Ann. appl. Biol. (1983), 103, 191-200 Printed in Great Britain

191

Methods of analysing data to compare effects on populations of carrot fly (Psila rosue) larvae on carrots of treatments with

exponentially-increasing doses of granular insecticide formulations

BY KATHLEEN PHELPS AND A. R. THOMPSON National Vegetable Research Station, Wellesbourne, Warwick CV35 9EF

(Accepted 23 May 1983)

S U M M A R Y

Effects of insecticide treatments were assessed by comparing the percentages of undamaged carrot roots on insecticide-treated and untreated check plots. A dose-response relationship based on a log-log transformation was derived and illustrated with data for six insecticides from two field experiments.

Formulae are provided for estimating doses corresponding to given levels of decrease in the numbers of carrot fly larvae. Guidance is given on sample sizes needed and constraints on the accuracy of the estimates are stated. Examples are given of the use of the dose-response relationship to compare insecticide treatments within and between experiments.

I N T R O D U C T I O N

As at least ElOm are now needed to take a new insecticide from the test-tube to the market place (Braunholtz, 198 l), only a few multinational agrochemicals companies concentrating on the principal pests of the major world crops can afford to invest in the research needed. Much of the responsibility for the development of insecticides for so-called ‘minor-uses’ now rests with public-sponsored organisations. A major objective of some research at NVRS has been to help meet this need on UK vegetables.

To make insecticide-evaluation procedures more reliable and cost-effective, novel designs for experiments have been devised (Thompson & Wheatley, 1977), specialised insecticide- application machinery has been developed for use with field-sown crops in small plots (Thompson, Percivall, Edmonds & Lickorish, 1983) and methods of recording data from field-samples have been simplified (Phelps, Draycott & Hutt-Dixon, 1982). However, appropriate statistical methods for analysing data from trials using these modified procedures were not available. This paper presents methods suitable for data on the performance of insecticide treatments against carrot fly (Psila rosae F.) on carrots.

Complete information on relationships between doses of insecticides and their effects on attacking insect populations is difficult to obtain using constant doses applied to discrete field plots. However, by applying a range of doses to individual plots, patterns of doselresponse can be investigated in experiments of manageable size (Thompson & Wheatley, 1977). Thus, in NVRS experiments to evaluate the performance of insecticide treatments against carrot fly, continuous exponentially-increasing doses of granular insecticide formulations are applied to individual plots, each of which comprises a twin-row of carrots. Using three replicated blocks in each experiment, insecticide-treated plots are deployed at random within a systematic grid in which every third plot is untreated. This grid of ‘check’ plots enables patterns of pest damage over an experiment to be assessed and damage on treated plots to be compared with that on appropriate check plots. As carrot fly damage to roots of carrots varies within, as well as between, check plots an average baseline level is often used in comparison for each block.

@ 1983 Association of Applied Biologists

192 K A T H L E E N P H E L P S A N D A . R. T H O M P S O N

Effects of insecticide treatments are estimated by comparing the survival of insects on insecticide-treated and check plots. With foliage-feeding species, the numbers of individuals on a plant can often be assessed directly. This is impracticable with the root-feeding larvae of carrot fly. However. indirect estimates of the numbers of these larvae can be obtained simply by recording the presence or absence of mines in the roots (Wheatley & Freeman, 1982). The efficiencies of insecticide treatments in decreasing attacking carrot fly populations (Wheatley, 1973. 1974) can then be estimated by comparing the proportions of undamaged roots on insecticide-treated and check plots, provided the initial distribution of larvae is similar overall (Wheatley. 1969a. 1969b; Wheatley & Freeman, 1982).

Plots treated with continuous, exponentially-increasing doses of insecticides are separated into ten consecutive subplots of equal length prior to root damage being assessed (Thompson & Wheatley. 1977). Previously. the estimated decrease in the numbers of carrot fly larvae given in each sub-plot of insecticide-treated plots was plotted on logarithmic-probability paper against the median dose applied to the subplot. However, regression analysis of these dose/response data was difficult because the actual numbers of carrot fly larvae were not known. The use of the measured response, the proportion of undamaged roots in each subplot, was therefore explored as a reliable means of statistical estimation of dose-response relationships. This paper shows how the log-log function (Mather, 1949) of the proportions of undamaged roots provides a simple procedure for estimating larval-mortality/dose relationships in experiments using continuous, exponentially-increasing doses of insecticides (Phelps, 1979).

