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Investigating strategies for minimising damage caused by the sugarcane pest Eldana saccharina
Agricultural Systems 74 (2002) 271–286 www.elsevier.com/locate/agsy
Investigating strategies for minimising damage caused by the sugarcane pest Eldana saccharina Petrovious M. Hortona, John W. Hearnea,*, Joseph Apalooa, Desmond E. Conlongb, Michael J. Wayb, Pieter Uysa a
School of Mathematics, Statistics and Information Technology, Private Bag X01, Scottsville 3209, South Africa South African Sugar Association Experiment Station, Private Bag X02, Mt Edgecombe, 4300, South Africa
b
Received 20 October 2000; received in revised form 31 March 2001; accepted 17 August 2001
Abstract The control of Eldana saccharina Walker (Lepidoptera: Pyralidae) in sugarcane of KwaZulu-Natal, South Africa has proved problematical. Among various methods of control available are early harvesting and the use of insecticides. A precise and detailed simulation model is developed to investigate the effectiveness of such methods of control and in particular the optimal timing of such applications. The model is cohort-based and includes the effect of temperature on the physiological development of individuals in each life-stage of the insect. Further, the model gives a sugarcane damage index which indicates levels of damage on any given day of the simulation. Relationships are obtained involving the damage index, timing of harvest and duration of insecticide effectiveness under selected temperature patterns. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Pest control model; Degree-days; Eldana saccharina; Sugarcane
1. Introduction Eldana saccharina Walker (Lepidoptera: Pyralidae) has become a pest of increasing proportions in South African sugarcane since 1971, spreading throughout the industry (Carnegie, 1974; Conlong, 1994a; Way, 1994). The insect is indigenous to Africa, where it occurs naturally in numerous wetland sedges and indigenous grasses (Girling, 1972; Atkinson, 1979; Conlong, 1994b). It has been a pest of graminaceous * Corresponding author. Tel.: +27-33-260-5626; fax: +27-33-260-5648. E-mail address: [email protected] (J.W. Hearne). 0308-521X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0308-521X(01)00089-0
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crops in other parts of Africa for over 100 years, first being described in 1865 from sugarcane in Sierra Leone (Walker, 1865). It has also been recorded in sugarcane, maize and sorghum (Conlong, 1994a). The shift by E. saccharina from its indigenous hosts to the crop hosts was postulated to have occurred because the crop plants were cultivated in swampy areas containing many of E. saccharina hosts, placing these crops in contact with the insect (Atkinson, 1980). It is hypothesised that the morphology of the crop host (by providing cryptic oviposition sites) and the behaviour of the female moth, by placing its eggs in hidden positions using its prehensile ovipositor (Conlong, 1994b, 1995), enabled it to successfully colonise the new crop hosts. The inability of the existing natural enemies to successfully find the E. saccharina life stages hidden cryptically in the new host plants may have further helped the insect to establish on them (Conlong, 1995). Atkinson and Carnegie (1989) describe the dynamics and physiological development of E. saccharina. The cryptic nature of the different life stages of this insect living on sugarcane is well described by Dick (1945) and Carnegie (1974). A recent estimate of the damaging nature of this insect to South African sugarcane is about US$10 million per annum (Black et al., 1995). It is estimated that its larval feeding habit causes 0.1% sucrose loss for every 1% of sugarcane stalks damaged. Various methods, biological, chemical and ecological, have been proposed for the control of E. saccharina in sugarcane (Carnegie, 1981). These research options and trials take at least a year or two to complete and assess. In order to obtain a much quicker insight into the interactions of E. saccharina and its various control measures, computer simulation of these interactions was commenced. The first computer simulation model to describe the dynamics of E. saccharina in sugarcane was developed by Hearne et al. (1994). The purpose was to test various management strategies to aid and enhance research on biological control of E. saccharina using the parasitoid Goniozus natalensis Gordh (Hymenoptera: Bethylidae). A system of differential equations was used to describe the dynamics of the system. The biological control model system developed by Hearne et al. (1994) can be described as a hostparasitoid model system (Mills and Getz, 1996). This model, however, did not explicitly take in to account that the physiological development of E. saccharina is sensitive to temperature (Atkinson and Carnegie, 1989). Because of the cryptic nature of E. saccharina and its multivoltine population cycle, the timing of control measures to affect a vulnerable stage of the insect’s life cycle is of critical importance. A model to analyse control strategies cannot aggregate all individuals of a particular stage into a single cohort to be represented by a single variable as done in Hearne et al. (1994). For example, eggs laid on a certain day might experience a sequence of temperatures quite different from eggs laid a few days later. The consequence of this is that the development rates of the two groups would be different. Thus, it is inaccurate for our present purposes to group together all eggs in existence at any one time and to represent them by a single variable. The aim of the E. saccharina model developed here was to test various management strategies so as to aid decisions on when to harvest and when to effect insecticide application. Unlike many other biological control investigations (Axelson, 1994; Yang et al., 1997; Wilder, 1999), this is a single species model. There is no
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feedback between the pest and its host sugarcane, nor are any parasitoids included such as in the models reviewed by Mills and Getz (1996). The model developed here is a stage-structured population model which uses degree days for the development of each stage in the E. saccharina life cycle. Each stage in the E. saccharina life cycle is further subdivided into a number of cohorts. On each day of the simulation, the cohorts of the different life stages coming into existence are identified and monitored separately from the other cohorts already represented in the model. All cohorts, new ones and those from previous days, are separately updated each day of the simulation. A cohort ceases to exist when all individuals belonging to that cohort have matured to the next stage class. The model is used to investigate the effectiveness of insecticide control and early harvesting.
2. Qualitative description of the model For the purposes of the model to be described below, we will assume that the E. saccharina life cycle consists of five distinct stages namely, egg, small larva (instars I– III), large larva (instars IV and above), pupa and moth stages. A detailed account of these stages can be found in Atkinson and Carnegie (1989). We have divided the larval stage into two in order to monitor the effects of insecticide application on the more susceptible small larvae which spend their time outside the cane stalk and also to monitor damage to sugarcane due to the larger larvae which bore into the cane stalk to feed on the soft tissue inside. Initial values for a set of egg cohorts are chosen to represent eggs laid by immigrant moths searching for oviposition sites in a field otherwise free from E. saccharina. Since E. saccharina moths normally lay their eggs on dead leaf cane material (Conlong, 1994b; 1995), the timing of the introduction of initial egg cohorts is based on the age of cane. New egg cohorts are formed on a daily basis until the first set of moth cohorts resulting from these initial egg cohorts emerge. These will then be responsible for creating subsequent cycles. On any given day, some of the eggs in each egg cohort of sufficient physiological age (the physiological time scale is discussed in the next section) hatch out as small larvae. The aggregate of all small larvae hatching out from all of the egg cohorts in existence on that day forms a cohort of small larvae. Thus, in general, the newly formed cohort of small larvae consists of individuals from more than one egg cohort. In due course, once sufficient time has passed and the cohort of small larvae has reached the right physiological age, individuals begin to bore into the cane stalk as large larvae. All small larvae that bore into the cane stalk on the same day form a cohort of large larvae. When a cohort of large larvae reaches a certain physiological age, individuals begin metamorphosis into pupae and form pupae cohorts with others that become pupa on the same day. By a similar process, moth cohorts are formed. The whole cycle then repeats. A record in a database represents each of these cohorts. Various fields in the record keep track of information such as the day when a cohort came into existence,
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the number of individuals in the cohort and its physiological age. When updating takes place each day, all fields, i.e. all attributes of each cohort are adjusted. This must be done separately for all of the cohorts. This creation and demise of cohorts is shown schematically in Fig. 1. The dynamics of a typical cohort is shown in Fig. 2. The model has a daily time step and thus new cohorts are formed once a day. Once a cohort has come into existence it does not receive any further recruits on later days. Some members of a typical cohort may die during any given day. These individuals are removed from the system during the daily update. Further, the
Fig. 1. Example of inter-relationships between cohorts on successive days.
