak NN probabilities in the second half of the season suggests that spraying might be concentrated on the interval of inoculation dates generating the peak probabilities, to ‘flatten’ them to acceptable levels. Although the USDA-ERS field experiments were designed to study the impact of inoculation dates on NN probabilities, the experiments shed some light on the combined effect of inoculation date and storage time, as harvested potatoes were examined after varying storage periods (see Tables 1 and 2). As
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discussed below, the NN probability curves estimated from the 1982 data respond systematically, in biologically reasonable ways, to increases in the storage period. In contrast, the NN probability curves estimated from the 1983 data (Figure 2) do not respond systematically to increases in the storage period. This is evidenced in the 1983 regression results (Table 3) where explanatory variables including storage time have estimated coefficients that are not significantly different from zero. The failure of the 1983 experiment to replicate the storage results of the 1982 experiment may indicate that, although the total sample size of tubers was more than adequate to statistically link inoculation dates with NN probabilities in each year, the sample size of tubers in each examination period may possibly be too small to consistently generate systematic ‘population’ storage results over the 2 years. Despite this possible problem, our statistical analysis of the 1982 data uncovers some interesting and potentially useful patterns in the combined impact of inoculation dates and storage time on NN probabilities. We believe the results are worth documenting for future comparison with the results of experiments focused on storage time to a larger extent. Increasing the storage period systematically shifted the 1982 NN probability curves upward (Figure I). Thus, consistent with the estimated positive interaction coefficient (6x2,4) reported in Table 3, the longer tubers remain in storage, the more likely they are to express NN. Moreover, as the curves shift upward, the discrepancy between the minimum and maximum NN probabilities increases. For example, the curve for a ‘short’ 50 day storage interval has a minimum NN probability of approximately 3% and a maximum of just over 5%, whereas the curve for a ‘long’ 200 day storage interval has a minimum of about 8% and a maximum of just over 30%. In sum, shorter storage intervals generate relatively flat and small NN probabilities over the course of the growing season, whereas longer storage intervals decrease the dispersion of probabilities around relatively larger minimum and maximum NN probabilities, thereby creating steeper probability curves. The steeper curves indicate that NN probabilities increase at a faster rate in the middle portion of the growing season as storage intervals increase. Let us assume, for the sake of discussion, that the systematic tradeoff between inoculation date and storage time in the 1982 data is validated in future studies. The management implications become clear if the NN probability curves are interpreted as representing the risk of a no-spraying policy. Growers may choose to store potatoes after harvest for increased marketing flexibility, or may be required to do so for an undetermined period by pre-season contracts with processors. Pre-season contracts often contain terms allowing processors to determine the storage period, and to reject, or pay decreased prices, for storage lots exceeding a target level of NN. This places the risk of storage squarely on the growers. The 1982 data show that short storage periods generate NN probabilities that are relatively low and ‘flat’ across inoculation dates. However, as the storage interval increases, the
Potato leaf roll virus, planting and inoculation: probabilities group at higher peaks, and the rate at which the probabilities increase for later inoculation dates increases. Thus, the penalty for postponing spraying for another inoculation day increases with the storage interval. Consequently, growers may be able to ‘insure’ themselves against the added risk of a relatively long storage interval by modifying the NN probability curve consistent with such an interval, and (as discussed above) concentrating spraying on the interval of inoculation dates associated with the peak probability so that the curve is ‘flattened’ to an acceptable probability level.
The authors wish to thank Lee Fox and Harold Toba for providing the data, and Lee Fox for his helpful explanations on the experimental design. References T. (1981) Qualitative
cultural methods for suppressing the green peach aphid as a vector of virus diseases of potatoes and sugarbeet. Bulletin 0900 College of Agriculture Research Center, Washington State University, Pullman Hosmer,
D. W. Jr and Lemeshow,
S. (1989) Applied Logistic
Regression. John Wiley, New York
Manzer, F. E., Merriam, D. C., Starch, R. H. and Simpson, G. W. (1982) Effect of time of inoculation with potato leafroll virus on development of net necrosis and stem-end browning in potato tubers. Am. Potato J. 59, 337-349 Mead, R., Curnow, R. N. and Hasted, Methods
in Agriculture
and Experimental
A. M. (1993) Statistical Biology. Chapman and
Hall, London Powell, D. M. and Mondor, W. T. (1972) Development of net necrosis in stored Russet Burbank potatoes. Proc. llth Annual Washington Potato Co@., Moses Lake, WA, USA
Acknowledgements
Amemiya,
J. Roosen et al.
response
models:
a survey. J.