The primary objective of evaluation experiments is to test whether the performance of treatments with candidate insecticide formulations is significantly better, or worse, than that of treatments with insecticides used as 'standards'. Frequently, the performance of similar treatments in different experiments also requires comparison. Some of the data obtained from soil treatments with six granular insecticide formulations in two field experiments at NVRS are used in this paper to show, firstly. how well the log-log function describes the data and, secondly, how dose/response relationships can be compared using standard statistical techniques.

M E T H O D S

The basic statistical model and its application The proposed relationship between the proportion of undamaged carrot roots given in

particular experimental conditions by a treatment with insecticide i on subplot j , qii, and the dose applied. d,i mg a.i./m row, is described by the basic model

In denotes natural logarithms and log denotes logarithms to the base 10. In a particular experiment. the value of the parameter a; is assumed to depend on the insecticide treatment and the level of carrot fly damage, that of parameter p, only on the insecticide treatment. To compare the performance of insecticide treatments between experiments with different levels of carrot fly damage. the parameter a; is partitioned into a parameter ai specific to an insecticide treatment in one experiment and a constant ck representing the base level of carrot fly damage in that experiment. ck is the proportion of undamaged carrot roots in check subplots appropriate to the positions of the treated subplots and is expressed on a log-log scale. Thus the basic model to be fitted to the observed numbers of undamaged roots is

in (-In qi i ) = In (-In ck) + a, + pilog dii

Having calculated the parameters ck, a,. p,, equation (2) may be rearranged as follows:

In (-In ql,) - In (-In ck) = ai + pi log d,, (3)

Effects of insecticide treatments on carrot fly larvae 193

A slight modification of Wheatley & Freeman’s (1982) equation relating the level of infestation of carrot fly larvae to the proportions of undamaged carrot roots allows the left-hand side of equation (3) above to be described in terms of the relative numbers of carrot fly larvae on insecticide-treated and check subplots (N2/Nl) i i :

In (Nz /N , )v = In (-ln qii) - In (-In c,) (4)

Thus the basic model (equation 1 ) may be rewritten in terms of the relative numbers of larvae:

In (N2 /N& = ai + PI log dii ( 5 )

The formula for the percentage decrease in the numbers of larvae on subplot j of a plot with insecticide treatment i (Wheatley & Freeman, 1982) is:

(6)

Combining equations ( 5 ) and (6) gives an equation relating the dose dii of an insecticide i to the decrease in the population of larvae given by an insecticide treatment:

(7)

% decrease = lOO(1 - ( N Z / N l ) J

% decrease = lOO(1 - eal+8Jogdd 1 e being the base of natural logarithms.

The parameters ai and&. a, , the value of In (NZ/NJii when 1 mg of active ingredient is applied per m row, is itself of

little practical interest. However, in conjunction with pi, the slope parameter, it provides two useful estimates of insecticide performance. Firstly, the % decrease in the numbers of larvae given by an insecticide dose dii can be estimated using equation (7). Secondly, equation (7) may be reformulated to obtain the dose d,, needed to give a % decrease of 1OOp:

1 log dif = - - (ai - In (1 -p) ) (8)

Pi

Comparison of dose-response relationships.

relative numbers of carrot fly larvae on a subplotj can be described by the equation: Equation ( 5 ) shows that the effects of treatments with any two insecticides A and B on the

(9) In ( N z / N l ) , = a, + pi log dii

In (Nz/Nl) i i = a, + plog dii

i = A or B

If the effects of the two insecticide treatments can be described by parallel lines then:

i = A or B (10)

If the effects of the two insecticide treatments can be described by identical lines then:

In (iV2/Nl)ii = a + Plog d , (1 1 )

Field experimentation Data from two field experiments at NVRS with different carrot densities and different levels of

carrot fly damage on check plots were selected to illustrate the methods of statistical analysis. Carrot seed (cv. Autumn King) was sown with tractor-mounted, Russell close-row seeder

units on 13 May 1975 and 17 May 1978, sowing approximately 40 and 100 seeddm row respectively. Plots comprised 9-m lengths of twin rows, 15 cm apart and at 71-cm centres. Twelve granular insecticide formulations were evaluated in 1975 and eight in 1978; details of those discussed in this paper are given in Table 1. Each insecticide was assigned at random to

194 K A T H L E E N P H E L P S A N D A . R . T H O M P S O N

Table 1. Granular insecticide formulations evaluated injield experiments at Wellesbourne for control of carrotfly on carrots

Granular formulation Dose-range applied to subplots A

I \ used in regression analyses Insecticide Yo a.i. Supplier (mg a.i./m each row of twin row)