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Fig. 2. The dynamics of a typical cohort.
physiological age of the cohort is updated by an amount depending on temperature and the life stage the cohort is in. If the cohort has reached sufficient physiological age on a given day, some of its members undergo metamorphosis to the next life stage on that day (for cohorts of small larvae, members will begin to bore into the cane stalk as large larvae). These members contribute to the formation of a new cohort (Fig. 2). It is important to note that simultaneously, other cohorts comprising individuals of the same life stage may also contribute to members of this new cohort (Fig. 1). The updating process includes the determination of mortality numbers and numbers maturing onto the next life stage. These calculations are based on a set of functions using as arguments, certain fields in the record representing the cohort. A mathematically detailed account of the relationships described above and the dynamics involved is presented in the next section.
3. Mathematical description of the model Let xji(t) denote the number of individuals on day t in the cohort that commenced stage j on day i. Here the stages egg, small larva, large larva, pupa and moth are indexed by j=0, 1, 2, 3, 4 respectively. Thus x05(10) represents the number on day 10 of the simulation, of eggs remaining from the cohort of all eggs that were laid on day 5 of the simulation. Let aji(t) denote the physiological age on day t of the cohort that commenced stage j on day i. Note that in general, insects of the same physiological age will not necessarily move on to the next life stage at the same time. The rate of maturation from one stage to another is distributed about a mean physiological age required for maturing to the next stage. Let pjmin denote the minimum physiological age at which members of a cohort in stage j begin to move onto the next stage and pjmax denote the physiological age by which all members of a cohort in stage j will have made the transition to the next stage. The fraction of members that die on day t from a cohort that commenced stage j on day i will be denoted by di j(t). Similarly, for a cohort that commenced stage j on day i, we denote the fraction that mature to the next stage on day t by mji(t). In order
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to index all cohorts in stage j that are in existence on day t, we define a set Sj(t) as follows: Sj ðtÞ ¼ t; t 1; . . . ; t Lj where Lj is such that ajLj ðtÞ 4 pjmax and ajLj 1 ðtÞ > pjmax . With the above notation, the dynamics of the E. saccharina population in the various stages and cohorts can be modelled by the system of difference equations xji ðt þ 1Þ ¼ xji ðtÞ 1 d ji ðtÞ m ji ðtÞ ; for all i 2 Sj ðtÞ and j ¼ 0; 1; 2; 3 The initial conditions of the above system are given by x0t ðtÞ ¼ x0ini ðtÞ, before first moths are generated by the system P x0t ðtÞ ¼ K2S4 ðtÞ O x4k ðtÞ x4k ðtÞ, after system has generated its own moths, and P j1 xjt ðtÞ ¼ i2Sj1 ðtÞ mj1 i ðtÞ xi ðtÞ, j=1, 2, 3, 4 where x0ini ðtÞ isthe number of eggs used in the initialisation process based on the age of cane and O x4k ðtÞ is the oviposition rate of moth cohort k on day t. The detailed formulations of the above are discussed later. The mortality rate of a cohort on any given day depends on the life stage of the cohort and also on the day’s average temperature. The South African Sugar Association Experiment Station (SASEX) has accumulated vast data on the stage specific mortality rates of E. saccharina and how temperature affects these rates. Table 1 shows the stage specific mortality rates at a temperature of 26 C and Table 2 shows how they vary at different temperatures. Let dj be the stage specific mortality rate given in Table 1. Then, the fraction of members of a cohort that die on any given day will be given by d ji ðtÞ ¼ d j f j ½TðtÞ
where the temperature function f j is a cubic polynomial. This was determined by finding the lowest degree polynomial that gave a satisfactory least squares fit to the data in Table 2. The time (i.e. physiological time) spent in each stage in the E. saccharina life cycle is temperature dependent and is measured in degree-days ( C d). Pruess (1983) discusses various ways of estimating the number of degree-days accumulated by insects Table 1 Stage-specific mortality rates (per day) for Eldana saccharina at a temperature of 26 C (source: SASEX)
Mortality rate (/day)
Eggs
Small larvae
Large larvae
Pupae
Moths
0.03
0.09
0.029
0.07
0.2
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Table 2 Collocation points for the temperature functions used to adjust mortality rates (source: SASEX)
Eggs Small larvae Large larvae Pupae Moths
10 C
19 C
22 C
26 C
30 C
0.00 0.00 0.00 0.00 0.00
0.64 0.58 0.58 0.44 0.56
0.78 0.78 0.78 0.54 0.71
1.00 1.00 1.00 1.00 1.00
1.10 1.10 1.10 1.10 1.10
on any given day. The method used here was chosen because the minimum temperatures experienced in the areas of interest to this study rarely fall below the required threshold temperatures for growth for each stage in the E. saccharina life cycle. Pruess (1983) argues that if this is the case, this method is similar to the more common sine wave method. The simplicity of this method compared to the sine wave method together with the fact that it gives similar results to the sine wave method when used for purposes similar to ours led to it being adopted here. Let T jth ( C), j=0, 1, 2, 3 be the threshold temperature for development for individuals in stage j of the E. saccharina life cycle. Let T(t) ( C) denote the average temperature on day t. The physiological age of each cohort will be modelled by the recurrence equations aji ðt þ 1Þ ¼ aji ðtÞ þ Daji ½TðtÞ ; with initial conditions aji ðtÞ ¼ 0; where Daji ½TðtÞ is given by TðtÞ t jth ; if TðtÞ > T jth j Dai ðTðtÞÞ ¼ 0; otherwise for all i 2 Sj ðtÞ and j=0, 1, 2, 3. Way (1995) calculated the time, in C d, spent in each stage in the E. saccharina life cycle, as well as the temperature threshold required for development for each stage (Table 3). The C d range pjmin and pjmax was determined from experimental data (Table 3). Maturation to the next stage begins when the physiological age of the cohort reaches pjmin and the fraction of individuals that undergo metamorphosis is estimated by mji ðtÞ
( 0; j ¼ ai ðtÞ p jmin = p jmax p jmin ; 1;
if aji ðtÞ 4 p jmin if p jmin < a ji ðtÞ < p jmax if aji ðtÞ 5 p jmax
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The oviposition rate of a moth cohort depends on how long (in days) the cohort has lived. On average, moths live for about 5 days and according to SASEX, moths mate soon after emerging and will lay eggs on a daily basis until they die. Table 4 shows the average number of eggs laid per moth n days after emergence. We then rewrite the initial conditions for egg cohorts as X x0t ðtÞ ¼ x4k ðtÞ FO n x4k ðtÞ ; k
where n x4k ðtÞ is the number of days after emergence for moth cohort k and FO is an oviposition function determined from the data in Table 4.
