A simulation model of population dynamics of the rusty grain beetle, Cryptolestes ferrugineus in stored wheat

Ecological Modelling, 48 (1989) 137-157

137

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

A SIMULATION MODEL OF POPULATION DYNAMICS OF THE RUSTY GRAIN BEETLE, CR YPTOLESTES F E R R U G I N E U S IN STORED WHEAT

H. KAWAMOTO

1,3,

S.M. WOODS 2, R.N. SINHA 2 and W.E. M U I R 1

aAgricultural Engineering Department, University of Manitoba, Winnipeg, Man. R3T 2N2 (Canada) 2Agriculture Canada Research Station, 195 Dafoe Road, Winnipeg, Man. R3T 2M9 (Canada) (Accepted 3 May 1989)

ABSTRACT Kawamoto, H., Woods, S.M., Sinha, R.H. and Muir, W.E., 1989. A simulation model of population dynamics of the rusty grain beetle, Cryptolestes ferrugineus in stored wheat. Ecol. Modelling, 48: 137-157. A simulation model of the population dynamics of Cryptolestesferrugineus in stored wheat was constructed using published and unpublished data. An isolated population in a homogeneous bulk of stored wheat was assumed to be exposed to a changing physical environment (temperature and relative humidity) without immigration or emigration. The model consists of submodels of the development, oviposition and mortality. An equation by Sharpe and DeMichele was expanded to describe the developmental rates of immatures at various temperatures and relative humidities. The Weibull distribution function was modified and expanded to describe the oviposition rates of females of various ages at various temperatures, relative humidities and adult densities, and to describe the adult mortality. Temperature was the primary physical variable and controlled the initial growth rate and the peak density of a C. ferrugineus population. After unlimited initial growth, the population growth was regulated mainly by density-dependent mortality of immatures.

INTRODUCTION

A stored grain bulk is a closed ecosystem where arthropods and microorganisms consume the energy stored in the grain, and interact with other species and the abiotic environment (Sinha, 1973). Although different species of insects and microflora occur either concurrently or in succession (Sinha, 3 Present address: Agriculture Canada Research Station, 195 Dafoe Road, Winnipeg, Man. R3T 2M9, Canada. 0304-3800/89/$03.50

© 1989 Elsevier Science Publishers B.V.

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H. KAWAMOTO ET AL.

1961; Sinha and Wallace, 1966), usually one or two species initiate major changes in the structure and function of such ecosystems. One such pest species is the rusty grain beetle, Cryptolestes ferrugineus (Stephens) (Coleoptera: Cucujidae), which is a cosmopolitan insect pest of unprocessed cereals and oilseeds (Freeman, 1952; Cotton, 1963; Sinha and Watters, 1985). In Canada, it is the most common and serious pest of stored grain on farms and in grain elevators in the Prairie Provinces. When freshly-harvested warm grain is stored in autumn for periods ranging from several months to years, C. ferrugineus often builds up a large population and becomes a major cause of grain germ damage, heating and spoilage of grain. Although several comprehensive studies have been made on the life history (Rilett, 1949; Bishop, 1959), intrinsic rate of increase (Smith, 1965) and ecology (Sinha and Wallace, 1966) of C. ferrugineus, few attempts have been made to develop mathematical models simulating the life stages, developmental and mortality rates of this species. Such biological models based on reproducible laboratory data are a prerequisite to developing comprehensive models of stored grain ecosystems that could be used to analyse the dynamics of the ecosystem, and to advise farmers on sound management of stored grain pests with minimal use of insecticides. A stored-product research group in Australia has pioneered the development of simulation models of environmental changes associated with the population increase of the rice weevil, Sitophilus oryzae (L.) (Hardman, 1978; Cuff and Hardman, 1980; Thorpe et al., 1982; Longstaff and Cuff, 1984). The grain storage research group in Winnipeg has developed models simulating the intergranular environment and its management by aeration within grain bulks (Yaciuk et al., 1975; Metzger and Muir, 1983). This report, as a part of an ongoing study involving simulation modelling of different components of the stored grain ecosystem, presents a simulation model of the population dynamics of C. ferrugineus over a wide range of temperatures and relative humidities. The model is based on published data of Rilett (1949), Bishop (1959) and Smith (1962, 1963, 1965, 1966, 1970, 1980) and unpublished data of the late Dr. L.B. Smith and of the authors (Kawamoto et al., unpublished). BASIC MODEL S T R U C T U R E A N D M O D E L L I N G M E T H O D