1975 Bendiocarb Carbofuran

Phorate

1978 Carbofuran Phorate Quinalphos R-73630

N-2596

5 5

10 10

5 10 5 5

Fisons Bayer Stauffer Cyanamid

Bayer Cyanamid Sandoz Plant Protection

21.3-148 23.9- 1 67 31.8-221 33.3-232

25.&174 34.3-239 24.7-172 30.8-215

one plot within the systematic grid of check plots in each of the three replicated blocks (Thompson & Wheatley, 1977). Exponentially-increasing doses of the insecticides were applied to vee-belt applicators (Wheatley & Niendorf, 1969) using an exponentially-grooved trough (Wheatley. 197 1) and incorporated in the soil at drilling by the bow-wave technique (Makepeace, 1965).

Plots were separated into 10, 90-cm long subplots 34 wk after drilling and roots of all carrots in each subplot were harvested, washed and graded for the presence of carrot fly damage. Data from the first and last subplots of each plot wereexcluded from the subsequent statistical analyses because ‘end effects’ in the application of insecticides caused anomalous effects (Thompson et al.. 1983).

Details of the computing procedure, using generalised linear modelling techniques (Nelder & Wedderburn, 1972), have been published elsewhere (Phelps, 1982).

Regression analyses were performed for each insecticide treatment separately, the model being fitted according to equation (2), using separate values for ck within each block of each experiment, so that estimates of the parameters ai and pi were obtained. The LD,, and LD,, were calculated for each treatment by substituting the values of a( and p, in equation (8). Regression lines for pairs of insecticide treatments were compared by using analysis of deviance to determine which of equations (9), (10) or (1 1) described the combined data adequately. This procedure is analogous to using analysis of variance to compare lines in conventional regression analysis, mean residual deviances corresponding to residual mean squares.

R E S U L T S

Sample size and the precision of transformed percentages The log-log transformation. like the logit and probit transformations, stretches out the % axis

at the ends of the range, accentuating differences particularly at the high end relative to the middle (Fig. 1). Fig. 2 shows that the most precise estimates of the transformed % undamaged roots relate to percentages <80. For example, sample sizes sufficient to obtain a given variance with 50%-80% undamaged roots would give a much larger variance with >90% undamaged roots: thus a ten-fold increase in sample size is required to make the variances with 50% and 95% undamaged roots equal on the transformed scale. Fig. 2 also shows the effect of changing sample sizes on the variance: doubling the total numbers of roots sampled per dose from 50 to 100 has a much greater relative effect than doubling it from 100 to 200. Doubling the sample size from 50 to 100 produces the same decrease in variance at 80% as doubling the sample size from 100 to 200 at 90%.

Effects of insecticide treatments on carro t jy larvae 195

3 C

L I

C .- W

m b 3

80

50 -

1975 phoratc

/ -

98

95

00

80

50

10

99

80

50

L

bendiocarb

- JJ I978

98

80

50

50

I l l 1

10 20 50 100200 500

98

95

80 h

M

- 2 m c 0

U e

90

70

30 1 1 " 1 1

99

98

95

90

70

30 I ' " 1 1

10 20 50 100 200 500 mg a.i./m row (log-scale) mg a.i./ni row (log scale)

Fig. 1. The relationship between insecticide doses applied to the soil, % undamaged carrot roots and estimated effects on the numbers of carrot fly larvae. ( t denotes value > ordinates.)

Examples of regression analysis with individual insecticide treatments The numbers of roots per subplot in 1975 were only about 60% of those in 1978 (Table 2) and

carrot fly damage was more severe in 1975, when only 7% of roots in check plots were undamaged (Table 2). Nevertheless, the"r/egression lines fitted the data from both experiments

I96 K A T H L E E N P H E L P S A N D A . R . T H O M P S O N

40 50 60 70 80 90 O o undamaged root<

Fig. 2. The change in variance, V. in relation to the proportion of undamaged carrot roots, ck, for samples with different numbers of roots. R .

( v = l - c k ) Re, (In c,)'

well (Fig. 1). For clarity, the y-axes were inverted to show increasing % undamaged roots (In (-ln q) decreases as 4 increases). Two ordinate scales were used to show the performance of the insecticide treatments in terms of (a) the YO undamaged roots and (b) the estimated % decrease in the numbers of carrot fly larvae (equation 6). The graphs provided good visual comparisons of the performance of the different insecticide treatments.