Econ. Literature 19, 1483-1536
Folwell, R. G., Fagerlie, D. L., Tamaki, I., Ogg, A. G., Comes, R. and Bartielle, J. L. (1981) Economic evaluation of selected
Rich, A. V. (1951) Phloem necrosis of Irish potato Washington. Wash. Agric. Exp. Stn. Bull. 528, l-49
tubers in
Starch, R. H. and Manzer, F. E. (1985) Effect of time and date of inoculation, plant age, and temperature on translocation of potato leafroll virus into potato tubers. Am. Potato J. 62, 137-143 White, K. J. (1993) Shazam: Econometrics Computer Program: User’s Reference Manual, Version 7.0. McGraw-Hill, New York Received 8 August 1996 Revised 27 January 1997 Accepted 19 March 1997
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16. No 6. pp. S-53'). 1497 6) 1997 Elsevier Science Ltd All nphts rewrvrd Prmted in Freal Britain 0261-2194197 $l7.cn+ll.llo
PII: SO261-2194(97)00032-X ELSEVIER
The relation of potato leaf roll virus net necrosis in potato tubers to the interval between planting and inoculation Jutta Roosen**, Ray G. Huffaker+, Raymond J. Folwell+, Thomas L. Marsh+ and Ronald C. Mittelhammer+ “Department of Economics, Iowa State University, Ames, IA 50071-1070, USA and +Department of Agricultural Economics, Washington State University, Pullman, WA 99164-6210, USA
The green peach aphid, Myzus persicae, is a vector of potato leaf roll virus. Inoculated potato plants may develop tubers expressing net necrosis at harvest or in storage, which can significantly reduce the crop’s commercial value. Insecticides have been traditionally used in a prophylactic manner to suppress the aphid population in the field thereby preventing inoculation and the advent of net necrosis. To analyze the rationale of such an insecticide application decision, data generated by two field experiments were used to establish an empirical relationship between the probability that a tuber will express net necrosis (NN probability) and the time after planting that inoculation occurs (inoculation interval). In contrast to past studies, the data analyzed here allow for the investigation of the impact of inoculation dates occurring over the entire growing season. This uncovers the previously unknown empirical result that NN probabilities may peak before monotonically declining in the second half of the growing season. It implies that insecticide spraying might profitably be concentrated on inoculation intervals generating peak probabilities, to ‘flatten’ the peaks to acceptable probability levels. The data also permitted a limited analysis of the systematic ways that increasing storage periods may alter the empirical relationship between NN probabilities and inoculation intervals. 0 1997 Elsevier Science Ltd Keywords: green peach aphid; potatoes; potato leaf roll virus; net necrosis
Introduction Potato leaf roll virus (PLRV) causes significant economic losses in US potato production, and has been identified as the single most important problem the industry faces (Folwell et al., 1981). The greatest loss owing to PLRV is the development of speckling or netting of discolored tissue in tubers, called net necrosis (NN), which leads to quality and price reductions. Not all tubers from an infected plant of a susceptible cultivar develop NN, and the time at which NN is expressed varies. Potato tubers that are not necrotic at harvest can become so in storage. Transmission of PLRV occurs when healthy potato plants are infected by viruliferous aphid vectors, predominantly the green peach aphid (GPA), Myzus persicae . One common management practice is to control aphid vectors in the field with insecticides in a prophylactic manner (Starch and Manzer, 1985). The recent reintroduction of aldicarb (Temik) into the pesticide market gives potato growers the choice of a *To whom correspondence
should be addressed
single pre- or post-emergent soil pesticide apphcation, or multiple applications of a sprayed foliar insecticide over the growing season. The objective of this research is to shed light on the application decision by using field-experiment data from the central Washington production region to establish an empirical relationship between the probability that a tuber expresses NN (for various fixed storage periods), and the time after planting that the associated cultivar is inoculated (inoculation interval). Identifying inoculation intervals of peak NN probability is an important first step toward establishing an optimized timing schedule that applies pesticides when they are the most effective, and foregoes their use when they are ineffective. Such fine-tuning will allow potato growers to minimize the use of pesticides with an acceptable level of production risk. Two previous studies have established the empirical relevance of PLRV-inoculation dates in other applications and geographic regions. Manzer, Merriam, Starch and Simpson (1982) conducted field experiments in Maine in 1958 and 1976. In 1958, the