4. Model application The reason for developing this cohort-based simulation model was to investigate the use of insecticides and early cutting as control measures for E. saccharina and to give an indication of the crop loss that could be expected if the control measure is implemented properly and works. To correspond with common practice in the sugar industry, the model calculates E. saccharina infestation in terms of the number of E. saccharina per 100 stalks of sugarcane crop. The notation of e/100s used by Hearne et al. (1994) is adopted here to denote this. The simulations assume that initial egg cohorts of two eggs per 100 stalks of sugarcane each enter a sugarcane field of about 3–4 months old on a daily basis until the moths generated within the system lay eggs at a rate exceeding this number. Table 3 The stage specific threshold temperatures for development T jjh and the duration p jmin P jmax in C d of each stage
Eggs Small larvae Large larvae Pupae
Threshold temperature ( C)
Duration ( C d) pjmin –Pjmax
5.3 10.2 11.7 10.7
102–136 185–253 371–439 120–200
Table 4 The number of eggs laid per female moth n days after emerging n
1
2
3
4
5
Eggs laid (/female moth)
6
14
30
16
12
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(E. saccharina is known to attack cane of about 3–4 months old, when the first small dead leaves appear. Usually, moths from a neighbouring mature field invade a young sugarcane field and lay their eggs on available dead leaves.) Each simulation runs for 24 months since in general the sugarcane cycle has a maximum of 24 months. A damage index is defined to provide a measure of crop damage due to E. saccharina. The damage index on day t [denoted Dind(t)] of the simulation is defined as the total number of larvae degree-days spent in the cane stalk up to that day. That is, on each day of the simulation, the crop damage index is updated as follows: Dind ðtÞ ¼ Dind ðt 1Þ þ LLARVðtÞ TðtÞ T2th where LLARV(t) is the total number of large larvae on day t. The reasoning behind the above definition is that it is the larger larvae that cause damage to the sugarcane stalk. It should also be noted that because the growth rate of E. saccharina is temperature driven, larval activity slows down on cold days and the amount of cane tissue consumed will not be as high as on a hot day when larval activity speeds up. Thus, updating the damage index by the product of large larvae and the number of C d gained on that day gives an indication of the amount of damage incurred on that day. Since E. saccharina numbers are measured in e/100s, the unit for the damage index defined above is (e/100s) C d. The relationship between actual damage to the crop and the damage index defined in this paper is still being investigated. Once this has been established, a critical damage index corresponding to the damage at which the crop must be harvested can be found. A rough estimate of the critical damage index that will be used for illustrative purposes is 35 000 (e/100s) C d. SASEX supplied actual daily maximum and minimum temperature data for the Tongaat area in Kwa-Zulu Natal, South Africa for the 30-year period between January 1966 and December 1997. This data set was used to run several simulations to test model response to various temperature scenarios. The temperature scenarios were also used to test harvesting and insecticide application strategies. We then ran the model for the entire temperature data set to investigate the frequency of high damage levels at key points in the cane’s growth cycle. It would have been useful to have compared model output with historical records of actual damage caused to crops. Unfortunately, no such records exist. In the past the main defence against E. saccharina has been to harvest early if infestation showed signs of becoming too severe. The mill would only reject cane if the damage was very severe. Mass was the only factor used by the mill to determine payment to farmers. For cane not rejected altogether, damage was irrelevant. Thus no damage was recorded. This has recently changed and a number of factors such as sucrose content are now included in the calculation to determine the payout to a particular farmer. Another problem is that there are large local differences in temperature so regional damage data (had it existed) would not be very useful. Some field trials are underway at present to collect the sort of data that we hope to be able to use for validation purposes but this will not be available for some time.
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5. Policy analysis 5.1. Harvesting Sugarcane may be harvested from as early as age 11 months, but it can be left on the field for up to 22 months as sucrose content increases as the crop matures. However, if E. saccharina is present, the sucrose yield is greatly affected and the farmer may need to harvest sooner rather than later. During the milling season which runs from April to November, the farmer monitors (among various other factors) the damage to the crop due to E. saccharina. If the damage reaches a certain critical level, the crop is harvested. For the period when mills are closed, a decision is made just before mill closure whether to harvest and forfeit a possible increase in sucrose yields when mills reopen or to leave the crop on the field and risk loss from damage due to E. saccharina. The decision is based on the age of the sugarcane crop, the E. saccharina infestation level at the decision date and the projected infestation level by the time mills reopen. Historical temperature data for the period during mill closure are used to determine expected infestation levels when mills reopen. The model can be used as a decision aid by running it using actual temperature data up to mill closure and historical temperature data during the mill closure period. This then gives an indication of whether the critical damage index will be reached before mill closure or not and the grower can be advised accordingly. As an example, the model was run using actual daily temperature data for a 24month period starting 1 August 1991. Fig. 3 shows the value of the damage index on specific days of the simulation. It can be seen that the damage index is still below the critical level of 35 000 (e/100s) C d when mills reopen. If this were not the case, then harvest before mill closure would be advised.
Fig. 3. Daily damage index for crop cycle beginning August 1991.
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We first investigated the effect of the planting date on the damage index at the decision date and when mills reopen. The model was run using temperature data collected over 30 years for crop cycles beginning in July, August, September, October and November. At the decision date, the crops are aged 16, 15, 14, 13 and 12 months, respectively, and would be ready for harvesting if damage was found to be too high. Table 5 shows the means and standard deviations for the results obtained from these simulations. From these results, we find that in the example of Fig. 3 (August crop cycle), there is a 3% chance that the damage index will be above the critical level of 35 000 (e/100s) C d when mills reopen. If the grower is willing to take this risk the crop can be left on the field until the mills reopen. The risk is about 54% for the July crop and is less than 0.5% for the other crop cycles considered. Table 6 shows a summary of the expected maximum damage index in November and in March at 90, 95 and 99% confidence for crop cycles beginning in July, August, September, October and November. Fig. 4 shows the graph of the expected maximum damage index at the specified degree of accuracy plotted against crop age for the August crop cycle. Suppose now that the farmer has a measure of the damage index at the decision date and wants to find out what the projected damage index will be by the time mills reopen. In order to answer this question, temperature data sets were prepared such that temperatures are fixed up to the decision date and varied using historical data for the mill closure period. This enabled us to get a fixed reading at the decision Table 5 Mean damage index [(e=100s) C d] and corresponding standard deviation for crop cycles beginning in July, August, September and October
November March
Mean S.D. Mean S.D.
July crop
August crop
September crop
October crop
November crop
27 113 599 35 147 1449
24 502 529 32 439 1346
21 746 619 29 805 1493
18 965 704 26 723 1664
166 20 554 24 661 1393
Table 6 The probability that the damage index [(e=100s) C d) will be below the given value in November and in March for the various crop cyclesa November
July crop August crop September crop October crop November crop
March
90%
95%
99%
90%
95%
99%
27 880 25 179 22 539 19 867 17 330
28 096 25 370 22 762 20 120 17 529
28 509 25 735 23 189 20 606 17 911
37 003 34 162 31 716 28 852 26 444
37 524 34 647 32 253 29 451 26 945
38 525 35 576 33 283 30 600 27 906
a For the August crop cycle, there is a 95% chance that the damage index will lie below the critical value at 19 months (i.e. in March).