An isolated population of C. ferrugineus in bulk stored wheat was assumed without immigration or emigration. The dynamics of the population were modelled in relation to the temperature, relative humidity and insect density in a homogeneous wheat bulk. The life cycle was divided into three stages: egg, immature (first-instar

POPULATION DYNAMICS OF CRYPTOLESTES FERRUGINEUS IN STORED WHEAT

139

I COHORtSTRUCIUREDPOPULATIONVECIOR EGGS, IMMAIURES, ADULIS

DEVELOPMENt/AGING I MORTALITY OVIPOSITION

ENVIRONMENT ~ ~

I

IEMPERAIURE HUMIDIIY DENSITY

NEXT COHORt VECTOR

Fig. 1. C o n c e p t u a l s t r u c t u r e o f t h e s i m u l a t i o n m o d e l o f dynamics.

Cryptolestes ferrugineus

population

larva through pupa) and adult (Fig. 1). Equations were devised for development and mortality rates of the egg and immature stages, and for oviposition and mortality rates of the adult stage. Each equation was chosen and its parameters were estimated after careful examination of all available data. The SAS ~ procedure N L I N was used to find a least square fit to non-linear equations by Marquardt's iterative m e t h o d (SAS ® Release 5.16 under VMS) (SAS, 1985). The estimate and standard error (s.e.) of a parameter are given in the form of (estimate _+s.e.) whenever the s.e. is available. Data whose type and structure were consistent with each other were pooled together to estimate simultaneously as m a n y parameters as possible to improve the overall fit of the model. In cases where parameters were estimated in two or more stages rather than simultaneously, the standard errors were computed regarding each stage as a model in itself. Therefore these standard errors should be interpreted more as stability indicators than as standard errors for a the complete model. In some cases, the function for the model is defined separately on different regions within the domain of the independent variable(s). The word threshold in the present paper refers to the b o u n d a r y between these regions and does not imply the biological threshold in a strict sense.

140

H. K A W A M O T O E T AL.

DEVELOPMENTAL RATES OF EGG A N D I M M A T U R E STAGES

Developmental rate of egg The duration of the egg stage was measured at 19, 25, 30, 32 and 35 °C and 50, 60, 70, 80 and 90% relative humidity (RH) by Kawamoto et al. (unpublished), at 32 and 3 8 ° C and 75% RrI by Rilett (1949), and at 3 2 ° C and 40, 50, 60, 70, 80, 90 and 95% RH by Bishop (1959). Relative humidity is not included in the model because it showed no significant effect on egg duration. The developmental rate of eggs, R e , which is defined as the inverse of the duration in days of the egg stage under a constant environment, was estimated based on Kawamoto et al. (unpublished). Because the duration of the egg stage is short compared to the larval and pupal stages, a linear developmental rate equation was considered adequate (Fig. 2): Re=

0.333 PDE(T-- TDE) 0

35 < T TOE < T < 35 T < TDE

(1)

where R e is developmental rate of egg (day-l), and T is temperature (°C).

fO 13 ~

O. 3

4.3 r ~ E

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90~RH

r-I

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O V /' R

70~RH 60~RH 50~RH R:[1

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Fig. 2. Developmental rate of eggs of C. ferrugineus. The linear function was estimated based on Kawamoto et al. (unpublished) represented by symbols for 50-90% Rn. The observed values at 75% gn from Rilett (1949) are shown by the letter R.