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Potato leaf roll virus, planting and inoculation:
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Green Mountain cultivar was planted on six dates and inoculated on four dates over the first half of the growing season. Harvested tubers were examined for NN after approximately 4 months of storage at 10°C. A quadratic relationship was estimated between the percentage of tubers with NN and the number of days between planting and inoculation (Manzer et al., 1982, Fig. 2). The minimum of the function occurred increased 40 days after planting, and thereafter monotonically until the last inoculation date (80 days after planting). The 1976 experiment consisted of four plantings and six inoculations. NN frequencies (plotted in a bar diagram) monotonically increased at an increasing rate with later inoculation dates (Manzer et al., 1982, Fig. 3). Alternatively, Starch and Manzer (1985) set up field experiments in Maine over a 3 year period (1974-1976) to estimate the impact of the infection period over the latter half of the growing season (the time from inoculation date to harvest) on the of plants developing PLRV. The percentage incidence of NN in tubers was not of interest. Specifically, they planted on a single date, began inoculations in 3 day intervals over the latter part of 20 August to the growing season (from mid-September), harvested all tubers from each plant five times for each inoculation date (3, 6, 9, 12 and 15 days after each inoculation), stored tubers at 3°C until they were planted the following spring, and, finally, examined the produced plants for presence of PLRV. Although the percentage of plants developing PLRV increased with the infection period, there was no trend of increasing or decreasing numbers of leaf roll infected tubers from early to late inoculation. Similar to Manzer et al. (1982) and in contrast to Starch and Manzer, this research focuses on the statistical relationship between the probability that a tuber will express NN and the time interval between planting and inoculation. In contrast to the limited inoculation periods analyzed in the above studies, this research analyzes data generated by two US Department of Agriculture-Economic Research Service (USDA-ERS) field experiments that measured the impacts of inoculation over the entire potato growing season (from early July until mid-September). The concealed present analysis reveals a previously empirical result: NN probabilities peak at inoculation dates between the two time intervals examined in the prior studies, and later inoculation dates lead to monotonically declining NN probabilities for the remainder of the growing season. In other words, NN probabilities over the last half of the growing season do not monotonically increase as a continuation of the curve of Manzer et al. (1982) fitted for the first half. This result has important farm-management implications that are addressed in the discussion section of the paper. The USDA-ERS field experiments underlying this study were designed to measure the impact of inoculation date on the expression of NN, and this is the paper’s emphasis in analyzing them. However, the experiments also provided limited information on the combined effect of inoculation interval and storage time on the expression of NN, as harvested potatoes
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were examined after varying storage periods. The results imply potential gains from coordinating the timing of pest-control and marketing activities that can be validated in future studies focusing on the impact of storage time to a greater extent. A final contribution is that the regression model used here has more reliable statistical properties. The two prior studies apply probability models that fail to restrict estimated NN probabilities to the O-l range. The failure to impose this restriction on the regression can produce inefficient parameter estimates and biased variance estimates. Consequently, hypothesis tests can lead to incorrect inferences. Alternatively, the research reported herein uses a logistic regression model restricting the estimated probabilities to the proper O-l range.