Comparison of the lack of fit mean deviance and the corresponding between-replicate (residual) mean deviances in Table 2 indicated that the lines fitted well. Values of a, and pi (equation (2)) are given in Table 3. The standard errors of these parameters were high with insecticides which performed well, an inevitable consequence of the rapidly changing variance. The statistical significance of the slope was assessed using a t-test. Estimated LD5,,'s and LD,,,'s, calculated by substitution in equation (8), are given in Table 3 to indicate the relative toxicities of the insecticide treatments, as in conventional toxicological assays.

Effects of insecticide treatments on carrotfy larvae 197

Table 2. Goodness of f i t of model for linear dose-response relationships with insecticide treatments evaluated in 1975 and I978 for control of carrot fly on carrots

Mean residual deviance for model

Mean nos. Lack of fit Between-replicate I

A \

Insecticide/Year roots/subplot (6 D.F.) (16 D.F.)

1975* Bendiocarb Carbofuran

Phorate 1978* Carbofuran Phorate Quinalphos

N-2596

R-73630

43 43 48 37

74 72 69 73

2.89 4-02 2.81 2.08

2.19 1.16 1.75 1.98

1.68 4.95 3.78 3-10

3.75 1.38 3.71 2.21

* Mean numbers of roots/subplot and mean overall level of undamaged roots for untreated check plots were: 44 and 7% (1975), 77 and 28% (1978).

Table 3. Parameters of linear dose-response relationships for insecticide treatments evaluated in I975 and I978 and estimates of doses for two selected responses

Dose estimates (mg a.i./m row)

Paramcters (k s.E.) ‘I A r 95% fiducial 95% fiducial Insecticide/Year ai Pi LD,, limits LD, limits

1975 Bendiocarb Carbofuran

Phorate 1978 Carbofuran Phorate Quinalphos

N-2596

R-73630

2.8 k 0.29 -2.1 k 0.17 45.4 3.8 f 0.45 -3.5 2 0.28 18.6 1.9 f 0.32 -1.8 t 0.17 28.9 0.5 k 0.56 -1.6 k 0.30 5.1

2.1 f 0.37 -2.2 f 0.22 17.8 2.9 k 0-67 -3.1 f 0.38 14.8 0.8 k 0.36 -1.4 f 0.21 10.8 1.0 2 0.35 -1.4 0.19 16.3

259

23 7 53.8

57.3

93.1 49.7

146 233

205;354

190;324 49.2;59.6

43.7;7 1.2

80.2;114 43.2~56.3 111;234 173;382

Comparing pairs of linear dose-response relationships The relative performance of soil treatments with (a) candidate insecticides and a standard

(phorate) in 1975 and 1978 and (b) phorate and carbofuran evaluated in both years were compared (Table 4).

With phorate and R-73630 in 1978, the parallel-lines model reduced the deviance from the single-line model considerably. The mean deviance ratio for the comparison of the non-parallel lines and parallel lines models was much smaller (P < 0.01) but nevertheless rather large to ignore. Therefore, it was concluded that the lines for the two treatments differed in intercept and slope, the differences in the intercepts being more important. In contrast, the comparison of the performance of phorate and N-2596 treatments in 1975 showed no reduction in deviance at the final stage (Table 4), indicating that, within the limitsofexperimentalerror, thetwo lines were parallel.

A similar analysis was used to test the consistency in performance of the carbofuran and phorate treatments in 1975 and 1978. The comparison between the results obtained with phorate was much less sensitive than that for carbofuran because very few roots were damaged with phorate in 1978. The deviances (Table 4) indicated that the phorate lines had different slopes, although similar intercepts, in the two years while for carbofuran the two lines were parallel.

198 K A T H L E E N P H E L P S A N D A . R . T H O M P S O N

Table 4. Comparison by analysis of deviance of linear dose-response relationships obtained with soil treatments with granular insecticide formulations in field experiments at

Wellesbourne in I975 and I978

Insecticidesimodels

Candidate insecticides 1's. phorare N-2596(1975): Single line (eq. 11)

Parallel lines (eq. 10) Non-parallel lines (eq. 9)

R-73630( 1978): Single line (eq. 1 1 ) Parallel lines (eq. 10) Non-parallel lines (eq. 9)

Insecticides in difler~nt e.uperirnenis Carbofuran ( 1 9 7 5 ~ s . 1978): Single line (eq. 11 )

Parallel lines (eq. 10) Non-parallel lines (eq. 9)

Phorate (1975vs.1978): Single line (eq. 1 I )

Parallel lines (eq. 10) Non-parallel lines (eq. 9)

Residual deviance I-*------, Mean

Total (D.F.) change ratio Mean deviance

- 104.4 (46) - 4.5 2.2 99.9 (45)

90.7 (44) 9 . 2 4.5

D I S C U S S I O N

The log-log function of the proportion of carrot roots undamaged by carrot fly larvae was considered because it allows measured responses to be transformed readily to a scale based on the efficiency of insecticides in decreasing the attacking carrot fly population (Wheatley & Freeman, 1982). A further advantage of the log-log scale is that it emphasises differences in the performance of insecticide treatments at low levels of damage. It is in this region that interest is concentrated in insecticide evaluation experiments, differences between relatively inefficient insecticides being of negligible practical interest. Application of the function to the data on carrot fly control presented in this paper indicated that it provided an excellent dose/response function, no serious departures from linearity being found.