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Fig. 4. Expected maximum damage index against crop age. The confidence curves give the likelihood that the damage index will be below the given value at the specified crop age.
date and various possible levels when mills reopened. Table 7 shows the value of the damage index at the decision date together with the corresponding mean and standard deviation of the expected damage index when mills reopen. With the results shown in Table 7, given a damage index at the decision date, we can find the minimum expected damage index when mills reopen based on the risk the cane grower is willing to take. Fig. 5 shows the expected minimum damage index at 95% confidence levels. Expected minimum damage indices for intermediate values can be found by interpolation. For example, suppose the grower is willing to take a risk of only 5%. Using interpolation and the results of Fig. 5, we find that the damage index at the decision date whose expected damage index when mills reopen will be above 35 000 (e/100s) C d at a risk of 5% is 26 740 (e=100s) C d. That is, if a grower is willing to take a 5% risk, his cut off level at the decision date is 26 740 (e/100s) C d. 5.2. Insecticide application Insecticide spraying is normally done soon after a moth peak is observed in the field. The first instar larvae are considered the most vulnerable to insecticide application because just after eclosion they disperse from the oviposition sites, leaving them exposed. Second and third instar larvae will still be vulnerable as they spend their time scavenging on the outside of the sugarcane stalk, but not to the extent of first instar larvae. The large larvae are considered to be well protected from insecticides as they spend their time hidden inside the cane stalk. The insecticide kill rate is thus a function of the physiological age (in C d) of the small larvae. For the purpose of these simulations, a kill rate of 60% for first instar
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Table 7 Mean and standard deviation for the expected damage index when mills reopen given a particular damage index at the decision date Damage index in November [(e/100s) C d]
13 200 18 900 24 800 30 300 35 900
Expected in March Mean
S.D
21 131 26 306 32 738 38 297 43 909
173 212 172 168 173
Fig. 5. The value of the expected damage index (at 95% confidence) in March based on a known damage index for the previous November.
larvae a2i ðtÞ 4 80 C d , 40% for larvae 80 C d < a2i ðtÞ 4 150 C d 2second instar and 20% for third instar larvae ai ðtÞ > 150 C d was assumed. These rates need to be adjusted by a function f(n) where n is the time elapsed since the insecticide was applied. SASEX estimates that the strength of the insecticides they use decays slowly initially but more rapidly later. A function with these properties is given by
n 3 fðnÞ ¼ 1 ; N where n is the number of days elapsed since insecticide application and N is the number of days the insecticide remains effective in the field. The aim is to find the relationship between the duration of insecticide effect and the reduction in the damage index. The long lasting insecticides may be cheaper to
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apply in terms of labour costs and may even have a better kill rate, but a strong dose of a well-timed application may result in a better kill rate. We investigated insecticides whose effect lasts for 2 weeks, 1 month and 2 months and compared the resulting reduction in the damage index. This was done by running simulations for crop cycles beginning in August over the 30-year period from 1967 to 1997 with insecticide application effected whenever a moth peak of more than 0.75 e/100s was reached. Table 8 shows the means and standard deviations of the percent reduction in the damage index in November (at 15 months) and in March (at 19 months). Fig. 6 shows the minimum percent reduction in damage index that the farmer can be confident, to the specified degree of accuracy, that the insecticides used can achieve at the specified date. From the results shown in Fig. 6 it can be concluded that the insecticides whose effect lasts for 28 days achieves the best percent reduction in
Table 8 Mean percent reduction in the damage index and the corresponding standard deviation for insecticide duration of 14, 28 and 56 days 14 Days
Mean % reduction Standard deviation
28 Days
56 Days
November
March
November
March
November
March
56.1 5.38
60.4 4.13
66.3 4.84
68.9 3.59
63.7 7.35
71.0 5.27
Fig. 6. Minimum percent reduction in the damage index for various durations of insecticide effect. The confidence levels indicate the probability that the percent reduction in damage will be above the given value.
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the damage index, the next best results being obtained from insecticides whose effect lasts for 56 days.
6. Conclusion A model of the sugarcane pest E. saccharina has been formulated that improves upon a previous model of this pest in that it includes temperature effects explicitly. This enabled a more accurate index to be formulated of the extent of cane damage under different temperature patterns. It was illustrated how this damage index can be used to determine whether to harvest the crop just before mill closure or to leave it on the field until mills reopen based on the risk that may be incurred if the crop was not harvested. When investigating insecticide application policies, the cohort structure of the model made it possible to target specific larval age groups whose susceptibility to insecticides varies. Results of these investigations give an indication of the relationship between the duration of insecticide effect and the reduction in the damage index. Although, as illustrated, the model is useful as a decision aid in its present form, the economic implications have not been dealt with. Further research is planned to incorporate the costs and benefits of both the timing of the harvest and various insecticide application strategies. When this has been achieved, the model will provide crop growers and managers information that gets to the very core of their problem—profit margins. References Atkinson, P.R., 1979. Distribution and natural hosts of Eldana saccharina Walker in Natal, its oviposition sites and feeding patterns. Proc. South Afr. Sugar Technol. Ass. 53, 111–115. Atkinson, P.R., 1980. On the biology, distribution and natural host-plants of Eldana saccharina Walker. J. Entomol. Soc. South Afr. 43, 171–194. Atkinson, P.R., Carnegie, A.J.M., 1989. Population dynamics of the sugarcane borer, Eldana saccharina Walker (Lepidoptera: Pyralidae), in Natal, South Africa. Bull. Entomol. Res. 79, 69–80. Axelson, J.A., 1994. Host-parasitoid interactions in an agricultural ecosystem: a computer simulation. Ecological Modelling 73, 189–203. Black, K.G., Huckett, B.I., Botha, F.C., 1995. Ability of Pseudomonas flourescence engineered for insecticidal activity against sugarcane stalk borer, to colonise the surface of sugarcane plants. Proc. South Afr. Sugar Technol. Assoc. 69, 21–24. Carnegie, A.J.M., 1974. A recrudescens of the borer Eldana saccharina Walker (Lepi-doptera: Pyralidae). Proc. South Afr. Sugar Technol. Assoc. 48, 107–110. Carnegie, A.J.M., 1981. Combating Eldana saccharina Walker: a progress report. Proc. South Afr. Sugar Technol. Assoc. 55, 116–119. Conlong, D.E., 1994a. A review and perspectives for the biological control of the African stalkborer Eldana saccharina Walker (Lepidoptera: Pyralidae). Agriculture, Ecosystems and Environment 48, 9–17. Conlong, D.E., 1994b. Host-parasitoid interactions of Eldana saccharina (Lepidoptera: Pyralidae) in Cyperus Papyrus. Unpublished PhD thesis, Department of Zoology and Entomology, University of Natal, Pietermaritzburg, South Africa. Conlong, D.E., 1995. Biological control of Eldana saccharina walker in South African sugarcane: constraints identified from 15 years of research. Insect Sci. Applic. 17, 69–78.