Materials and methods The data were generated from two field experiments conducted by USDA-ERS-Yakima from 1982 to 1983. The site of the 1982 experiment was the Moxee farm in the Yakima valley. Four test plots were arranged in a single-block design with a 10 ft buffer around th.e block’s perimeter. E,ach plot (measuring 70 ft long and 3 ft wide) contained five plants spaced 14 ft apart. The Russet Burbank variety was planted on 25 May, and each plant was inoculated with PLRV once on one of four dates: 2 July, 28 July, 16 August and 7 September. There were five replications on each inoculation date, and also five replications of an uninoculated control plant throughout the growing season. On the specific inoculation date, the selected potato plants were inoculated with PLRV by placing five apterous, viruliferous GPAs on each of the selected plants and allowing them to feed for 2 days. Afterwards, the entire test plot was sprayed with the insecticide ethylene dibromide (Dibrome). The plants were protected by cages to prevent uncontrolled infection, and periodically inspected visually for indications of other diseases that might cause NN or other physiological disorders. The potatoes were harvested on 1 October and put in storage under commercial potato storage conditions. In 2 month intervals, from November 1982 to May 1983, potato samples, randomly selected for each inoculation date, were taken out of storage and visually examined for NN. The sample consisted of 281 examined potato tubers of which 39 expressed NN. The 1983 experiment also was conducted at the Moxee farm, and was designed similarly to the 1982 effort. The potatoes were planted on 29 April 1983, inoculated on 10 June, 5 July, 1 August and 6 September, and harvested on 5 October. Out-ofstorage tests were carried out on 7 November, 9 January, 7 March and 30 April. The sample consisted of 318 examined potato tubers of which 63 expressed NN. Tables I and 2 summarize the basic field data used to statistically estimate the NN probability curves for the experiments in 1982 and 1983, respectively. The right-most columns of each table show the total number of examined tubers (N) and the proportions
Potato leaf roll virus, planting and inoculation: J. Roosen et al. Table 1. Number of observations
and proportions
of infected tubers for each inoculation
and storage interval, 1982
Time in storage 48 days
i 68days
1118days
22X days
Time between planting and inoculation (days)
N
I’
N
I’
N
I’
3x 64 X3 10s Total
IO IO 10 IO 40
0.20 0 0.10 0. IO 0. IO
IO IO IO 10 40
0.10 0 0 0 0.03
24 34 2X 20 I06
0.13 0.M 0.25 0.05 0. I2
tubers (p) for each inoculation interval (time elaDsed between planting and inoculation). The interior dolumns of each table sort these figures by the number of days that the tubers were in storage before examination. of necrotic
Statistical model The purpose of our statistical analysis is to explain the probability that PLRV is expressed in a potato tuber, given that the tuber comes from an infected plant. As mentioned above, past work estimated such probabilities using linear regression equations that fail to restrict probabilities within the theoretically proper O-1 interval [see Manzer et al. (1982), p. 3423. This section introduces the well-known logistic transformation of the linear regression model that statisticians employ to restrict probabilities within the proper interval (see Amemiya, 1981; Hosmer and Lemeshow, 1989; Mead et al., 1993). Let us consider a generalized version of the linear regression model used in previous studies. Let yj = 1 indicate the presence of necrotic tissue in the ith tuber sampled, and y; = 0 indicate the absence of necrotic tissue, where I = 1, . . . , N tubers in the sample. The linear regression model attempts to explain the presence of necrotic tissue with a linear combination of explanatory variables including, for example, the time interval between planting and inoculation, The linear regression model for the ith sampled tuber can be written as ?‘,= h;, x,, +b;zX;2+.
+b;kX,k+u,
and proportions
2s 30 21 I9 9s
I’
N
I’
0.12 0.23 0.3x 0. I6 0.22
69 x4 69 59 2x1
0. I3 0. I I 0.23 0.08 0.14
between planting and inoculation of the potato plant from which the ith sampled tuber was harvested. The his represent regression coefficients statistically tying measurements on the explanatory variables to whether necrotic tissue appears in the ith sampled tuber. Finally, ui is an error term needed because the linear model generally does not account for all the reasons that NN can occur in the ith sampled tuber. Linear regression models typically assume the error term to be an independently and identically distributed random variable. Using matrix notation, the linear regression model in equation (1) can be rewritten more compactly as y;=Xib+~l,,i=l,__.,
N
(2) In equation (2), Xi = (Xl, XI, . . . , Xk) is the (1 x k) vector of measurements on the explanatory variables associated with the ith sampled tuber, b= T‘ is the (k x 1) coefficient vector, and (ht,h2, . . ..hk) the superscript T denotes the transpose operator. The compact form of the linear regression model in equation (2) is much more convenient to use in the derivations that follow than the expanded form in equation (1). As mentioned above, statisticians use a logistic transformation of the linear model to ensure that predicted levels of the y,s fall within the O-l interval required for statistically reasoqfble probabilities. The logistic transformation convertmg the linear model into a probability model is Pr[yi = l( Xi] = F(Xib) =
(1)
for the I = 1, . . ., N tubers in the sample. The X,s represent the measurements on the explanatory variables for the ith sampled tuber, and there are j=l 5 .-., k of them. For example, the first explanatory variable, X;,, could measure the time interval
Table 2 Number of observations
N
Total
exp(Xib)
(3)
1 + exp(Xb)
In equation (3), Pr[yi = llXj] denotes the probability that the ith sampled tuber exhibits NN (i.e. that yi = 1) given the corresponding measurements on the explanatory variables Xi, and F(Xib) is the logistic