POPULATION DYNAMICS OF CRYPTOLESTES FERRUGINEUS IN STORED WHEAT

141

The estimated parameter values a r e : T D E , base temperature (15.3 + 0.3 ° C); and PDE, coefficient ((1.69 + 0.03)× 10 -2 day -1 ° c - a ) . The development rate at 3 8 ° C observed by Rilett was significantly lower than the expected rate based on linear regression presumably due to high temperature inhibition. Therefore, it was considered adequate to assume a constant development rate at temperatures above 35 ° C.

Developmental rate of immature stage The development from the hatching of the first-instar larva to the emergence as an adult from the pupa is treated as one immature stage. Although a preliminary analysis of Rilett's (1949) and Bishop's (1959) data showed that the effects of temperature and relative humidity on developmental rate differ for each larval instar and the pupa, a c o m m o n developmental model for immatures was devised. A single model of the combined immature stages allowed the use of 38 observations under various temperature-humidity combinations reported by Rilett (1949), Bishop (1959), Sinha (1965) and Smith (1965). If separate models had been devised for each larval instar and the pupa only 14 observations could have been used. The developmental rate of the immature stage, Rim(T' , W), is expressed as a function of absolute temperature, T ' (K) ( T ' = 273.2 + T ( ° C)), and relative humidity, W (%). A preliminary examination of the data did not indicate an interaction between the effects of temperature and relative humidity on developmental rate. Therefore those effects are assumed independent and are expressed in the equation as a product: R i m ( r ' , W ) = P(W) Q(T')

(2)

where P ( W ) is modification factor for low relative humidity (0 < P ( W ) < 1); and Q(T') is developmental rate at T ' (K) without the effect of low humidity. P(W) is defined as:

P(W) = { exp(--B(WT --1

W))

W~--wTW < WT

(3)

The estimated parameter values are: WT, threshold relative humidity (75%); and B, coefficient ((1.40 _+ 0.14) × 10-2% RH-1). The temperature-dependent rates of development are expressed by Sharpe and DeMichele's (1977) equation. The applicability of this equation to the developmental rates of insects and other poikilotherms has been presented by Schoolfield et al. (1981) and Wagner et al. (1984). In a preliminary analysis, this equation explained 99.8% of the total variance of the immature development rates at 70% RH and ten different temperatures from 20 to

142

H. KAWAMOTO ET AL.

42.5 °C observed by Smith (1965). Therefore, this equation was applied for all available data as follows:

Q(T')=R25298. 2

[(1

I+fL(T')+fH(T')

fa(T') = exp H a 298.2

fL(T')=exp

[

(1 H L T£

[ (1 f H ( T ' ) = e x p HH Tt~

T' 1) T' 1) T'

(4)

The estimated parameters are: R25, standard developmental rate at 298.2 K (25°C) ((4.13 + 5.79) × 10 -2 day-l); TL, T~, temperatures (T L = 293.0 + 32.3 K, TH= 303.7+26.8 K) at which the basic developmental rate (R25(T'/298.2) fa(T')) is reduced by about one-half by the inhibitive effect of low or high temperature; and H a , H E , H H , parameters expressing the magnitude of the effects of temperature ( H a = (1.26 + 5.23)× 104, H E = ( - 2 . 3 8 ___5.45) X 104, H n = (1.76 + 3.57) × 104). During the parameter estimation, Wx was changed in steps of 1.0% and entered into equation (3) as a constant. Then the remaining parameters in equations (2), (3) and (4) were simultaneously estimated by nonlinear regression. The value of WT which gave the smallest residual error was chosen. The available data were weighted by the product of the number of observations and the developmental time. The high standard errors of the parameters are associated with high correlations between parameters; the absolute values of correlations between all parameters except B range from 0.658 to 0.999. The reasons for these high standard errors are the complexity of Sharpe and DeMichele's equation and the variation in source data between authors. The model, however, explains 99.4% of the weighted variance of the data (Fig. 3). OVIPOSITION RATE

The oviposition rate, or the number of eggs produced per female per unit time, is described by an equation originally proposed by Weibull (1951) and expanded by Yang et al. (1978). The equation was modified in the present study to include the effects of adult aging, low and high temperature, low relative humidity and density. In a preliminary analysis of the oviposition data (Smith 1963, 1965, unpublished), the parameters of the Weibull distribution function were