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Dick, J., 1945. Some data on the biology of the sugarcane borer (Eldana saccharina Walk.). Proc. South Afr. Sugar Technol. Assoc.. 19 75-79. Girling, D.J., 1972. Eldana saccharina Wlk. (Lepidoptera: Pyralidae), a pest of sugarcane in East Africa. Proc. Int. Soc. Sugarcane Technologists 14, 429–434. Hearne, J.W., van Coller, L.M., Conlong, D.E., 1994. Determining strategies for the biological control of a sugarcane stalk borer. Ecological Modelling 73, 117–133. Mills, N.J., Getz, W.M., 1992. Modelling the biological control of insect pests: a review of host-parasitoid models. Ecological Modelling 92, 121–143. Pruess, K.P., 1983. Day-degree methods for pest management. Environ. Entomol. 12, 613–619. Walker, P., 1865. List of specimens of Lepidopterous insects in the collection of the British Museum. British Museum (Natural History). Part 32. Suppl. Part 2, pp. 632–633. Way, M.J., 1994. Preliminary assessment of the effects of different constant temperatures on the reproduction of Eldana saccharina (Lepidoptera: Pyralidae). Proc. South Afr. Sugar Technol. Assoc. 68, 16–18. Way, M.J., 1995. Developmental biology of the immature stages of Eldana saccharina Walker (Lepidoptera: Pyralidae). Proc. S. Afr. Sugar Technol. Assoc. 69, 83–86. Wilder, J.W., 1999. A predictive model for gypsy moth population dynamics with model validation. Ecological Modelling 116, 165–181. Yang, Y., Allen, J.C., Knapp, J.L., Stansly, P.A., 1997. An age-structured population model of citrus rust mite: a fruit-mite-fungal pathogen system. Ecological Modelling 104, 71–85.
Investigating strategies for minimising damage caused by the sugarcane pest Eldana saccharina Petrovious M. Hortona, John W. Hearnea,*, Joseph Apalooa, Desmond E. Conlongb, Michael J. Wayb, Pieter Uysa a
School of Mathematics, Statistics and Information Technology, Private Bag X01, Scottsville 3209, South Africa South African Sugar Association Experiment Station, Private Bag X02, Mt Edgecombe, 4300, South Africa
b
Received 20 October 2000; received in revised form 31 March 2001; accepted 17 August 2001
Abstract The control of Eldana saccharina Walker (Lepidoptera: Pyralidae) in sugarcane of KwaZulu-Natal, South Africa has proved problematical. Among various methods of control available are early harvesting and the use of insecticides. A precise and detailed simulation model is developed to investigate the effectiveness of such methods of control and in particular the optimal timing of such applications. The model is cohort-based and includes the effect of temperature on the physiological development of individuals in each life-stage of the insect. Further, the model gives a sugarcane damage index which indicates levels of damage on any given day of the simulation. Relationships are obtained involving the damage index, timing of harvest and duration of insecticide effectiveness under selected temperature patterns. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Pest control model; Degree-days; Eldana saccharina; Sugarcane
1. Introduction Eldana saccharina Walker (Lepidoptera: Pyralidae) has become a pest of increasing proportions in South African sugarcane since 1971, spreading throughout the industry (Carnegie, 1974; Conlong, 1994a; Way, 1994). The insect is indigenous to Africa, where it occurs naturally in numerous wetland sedges and indigenous grasses (Girling, 1972; Atkinson, 1979; Conlong, 1994b). It has been a pest of graminaceous * Corresponding author. Tel.: +27-33-260-5626; fax: +27-33-260-5648. E-mail address: [email protected] (J.W. Hearne). 0308-521X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0308-521X(01)00089-0
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crops in other parts of Africa for over 100 years, first being described in 1865 from sugarcane in Sierra Leone (Walker, 1865). It has also been recorded in sugarcane, maize and sorghum (Conlong, 1994a). The shift by E. saccharina from its indigenous hosts to the crop hosts was postulated to have occurred because the crop plants were cultivated in swampy areas containing many of E. saccharina hosts, placing these crops in contact with the insect (Atkinson, 1980). It is hypothesised that the morphology of the crop host (by providing cryptic oviposition sites) and the behaviour of the female moth, by placing its eggs in hidden positions using its prehensile ovipositor (Conlong, 1994b, 1995), enabled it to successfully colonise the new crop hosts. The inability of the existing natural enemies to successfully find the E. saccharina life stages hidden cryptically in the new host plants may have further helped the insect to establish on them (Conlong, 1995). Atkinson and Carnegie (1989) describe the dynamics and physiological development of E. saccharina. The cryptic nature of the different life stages of this insect living on sugarcane is well described by Dick (1945) and Carnegie (1974). A recent estimate of the damaging nature of this insect to South African sugarcane is about US$10 million per annum (Black et al., 1995). It is estimated that its larval feeding habit causes 0.1% sucrose loss for every 1% of sugarcane stalks damaged. Various methods, biological, chemical and ecological, have been proposed for the control of E. saccharina in sugarcane (Carnegie, 1981). These research options and trials take at least a year or two to complete and assess. In order to obtain a much quicker insight into the interactions of E. saccharina and its various control measures, computer simulation of these interactions was commenced. The first computer simulation model to describe the dynamics of E. saccharina in sugarcane was developed by Hearne et al. (1994). The purpose was to test various management strategies to aid and enhance research on biological control of E. saccharina using the parasitoid Goniozus natalensis Gordh (Hymenoptera: Bethylidae). A system of differential equations was used to describe the dynamics of the system. The biological control model system developed by Hearne et al. (1994) can be described as a hostparasitoid model system (Mills and Getz, 1996). This model, however, did not explicitly take in to account that the physiological development of E. saccharina is sensitive to temperature (Atkinson and Carnegie, 1989). Because of the cryptic nature of E. saccharina and its multivoltine population cycle, the timing of control measures to affect a vulnerable stage of the insect’s life cycle is of critical importance. A model to analyse control strategies cannot aggregate all individuals of a particular stage into a single cohort to be represented by a single variable as done in Hearne et al. (1994). For example, eggs laid on a certain day might experience a sequence of temperatures quite different from eggs laid a few days later. The consequence of this is that the development rates of the two groups would be different. Thus, it is inaccurate for our present purposes to group together all eggs in existence at any one time and to represent them by a single variable. The aim of the E. saccharina model developed here was to test various management strategies so as to aid decisions on when to harvest and when to effect insecticide application. Unlike many other biological control investigations (Axelson, 1994; Yang et al., 1997; Wilder, 1999), this is a single species model. There is no
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feedback between the pest and its host sugarcane, nor are any parasitoids included such as in the models reviewed by Mills and Getz (1996). The model developed here is a stage-structured population model which uses degree days for the development of each stage in the E. saccharina life cycle. Each stage in the E. saccharina life cycle is further subdivided into a number of cohorts. On each day of the simulation, the cohorts of the different life stages coming into existence are identified and monitored separately from the other cohorts already represented in the model. All cohorts, new ones and those from previous days, are separately updated each day of the simulation. A cohort ceases to exist when all individuals belonging to that cohort have matured to the next stage class. The model is used to investigate the effectiveness of insecticide control and early harvesting.