of infected tubers for each inoculaGon and storage interval, 1983 Time in storage
36 days
99 days
200 days
146 days
Total
Time hctween planting and inoculation (days)
N
P
N
P
N
P
N
I’
N
P
42 67 94 I30 Total
20 20 20 20 80
0.21) 0.30 0.20 0.10 0.20
20 20 20 I9 79
0.10 0.30 0.25 0.2 I 0.22
20 20 20 20 X0
0.10 0.35 0.10 0.10 0.12
20 I9 20 20 79
0.15 0.40 0.20 0. IO 0.22
80 79 80 79 31X
0.14 0.34 0.14 0. IO 0.20
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Potato leaf roll virus, planting and inoculation: J. Roosen et al. cumulative distribution function (cdf) that forces the values associated with the linear model &b onto the O-l interval. It has the desired properties of a cdf: and F(Xib) is monotonically F(-co)=O, F(cc)=l, increasing in i&b. As F(Xib) is a nonlinear transformation of the linear regression function, the associated parameters b cannot be used as in the linear model Xib to directly translate a change in an explanatory variable into the change of the probability Pv[yi = l]Xi], Generally, the elasticity at means is calculated to interpret the effect of the explanatory variables on the probability that a tuber expresses NN. It gives the percentage change in NN probability if the kth explanatory variable (X,) changes by 1%. The elasticity at means is calculated as
(4) where Xk is the arithmetic mean of the kth explanatory variable, and all variables are evaluated at their means. In equation (4),
measures the change in NN probability owing to an incremental change in the kth explanatory variable, where f(B) is the logistic probability density function
To measure the goodness of fit of the logistic model, White (1993) suggested several conventional R2 statistics. Although the R* statistics are different in magnitude, each statistic can provide consistent comparisons of the relative goodness of fit across various estimated functional forms of the explanatory variables. Here the Cragg-Uhler R2 is reported, which is computed as R2 = l-exp{2[L(O)-L(~)]/N} 1 -exp[2L(O)/fVj where L(0) denotes the likelihood function estimated with the constant term only, and t(h) denotes the likelihood function estimated with all the variables included. The Cragg-Uhler R2 is not an absolute measure for the goodness of fit in a logistic regression as the R2 statistic is in an ordinary least-squares regression, and as a result it is not bounded within the O-l interval. Another measure for the goodness of fit is the percent of right predictions. It calculates the ratio of the correctly predicted observations at y; = 0 and y, = 1 to the total number of observations in the sample. We used both statistics to compare various functional forms of the explanatory variables specified in X. In our empirical model, we propose that the probability of y, = 1 (which indicates the presence of necrotic tissue in a tuber) and the probability y; = 0
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(which indicates no necrotic damage in the tuber) can be significantly influenced by two important variables. These variables are the number of days between planting and inoculation, hereafter the ‘inoculation interval’, which is denoted as Xi,, and the number of days the potatoes are in storage, hereafter the ‘storage interval’, which is denoted as XZz. The importance of the inoculation interval was established in the literature review discussed above. Studies by Rich (1951) and Powell and Mondor (1972) suggest that the probability that PLRV infected tubers express NN is contingent upon the storage interval. Once an empirical relationship is reliably established, potato growers can control these variables to decrease the probability that net necrosis will be expressed at harvest or in storage. A priori, it was expected that the number of tubers with net necrosis either increases with the storage interval or remains constant once all infected tubers have developed visual symptoms. The inoculation interval should play an important part in determining the impact of the storage interval, with potato plants inoculated early (late) in the season probably yielding necrotic tubers after relatively short (long) storage intervals. To model this effect an interaction term (X1X2) was included in the regression equation. As the inoculation and storage intervals change simultaneously, the interaction term allows the effect of storage to vary directly with the inoculation date. To arrive at the final functional forms of the linear structure xb for the 1982 and 1983 samples, combinations of transformations of the explanatory variables cubic, interaction, etc.) were (1inear, squared, included. Then, non-significant terms were gradually dropped out, based on standard t-statistics, likelihood ratio test, Cragg-Uhler R2, and prediction success tables. The standard t-statistics were used to test whether each estimated coefficient was significantly different from zero. They can be calculated as the absolute value of the ratio of an estimated coefficient to its standard error. The likelihood ratio statistics were used to test whether a set of estimated coefficients were significantly different from zero. The likelihood ratio test procedure compares the maximum value of the likelihood function under the assumption that each coefficient in the set is zero L(bo) to the maximum value of the unrestricted likelihood function L(b). Under the null hypothesis, the asymptotic likelihood ratio statistic is calculated as which is distributed as a x2 2{ln[L(b)J-ln[L(bo)]}, random variable with degrees of freedom q equal to the number of coefficient restrictions. The equations were estimated using a maximum likelihood estimation procedure in the statistics package Shazam by White (1993) which automatically computes the various measures of fit. The functional forms resulting in the best fits for the 1982 and 1983 data, respectively, were
X%3 =hx3,t,+&,,Xr
+bK0,*X:+b83,3X,X2+bX3,~~
where bx2.o and bH3,,)are intercept and 1983 regressions, respectively.