The precision of parameter estimates based on the dose/response relationship depends on the levels of carrot fly damage to roots on insecticide-treated and check plots. The most precise estimates relate to insecticide treatments achieving a maximum of 80% undamaged carrots on any subplot. Wheatley & Freeman (1982) discussed the relationship between infestation levels of carrot fly on carrots, the efficiency of control measures and the numbers of carrot fly larvae surviving the treatments. Their nomogram (Fig. 6) indicates the combinations of results from insecticide-treated and check plots which lead to a decrease of >90% in the numbers of larvae, the criterion recommended by Wheatley (1969b) as the minimum requirement for soil-applied insecticide treatments to protect main and late carrots against carrot fly. This level of control can occur in conjunction with maximum precision (<SO% undamaged carrots) of estimation only if (10% of the carrots on the check plot are undamaged. To avoid interrelationships between host-plant density and the proportion of undamaged roots, which are likely to be complex, plant populations on insecticide-treated and check plots should be similar (Wheatley & Freeman. 1982). Study of sample size requirements suggests that increasing sample sizes to > 100 roots per dose increases the precision of estimates relatively little. Thus, to maximise cost-efficiency in experiments with three replicates, it is desirable to use total numbers of 100

Effects of insecticide treatments on carrot Jly larvae 199

roots per dose, sampled at random if damage is not assessed on entire rows of plants, and carrot fly damage should be assessed when levels on untreated check plots are as high as possible, but below 100%.

Parameter estimated are valid only if the slopes of the regression lines differ significantly from zero, otherwise the mean % decrease in the numbers of larvae over all doses should be quoted. Non-significant slopes will be obtained with insecticide treatments giving an extremely high percentage of undamaged roots at all doses and with treatments having little effect on the numbers of larvae over the dose range tested. Comparisons should generally be based on estimates of relative potencies at specified levels of response, such as LD,,,'s or LD,,'s, as there is no justification for assuming parallelism.

Comparison of the % undamaged carrot roots on insecticide-treated and check plots is appropriate only when the relationship between the distribution of carrot fly larvae and the intensity of damage to the carrots is not affected significantly by the treatments (Wheatley & Freeman, 1982). Investigations so far, including those for the determination of responses to soil treatments with the insecticides phorate, carbofuran and aldicarb in evaluation experiments (Thompson & Wheatley, 1977), suggest that insecticide treatments do not affect this relationship systematically (Wheatley & Freeman, 1982), and so indirect assessment of effects of treatments on the numbers of larvae seems appropriate for carrots. The distribution of root-feeding stages of other insect species on other crops has not been investigated as fully as that of carrot fly on carrots and parsnips. However, limited data with radish from field plots either not treated with insecticide or treated with chlorfenvinphos showed that the relationship between the log-log function of the % radish undamaged by cabbage root fly (Delia radicum L.) larvae and the logarithm of the mean number of mines per radish was linear (G. H. Freeman & A. R. Thompson, unpublished). The method described in this paper for estimating dose/responses of insecticide treatments applied to carrots seems to be appropriate for cabbage root fly attack on radish.

The use of continuous. exponentially-increasing doses of granular formulations applied to individual plots in NVRS field experiments to evaluate the performance of insecticide treatments against carrot fly on carrots enables practical doses to be determined readily from dose/response curves. The statistical methodology described in this paper, together with the developments in experimental design, insecticide application equipment and data-collection techniques described previously (Thompson & Wheatley, 1977; Phelps et al., 1982; Thompson et al., 1983) provide the necessary elements of a sophisticated method of evaluating insecticide treatments that can now be recommended for general use.

We are grateful to Dr G. H. Freeman and Mr G. E. L. Morris for advice during preparation of the manuscript and to Mr G. H. Edmonds and Miss Louise Hutt-Dixon for computing assistance.

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Insecticide and Fungicide Conference 3.99 1-1004.

(Received 23 Nooember 1983)