2. Qualitative description of the model For the purposes of the model to be described below, we will assume that the E. saccharina life cycle consists of five distinct stages namely, egg, small larva (instars I– III), large larva (instars IV and above), pupa and moth stages. A detailed account of these stages can be found in Atkinson and Carnegie (1989). We have divided the larval stage into two in order to monitor the effects of insecticide application on the more susceptible small larvae which spend their time outside the cane stalk and also to monitor damage to sugarcane due to the larger larvae which bore into the cane stalk to feed on the soft tissue inside. Initial values for a set of egg cohorts are chosen to represent eggs laid by immigrant moths searching for oviposition sites in a field otherwise free from E. saccharina. Since E. saccharina moths normally lay their eggs on dead leaf cane material (Conlong, 1994b; 1995), the timing of the introduction of initial egg cohorts is based on the age of cane. New egg cohorts are formed on a daily basis until the first set of moth cohorts resulting from these initial egg cohorts emerge. These will then be responsible for creating subsequent cycles. On any given day, some of the eggs in each egg cohort of sufficient physiological age (the physiological time scale is discussed in the next section) hatch out as small larvae. The aggregate of all small larvae hatching out from all of the egg cohorts in existence on that day forms a cohort of small larvae. Thus, in general, the newly formed cohort of small larvae consists of individuals from more than one egg cohort. In due course, once sufficient time has passed and the cohort of small larvae has reached the right physiological age, individuals begin to bore into the cane stalk as large larvae. All small larvae that bore into the cane stalk on the same day form a cohort of large larvae. When a cohort of large larvae reaches a certain physiological age, individuals begin metamorphosis into pupae and form pupae cohorts with others that become pupa on the same day. By a similar process, moth cohorts are formed. The whole cycle then repeats. A record in a database represents each of these cohorts. Various fields in the record keep track of information such as the day when a cohort came into existence,
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the number of individuals in the cohort and its physiological age. When updating takes place each day, all fields, i.e. all attributes of each cohort are adjusted. This must be done separately for all of the cohorts. This creation and demise of cohorts is shown schematically in Fig. 1. The dynamics of a typical cohort is shown in Fig. 2. The model has a daily time step and thus new cohorts are formed once a day. Once a cohort has come into existence it does not receive any further recruits on later days. Some members of a typical cohort may die during any given day. These individuals are removed from the system during the daily update. Further, the
Fig. 1. Example of inter-relationships between cohorts on successive days.
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Fig. 2. The dynamics of a typical cohort.
physiological age of the cohort is updated by an amount depending on temperature and the life stage the cohort is in. If the cohort has reached sufficient physiological age on a given day, some of its members undergo metamorphosis to the next life stage on that day (for cohorts of small larvae, members will begin to bore into the cane stalk as large larvae). These members contribute to the formation of a new cohort (Fig. 2). It is important to note that simultaneously, other cohorts comprising individuals of the same life stage may also contribute to members of this new cohort (Fig. 1). The updating process includes the determination of mortality numbers and numbers maturing onto the next life stage. These calculations are based on a set of functions using as arguments, certain fields in the record representing the cohort. A mathematically detailed account of the relationships described above and the dynamics involved is presented in the next section.
3. Mathematical description of the model Let xji(t) denote the number of individuals on day t in the cohort that commenced stage j on day i. Here the stages egg, small larva, large larva, pupa and moth are indexed by j=0, 1, 2, 3, 4 respectively. Thus x05(10) represents the number on day 10 of the simulation, of eggs remaining from the cohort of all eggs that were laid on day 5 of the simulation. Let aji(t) denote the physiological age on day t of the cohort that commenced stage j on day i. Note that in general, insects of the same physiological age will not necessarily move on to the next life stage at the same time. The rate of maturation from one stage to another is distributed about a mean physiological age required for maturing to the next stage. Let pjmin denote the minimum physiological age at which members of a cohort in stage j begin to move onto the next stage and pjmax denote the physiological age by which all members of a cohort in stage j will have made the transition to the next stage. The fraction of members that die on day t from a cohort that commenced stage j on day i will be denoted by di j(t). Similarly, for a cohort that commenced stage j on day i, we denote the fraction that mature to the next stage on day t by mji(t). In order
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to index all cohorts in stage j that are in existence on day t, we define a set Sj(t) as follows: Sj ðtÞ ¼ t; t 1; . . . ; t Lj where Lj is such that ajLj ðtÞ 4 pjmax and ajLj 1 ðtÞ > pjmax . With the above notation, the dynamics of the E. saccharina population in the various stages and cohorts can be modelled by the system of difference equations xji ðt þ 1Þ ¼ xji ðtÞ 1 d ji ðtÞ m ji ðtÞ ; for all i 2 Sj ðtÞ and j ¼ 0; 1; 2; 3 The initial conditions of the above system are given by x0t ðtÞ ¼ x0ini ðtÞ, before first moths are generated by the system P x0t ðtÞ ¼ K2S4 ðtÞ O x4k ðtÞ x4k ðtÞ, after system has generated its own moths, and P j1 xjt ðtÞ ¼ i2Sj1 ðtÞ mj1 i ðtÞ xi ðtÞ, j=1, 2, 3, 4 where x0ini ðtÞ isthe number of eggs used in the initialisation process based on the age of cane and O x4k ðtÞ is the oviposition rate of moth cohort k on day t. The detailed formulations of the above are discussed later. The mortality rate of a cohort on any given day depends on the life stage of the cohort and also on the day’s average temperature. The South African Sugar Association Experiment Station (SASEX) has accumulated vast data on the stage specific mortality rates of E. saccharina and how temperature affects these rates. Table 1 shows the stage specific mortality rates at a temperature of 26 C and Table 2 shows how they vary at different temperatures. Let dj be the stage specific mortality rate given in Table 1. Then, the fraction of members of a cohort that die on any given day will be given by d ji ðtÞ ¼ d j f j ½TðtÞ
where the temperature function f j is a cubic polynomial. This was determined by finding the lowest degree polynomial that gave a satisfactory least squares fit to the data in Table 2. The time (i.e. physiological time) spent in each stage in the E. saccharina life cycle is temperature dependent and is measured in degree-days ( C d). Pruess (1983) discusses various ways of estimating the number of degree-days accumulated by insects Table 1 Stage-specific mortality rates (per day) for Eldana saccharina at a temperature of 26 C (source: SASEX)
Mortality rate (/day)
Eggs
Small larvae
Large larvae
Pupae
Moths
0.03
0.09
0.029
0.07
0.2
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Table 2 Collocation points for the temperature functions used to adjust mortality rates (source: SASEX)
Eggs Small larvae Large larvae Pupae Moths
10 C
19 C
22 C
26 C
30 C
0.00 0.00 0.00 0.00 0.00
0.64 0.58 0.58 0.44 0.56
0.78 0.78 0.78 0.54 0.71
1.00 1.00 1.00 1.00 1.00
1.10 1.10 1.10 1.10 1.10
on any given day. The method used here was chosen because the minimum temperatures experienced in the areas of interest to this study rarely fall below the required threshold temperatures for growth for each stage in the E. saccharina life cycle. Pruess (1983) argues that if this is the case, this method is similar to the more common sine wave method. The simplicity of this method compared to the sine wave method together with the fact that it gives similar results to the sine wave method when used for purposes similar to ours led to it being adopted here. Let T jth ( C), j=0, 1, 2, 3 be the threshold temperature for development for individuals in stage j of the E. saccharina life cycle. Let T(t) ( C) denote the average temperature on day t. The physiological age of each cohort will be modelled by the recurrence equations aji ðt þ 1Þ ¼ aji ðtÞ þ Daji ½TðtÞ ; with initial conditions aji ðtÞ ¼ 0; where Daji ½TðtÞ is given by TðtÞ t jth ; if TðtÞ > T jth j Dai ðTðtÞÞ ¼ 0; otherwise for all i 2 Sj ðtÞ and j=0, 1, 2, 3. Way (1995) calculated the time, in C d, spent in each stage in the E. saccharina life cycle, as well as the temperature threshold required for development for each stage (Table 3). The C d range pjmin and pjmax was determined from experimental data (Table 3). Maturation to the next stage begins when the physiological age of the cohort reaches pjmin and the fraction of individuals that undergo metamorphosis is estimated by mji ðtÞ
( 0; j ¼ ai ðtÞ p jmin = p jmax p jmin ; 1;
if aji ðtÞ 4 p jmin if p jmin < a ji ðtÞ < p jmax if aji ðtÞ 5 p jmax
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The oviposition rate of a moth cohort depends on how long (in days) the cohort has lived. On average, moths live for about 5 days and according to SASEX, moths mate soon after emerging and will lay eggs on a daily basis until they die. Table 4 shows the average number of eggs laid per moth n days after emergence. We then rewrite the initial conditions for egg cohorts as X x0t ðtÞ ¼ x4k ðtÞ FO n x4k ðtÞ ; k
where n x4k ðtÞ is the number of days after emergence for moth cohort k and FO is an oviposition function determined from the data in Table 4.