(gb)
terms for the 1982
Potato leaf roll virus, planting and inoculation: J. Roosen et al. Table 3. Estimation
Table 4. Marginal effects
results 1982
Variable
I983
h X’,,, = 14.361’ (1.86, 7.7105) hxz., = -0.84847’ (2.28, 0.37204) h XL,>= 1.277E- 02” (2.33, 5.4808E-03) hxr..q= -6.139E-OS (2.41. 2538E-OS) h x2,4= 1.4E-04”’ (2.82, 4.9661E-OS)
Constant XI (XI )’ (XI ).? XJZ
h X3,(,= - 3.9587’ ’ (3.19, 1.2427) h xz,, = 7.388-01” (24. 3.0483E ~ 02) h Hi,Z= -4.4E-04” (2.6. 1.6921E-04)
h nq.?= - 2.hShE -OS (0.38, 6.9309E -OS) h xx,? = 9.4SE -06 (0.38, 2.4508E - OS)
(X,1’
16.533 (4 d.f.)’ 0. IO3 77.7%
Likelihood ratio test Cragg-Uhler R’ Percent of right predictions Numbers
,
in parentheses
8.49767 (4 d.f.)’ 0.042 69.1 r/r’
denotes signilicance
(r-statistic,
standard
error).
at the alpha = O.IO. 0.M.
0.01 level.
The estimated coefficients for equations (8a) and (8b), along with the summary statistics defined in the preceding section, appear in Table 3. The t-statistics reported in the table are used to test whether each estimated coefficient is significantly different from zero. They are calculated as the absolute value of the ratio of an estimated coefficient to its standard error. Figures I and 2 plot estimated NN probabilities 0.3s -
&
9
Il.30
-
I).?5 -
3.5 40
l
Stor=50
.
Stor=lOO
A
Stor=ISO
.50
45
Number
1983
0.69 0.12
-0.0612 -0.0012
71 163
83 120
against the time interval between planting and inoculation for fixed storage periods in the 1982 and 1983 experiments, respectively. The results are presented for each year separately. Results of 1982 experiment
represent
Results
+ 4
Elasticity at means (%) XI XZ Means (days) XI XZ
1982
5s
60
of days
65
70
between
Figure 1. Results of 1982 experiment.
l
7s
80
planting
xs
90
95
100
105
and inoculation
NN, Net necrosis
Stor=50
. Stor=100 A Stor=150 x
Stor=200
Each estimated parameter in the 1982 regression is significant according to an individual t-statistic. As explained above, because these parameters do not directly translate a unit change in the associated explanatory variables into a change in NN probability, we calculated the elasticities at means reported in Table 4. The elasticities are evaluated at mean inoculation and storage intervals of 71 days and 163 days, respectively. They indicate that when inoculation and storage intervals increase from their means by l%, NN probability increases by the smaller-than-unit percentages of 0.69% and 0.12%, respectively. In other words, the response of NN probability to percentage changes in both variables away from their means is inelastic. The above elasticities characterize the behavior of NN probability at fixed levels of the explanatory variables. The estimated NN probability curves in Figure 1 provide a wider prospective by displaying behavior over the entire range of inoculation intervals over the growing season. Each probability curve is associated with a different fixed storage interval, and exhibits the same general behavior. The curves first decrease to a minimum at g-55 day inoculation intervals, then increase toward a maximum at about and finally monotonically 85-90 day intervals, decrease for longer intervals. The summary statistics reported at the bottom of Table 3 relate to the overall fit of the estimated 1982 equation. The likelihood ratio test measures the joint significance of the parameters by comparing the likelihood function of the equation estimated with constant term only with the likelihood function of the entire estimated equation. The test statistic of 16.533 is highly significant at the 0.01 level, and thus reflects a good fit. The percent of right predictions for the estimated equation is a very respectable 77.7%, given the likely existence of other variables influencing the expression of NN that were not controlled in the field experiment. Results of 1983 experiment
0
I
I
I
!