4. Model application The reason for developing this cohort-based simulation model was to investigate the use of insecticides and early cutting as control measures for E. saccharina and to give an indication of the crop loss that could be expected if the control measure is implemented properly and works. To correspond with common practice in the sugar industry, the model calculates E. saccharina infestation in terms of the number of E. saccharina per 100 stalks of sugarcane crop. The notation of e/100s used by Hearne et al. (1994) is adopted here to denote this. The simulations assume that initial egg cohorts of two eggs per 100 stalks of sugarcane each enter a sugarcane field of about 3–4 months old on a daily basis until the moths generated within the system lay eggs at a rate exceeding this number. Table 3 The stage specific threshold temperatures for development T jjh and the duration p jmin P jmax in C d of each stage
Eggs Small larvae Large larvae Pupae
Threshold temperature ( C)
Duration ( C d) pjmin –Pjmax
5.3 10.2 11.7 10.7
102–136 185–253 371–439 120–200
Table 4 The number of eggs laid per female moth n days after emerging n
1
2
3
4
5
Eggs laid (/female moth)
6
14
30
16
12
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(E. saccharina is known to attack cane of about 3–4 months old, when the first small dead leaves appear. Usually, moths from a neighbouring mature field invade a young sugarcane field and lay their eggs on available dead leaves.) Each simulation runs for 24 months since in general the sugarcane cycle has a maximum of 24 months. A damage index is defined to provide a measure of crop damage due to E. saccharina. The damage index on day t [denoted Dind(t)] of the simulation is defined as the total number of larvae degree-days spent in the cane stalk up to that day. That is, on each day of the simulation, the crop damage index is updated as follows: Dind ðtÞ ¼ Dind ðt 1Þ þ LLARVðtÞ TðtÞ T2th where LLARV(t) is the total number of large larvae on day t. The reasoning behind the above definition is that it is the larger larvae that cause damage to the sugarcane stalk. It should also be noted that because the growth rate of E. saccharina is temperature driven, larval activity slows down on cold days and the amount of cane tissue consumed will not be as high as on a hot day when larval activity speeds up. Thus, updating the damage index by the product of large larvae and the number of C d gained on that day gives an indication of the amount of damage incurred on that day. Since E. saccharina numbers are measured in e/100s, the unit for the damage index defined above is (e/100s) C d. The relationship between actual damage to the crop and the damage index defined in this paper is still being investigated. Once this has been established, a critical damage index corresponding to the damage at which the crop must be harvested can be found. A rough estimate of the critical damage index that will be used for illustrative purposes is 35 000 (e/100s) C d. SASEX supplied actual daily maximum and minimum temperature data for the Tongaat area in Kwa-Zulu Natal, South Africa for the 30-year period between January 1966 and December 1997. This data set was used to run several simulations to test model response to various temperature scenarios. The temperature scenarios were also used to test harvesting and insecticide application strategies. We then ran the model for the entire temperature data set to investigate the frequency of high damage levels at key points in the cane’s growth cycle. It would have been useful to have compared model output with historical records of actual damage caused to crops. Unfortunately, no such records exist. In the past the main defence against E. saccharina has been to harvest early if infestation showed signs of becoming too severe. The mill would only reject cane if the damage was very severe. Mass was the only factor used by the mill to determine payment to farmers. For cane not rejected altogether, damage was irrelevant. Thus no damage was recorded. This has recently changed and a number of factors such as sucrose content are now included in the calculation to determine the payout to a particular farmer. Another problem is that there are large local differences in temperature so regional damage data (had it existed) would not be very useful. Some field trials are underway at present to collect the sort of data that we hope to be able to use for validation purposes but this will not be available for some time.
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5. Policy analysis 5.1. Harvesting Sugarcane may be harvested from as early as age 11 months, but it can be left on the field for up to 22 months as sucrose content increases as the crop matures. However, if E. saccharina is present, the sucrose yield is greatly affected and the farmer may need to harvest sooner rather than later. During the milling season which runs from April to November, the farmer monitors (among various other factors) the damage to the crop due to E. saccharina. If the damage reaches a certain critical level, the crop is harvested. For the period when mills are closed, a decision is made just before mill closure whether to harvest and forfeit a possible increase in sucrose yields when mills reopen or to leave the crop on the field and risk loss from damage due to E. saccharina. The decision is based on the age of the sugarcane crop, the E. saccharina infestation level at the decision date and the projected infestation level by the time mills reopen. Historical temperature data for the period during mill closure are used to determine expected infestation levels when mills reopen. The model can be used as a decision aid by running it using actual temperature data up to mill closure and historical temperature data during the mill closure period. This then gives an indication of whether the critical damage index will be reached before mill closure or not and the grower can be advised accordingly. As an example, the model was run using actual daily temperature data for a 24month period starting 1 August 1991. Fig. 3 shows the value of the damage index on specific days of the simulation. It can be seen that the damage index is still below the critical level of 35 000 (e/100s) C d when mills reopen. If this were not the case, then harvest before mill closure would be advised.
Fig. 3. Daily damage index for crop cycle beginning August 1991.
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We first investigated the effect of the planting date on the damage index at the decision date and when mills reopen. The model was run using temperature data collected over 30 years for crop cycles beginning in July, August, September, October and November. At the decision date, the crops are aged 16, 15, 14, 13 and 12 months, respectively, and would be ready for harvesting if damage was found to be too high. Table 5 shows the means and standard deviations for the results obtained from these simulations. From these results, we find that in the example of Fig. 3 (August crop cycle), there is a 3% chance that the damage index will be above the critical level of 35 000 (e/100s) C d when mills reopen. If the grower is willing to take this risk the crop can be left on the field until the mills reopen. The risk is about 54% for the July crop and is less than 0.5% for the other crop cycles considered. Table 6 shows a summary of the expected maximum damage index in November and in March at 90, 95 and 99% confidence for crop cycles beginning in July, August, September, October and November. Fig. 4 shows the graph of the expected maximum damage index at the specified degree of accuracy plotted against crop age for the August crop cycle. Suppose now that the farmer has a measure of the damage index at the decision date and wants to find out what the projected damage index will be by the time mills reopen. In order to answer this question, temperature data sets were prepared such that temperatures are fixed up to the decision date and varied using historical data for the mill closure period. This enabled us to get a fixed reading at the decision Table 5 Mean damage index [(e=100s) C d] and corresponding standard deviation for crop cycles beginning in July, August, September and October
November March
Mean S.D. Mean S.D.