I
I
I
,I, 45 50 55 hO65 70 7s Number
of days
I
I
I
I
I
I
x0
x5
90
YS
100
105
between
Figure 2. Results of 1983 experiment.
planting
I I10
I 115
and inoculation
NN, Net necrosis
I
I 12011~1v
I
The estimated coefficients associated with the inoculation-date variables are individually highly significant, whereas those associated with storage times are
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individually insignificantly different from zero. The elasticity at means is calculated to be -0.0612% with respect to the inoculation interval, and 0.0012% with respect to the storage interval. The mean inoculation interval is 83 days, and the mean storage interval is 120 days. The elasticity at means with respect to the inoculation interval is negative because the mean of 83 days lies on the decreasing portion of the NN probability curves. Similar to the 1982 results, the response of NN probability to each variable is highly inelastic at their means. FigL1~ 2 shows NN probability curves for each storage period as a function of inoculation intervals for the 1983 experiment. Similar to the 1982 curves in Figure I, the 1983 curves monotonically increase to maxima at approxiinoculation intervals, then 75-85 day mately monotonically decrease for longer intervals. Finally, the likelihood ratio test is significant at the 0.10 level, and the percent of right predictions is 69.1%. Both measures reflect a moderately good fit of the estimated equation to the 1983 data.
Discussion
The 1982 NN probability curves are identical in shape over a comparable period to the NN probability curve estimated by Manzer et al. (1982) for their 1958 experiment (see Manzer et al. (1982) Fig. 2). We recall that those workers looked at inoculation dates only over the first half of the growing season (about 80 days after planting) in that experiment, and stored the tubers for approximately 120 days after harvest. They estimated a curve monotonically decreasing toward a minimum at about 40 days from planting to inoculation, and then monotonically increasing at a steep rate for the remainder of the first half of the growing season. Although the minimum of our 1982 curve occurs approximately 10 days later for a similar fixed storage period, the shape and steepness of the curve are remarkably similar. In contrast, our 1983 curves do not initially monotonically decrease toward a minimum probability. The absence of this behavior was observed by Manzer et al. (1982) in the plotted NN frequencies resulting from their 1976 experiment. Interestingly, our 1982 and 1983 NN probability curves peak at inoculation dates after those studied by Manzer et al. (1982) and then monotonically decline. If NN probabilities were found instead to continue increasing for inoculation dates throughout the second half of the growing season, the grower might be well advised to undertake a continuously high spraying regimen to prevent these later inoculations. However, the existence of peak NN probabilities in the second half of the season suggests that spraying might be concentrated on the interval of inoculation dates generating the peak probabilities, to ‘flatten’ them to acceptable levels. Although the USDA-ERS field experiments were designed to study the impact of inoculation dates on NN probabilities, the experiments shed some light on the combined effect of inoculation date and storage time, as harvested potatoes were examined after varying storage periods (see Tables 1 and 2). As
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discussed below, the NN probability curves estimated from the 1982 data respond systematically, in biologically reasonable ways, to increases in the storage period. In contrast, the NN probability curves estimated from the 1983 data (Figure 2) do not respond systematically to increases in the storage period. This is evidenced in the 1983 regression results (Table 3) where explanatory variables including storage time have estimated coefficients that are not significantly different from zero. The failure of the 1983 experiment to replicate the storage results of the 1982 experiment may indicate that, although the total sample size of tubers was more than adequate to statistically link inoculation dates with NN probabilities in each year, the sample size of tubers in each examination period may possibly be too small to consistently generate systematic ‘population’ storage results over the 2 years. Despite this possible problem, our statistical analysis of the 1982 data uncovers some interesting and potentially useful patterns in the combined impact of inoculation dates