July crop
August crop
September crop
October crop
November crop
27 113 599 35 147 1449
24 502 529 32 439 1346
21 746 619 29 805 1493
18 965 704 26 723 1664
166 20 554 24 661 1393
Table 6 The probability that the damage index [(e=100s) C d) will be below the given value in November and in March for the various crop cyclesa November
July crop August crop September crop October crop November crop
March
90%
95%
99%
90%
95%
99%
27 880 25 179 22 539 19 867 17 330
28 096 25 370 22 762 20 120 17 529
28 509 25 735 23 189 20 606 17 911
37 003 34 162 31 716 28 852 26 444
37 524 34 647 32 253 29 451 26 945
38 525 35 576 33 283 30 600 27 906
a For the August crop cycle, there is a 95% chance that the damage index will lie below the critical value at 19 months (i.e. in March).
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Fig. 4. Expected maximum damage index against crop age. The confidence curves give the likelihood that the damage index will be below the given value at the specified crop age.
date and various possible levels when mills reopened. Table 7 shows the value of the damage index at the decision date together with the corresponding mean and standard deviation of the expected damage index when mills reopen. With the results shown in Table 7, given a damage index at the decision date, we can find the minimum expected damage index when mills reopen based on the risk the cane grower is willing to take. Fig. 5 shows the expected minimum damage index at 95% confidence levels. Expected minimum damage indices for intermediate values can be found by interpolation. For example, suppose the grower is willing to take a risk of only 5%. Using interpolation and the results of Fig. 5, we find that the damage index at the decision date whose expected damage index when mills reopen will be above 35 000 (e/100s) C d at a risk of 5% is 26 740 (e=100s) C d. That is, if a grower is willing to take a 5% risk, his cut off level at the decision date is 26 740 (e/100s) C d. 5.2. Insecticide application Insecticide spraying is normally done soon after a moth peak is observed in the field. The first instar larvae are considered the most vulnerable to insecticide application because just after eclosion they disperse from the oviposition sites, leaving them exposed. Second and third instar larvae will still be vulnerable as they spend their time scavenging on the outside of the sugarcane stalk, but not to the extent of first instar larvae. The large larvae are considered to be well protected from insecticides as they spend their time hidden inside the cane stalk. The insecticide kill rate is thus a function of the physiological age (in C d) of the small larvae. For the purpose of these simulations, a kill rate of 60% for first instar
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Table 7 Mean and standard deviation for the expected damage index when mills reopen given a particular damage index at the decision date Damage index in November [(e/100s) C d]
13 200 18 900 24 800 30 300 35 900
Expected in March Mean
S.D
21 131 26 306 32 738 38 297 43 909
173 212 172 168 173
Fig. 5. The value of the expected damage index (at 95% confidence) in March based on a known damage index for the previous November.
larvae a2i ðtÞ 4 80 C d , 40% for larvae 80 C d < a2i ðtÞ 4 150 C d 2second instar and 20% for third instar larvae ai ðtÞ > 150 C d was assumed. These rates need to be adjusted by a function f(n) where n is the time elapsed since the insecticide was applied. SASEX estimates that the strength of the insecticides they use decays slowly initially but more rapidly later. A function with these properties is given by
n 3 fðnÞ ¼ 1 ; N where n is the number of days elapsed since insecticide application and N is the number of days the insecticide remains effective in the field. The aim is to find the relationship between the duration of insecticide effect and the reduction in the damage index. The long lasting insecticides may be cheaper to
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apply in terms of labour costs and may even have a better kill rate, but a strong dose of a well-timed application may result in a better kill rate. We investigated insecticides whose effect lasts for 2 weeks, 1 month and 2 months and compared the resulting reduction in the damage index. This was done by running simulations for crop cycles beginning in August over the 30-year period from 1967 to 1997 with insecticide application effected whenever a moth peak of more than 0.75 e/100s was reached. Table 8 shows the means and standard deviations of the percent reduction in the damage index in November (at 15 months) and in March (at 19 months). Fig. 6 shows the minimum percent reduction in damage index that the farmer can be confident, to the specified degree of accuracy, that the insecticides used can achieve at the specified date. From the results shown in Fig. 6 it can be concluded that the insecticides whose effect lasts for 28 days achieves the best percent reduction in
Table 8 Mean percent reduction in the damage index and the corresponding standard deviation for insecticide duration of 14, 28 and 56 days 14 Days
Mean % reduction Standard deviation
28 Days
56 Days
November
March
November
March
November
March
56.1 5.38
60.4 4.13
66.3 4.84
68.9 3.59
63.7 7.35
71.0 5.27
Fig. 6. Minimum percent reduction in the damage index for various durations of insecticide effect. The confidence levels indicate the probability that the percent reduction in damage will be above the given value.
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the damage index, the next best results being obtained from insecticides whose effect lasts for 56 days.
6. Conclusion A model of the sugarcane pest E. saccharina has been formulated that improves upon a previous model of this pest in that it includes temperature effects explicitly. This enabled a more accurate index to be formulated of the extent of cane damage under different temperature patterns. It was illustrated how this damage index can be used to determine whether to harvest the crop just before mill closure or to leave it on the field until mills reopen based on the risk that may be incurred if the crop was not harvested. When investigating insecticide application policies, the cohort structure of the model made it possible to target specific larval age groups whose susceptibility to insecticides varies. Results of these investigations give an indication of the relationship between the duration of insecticide effect and the reduction in the damage index. Although, as illustrated, the model is useful as a decision aid in its present form, the economic implications have not been dealt with. Further research is planned to incorporate the costs and benefits of both the timing of the harvest and various insecticide application strategies. When this has been achieved, the model will provide crop growers and managers information that gets to the very core of their problem—profit margins. References Atkinson, P.R., 1979. Distribution and natural hosts of Eldana saccharina Walker in Natal, its oviposition sites and feeding patterns. Proc. South Afr. Sugar Technol. Ass. 53, 111–115. Atkinson, P.R., 1980. On the biology, distribution and natural host-plants of Eldana saccharina Walker. J. Entomol. Soc. South Afr. 43, 171–194. Atkinson, P.R., Carnegie, A.J.M., 1989. Population dynamics of the sugarcane borer, Eldana saccharina Walker (Lepidoptera: Pyralidae), in Natal, South Africa. Bull. Entomol. Res. 79, 69–80. Axelson, J.A., 1994. Host-parasitoid interactions in an agricultural ecosystem: a computer simulation. Ecological Modelling 73, 189–203. Black, K.G., Huckett, B.I., Botha, F.C., 1995. Ability of Pseudomonas flourescence engineered for insecticidal activity against sugarcane stalk borer, to colonise the surface of sugarcane plants. Proc. South Afr. Sugar Technol. Assoc. 69, 21–24. Carnegie, A.J.M., 1974. A recrudescens of the borer Eldana saccharina Walker (Lepi-doptera: Pyralidae). Proc. South Afr. Sugar Technol. Assoc. 48, 107–110. Carnegie, A.J.M., 1981. Combating Eldana saccharina Walker: a progress report. Proc. South Afr. Sugar Technol. Assoc. 55, 116–119. Conlong, D.E., 1994a. A review and perspectives for the biological control of the African stalkborer Eldana saccharina Walker (Lepidoptera: Pyralidae). Agriculture, Ecosystems and Environment 48, 9–17. Conlong, D.E., 1994b. Host-parasitoid interactions of Eldana saccharina (Lepidoptera: Pyralidae) in Cyperus Papyrus. Unpublished PhD thesis, Department of Zoology and Entomology, University of Natal, Pietermaritzburg, South Africa. Conlong, D.E., 1995. Biological control of Eldana saccharina walker in South African sugarcane: constraints identified from 15 years of research. Insect Sci. Applic. 17, 69–78.
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