and storage time on NN probabilities. We believe the results are worth documenting for future comparison with the results of experiments focused on storage time to a larger extent. Increasing the storage period systematically shifted the 1982 NN probability curves upward (Figure I). Thus, consistent with the estimated positive interaction coefficient (6x2,4) reported in Table 3, the longer tubers remain in storage, the more likely they are to express NN. Moreover, as the curves shift upward, the discrepancy between the minimum and maximum NN probabilities increases. For example, the curve for a ‘short’ 50 day storage interval has a minimum NN probability of approximately 3% and a maximum of just over 5%, whereas the curve for a ‘long’ 200 day storage interval has a minimum of about 8% and a maximum of just over 30%. In sum, shorter storage intervals generate relatively flat and small NN probabilities over the course of the growing season, whereas longer storage intervals decrease the dispersion of probabilities around relatively larger minimum and maximum NN probabilities, thereby creating steeper probability curves. The steeper curves indicate that NN probabilities increase at a faster rate in the middle portion of the growing season as storage intervals increase. Let us assume, for the sake of discussion, that the systematic tradeoff between inoculation date and storage time in the 1982 data is validated in future studies. The management implications become clear if the NN probability curves are interpreted as representing the risk of a no-spraying policy. Growers may choose to store potatoes after harvest for increased marketing flexibility, or may be required to do so for an undetermined period by pre-season contracts with processors. Pre-season contracts often contain terms allowing processors to determine the storage period, and to reject, or pay decreased prices, for storage lots exceeding a target level of NN. This places the risk of storage squarely on the growers. The 1982 data show that short storage periods generate NN probabilities that are relatively low and ‘flat’ across inoculation dates. However, as the storage interval increases, the
Potato leaf roll virus, planting and inoculation: probabilities group at higher peaks, and the rate at which the probabilities increase for later inoculation dates increases. Thus, the penalty for postponing spraying for another inoculation day increases with the storage interval. Consequently, growers may be able to ‘insure’ themselves against the added risk of a relatively long storage interval by modifying the NN probability curve consistent with such an interval, and (as discussed above) concentrating spraying on the interval of inoculation dates associated with the peak probability so that the curve is ‘flattened’ to an acceptable probability level.
The authors wish to thank Lee Fox and Harold Toba for providing the data, and Lee Fox for his helpful explanations on the experimental design. References T. (1981) Qualitative
cultural methods for suppressing the green peach aphid as a vector of virus diseases of potatoes and sugarbeet. Bulletin 0900 College of Agriculture Research Center, Washington State University, Pullman Hosmer,
D. W. Jr and Lemeshow,
S. (1989) Applied Logistic
Regression. John Wiley, New York
Manzer, F. E., Merriam, D. C., Starch, R. H. and Simpson, G. W. (1982) Effect of time of inoculation with potato leafroll virus on development of net necrosis and stem-end browning in potato tubers. Am. Potato J. 59, 337-349 Mead, R., Curnow, R. N. and Hasted, Methods
in Agriculture
and Experimental
A. M. (1993) Statistical Biology. Chapman and
Hall, London Powell, D. M. and Mondor, W. T. (1972) Development of net necrosis in stored Russet Burbank potatoes. Proc. llth Annual Washington Potato Co@., Moses Lake, WA, USA
Acknowledgements
Amemiya,
J. Roosen et al.
response
models:
a survey. J.
Econ. Literature 19, 1483-1536
Folwell, R. G., Fagerlie, D. L., Tamaki, I., Ogg, A. G., Comes, R. and Bartielle, J. L. (1981) Economic evaluation of selected
Rich, A. V. (1951) Phloem necrosis of Irish potato Washington. Wash. Agric. Exp. Stn. Bull. 528, l-49
tubers in
Starch, R. H. and Manzer, F. E. (1985) Effect of time and date of inoculation, plant age, and temperature on translocation of potato leafroll virus into potato tubers. Am. Potato J. 62, 137-143 White, K. J. (1993) Shazam: Econometrics Computer Program: User’s Reference Manual, Version 7.0. McGraw-Hill, New York Received 8 August 1996 Revised 27 January 1997 Accepted 19 March 1997
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