P O P U L A T I O N D Y N A M I C S OF CRYPTOLESTES F E R R U G I N E U S IN STORED W H E A T

143

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150 50ZRH 40ZRH

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30

35

40

TemDerature (°C)

Fig. 3. Developmental rate of immatures of C. ferrugineus at various temperatures and relative humidities.

estimated for each temperature using time as the random variable. While the estimated scaring parameter of the Weibull distribution function decreased with increasing temperature, its shape parameter showed no obvious trend• In the present model, the basic oviposition rate is assumed to be a function of the physiological age, A, measured in degree days after emergence above a threshold temperature, TAO. Values for the scaling parameter, B, and the shape parameter, C, of the Weibull distribution function, common to all temperatures, were estimated using physiological age as the

144

H. KAWAMOTOETAL.

random variable. The details of this application of the Weibull distribution function to insect oviposition rates will be published elsewhere. The physiological age, A, is calculated by a simple equation: dA ( T - TAG d t-~me = ~ 0

T >__TAG T < TAG

(5)

and A -- 0 at the time of adult emergence. The estimated parameter is: TAG, threshold temperature (16.6 + 0.4 ° C). From day i to day j, the number of eggs, G, produced by a female whose physiological age advances from A~ to Aj is expressed as follows:

G= EGG M(T, W, D)(exp(-(Ai/B) c) -exp(-(Aj/B)C))

(6)

where EGG, maximum total number of eggs produced by a female during her life time under an optimal condition (687 +_159 eggs per female); M(T, IV, D), modification factor (0 < M(T, W, D) <_1) due to low or high temperature, low relative humidity or high density; and B, C, the scaling parameter (B = 981 _+ 35) and the shape parameter (C = 1.26 -4- 0.03) of the Weibull distribution function. The modification factor is:

M(T, W, D)=

exp(--MLH -- MDRY -- MDEN)

where PML(TML-- T) MLH----

T < TML TML < T_< TMH

0 P M H ( T - - TMH )

T > TMn

0 MDRY=

PMDRy(100 --

W)(T-

0 MDEN ----

PMDEN 1og(Nad)

TMDRY)

Nad_< 1

Nad > 1

T _~ TMDRY r > TMDRY

(7)

The estimated parameters are: TML, PML, threshold temperature (TML = 29.4 ° C) and coefficient (PML = 0.229 +- 0.041 ° C - t ) for low-temperature inhibition factor; TMH, PMn, parameters (TMH----35.0°C, PMH = 0.286 +0.074 ° C-1) for high-temperature inhibition factor; TMDRY, PMDRY, parameters (TMDRY = 22.5°C, PMDRY= (1.82 + 0.77) × 10 -3 ° C - 1 % R H -1) for inhibition due to low relative humidity; and PMDEN, parameter for effect of adult density ( N a d = n u m b e r of females/g of wheat) (PMDEN = 0.520 +

0.060). The values of TAG, B, and C were simultaneously estimated using data of the late L.B. Smith (1963, 1965, unpublished). The values of EGG, TML,

POPULATION DYNAMICS OF CRYPTOLESTES FERRUGINEUS IN STORED WHEAT

morleZ xL

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60

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,

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aclult

,

,~', 120

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Fig. 4. Oviposition rates of C. ferrugineus at different temperatures and 70% RH. Data of Smith (1963, 1965, unpublished), were simulated by the modified Weibull distribution.

TMI-I, TMDRY,PML, PMH, PMDRY were then estimated using Smith's (1965) data, manually changing the TML, TMH, TMDRYvalues by 0.1°C to obtain the minimum residual sum of squares. The equation of MDEN and the value of PMDEN were determined based on Smith's (1966) data. The oviposition rates predicted by these equations are shown in Fig. 4. The equation simulates realistically the observed responses of oviposition rates to environmental conditions. These are the low oviposition rate and long oviposition period at low temperatures, the clear and high oviposition

146

H. K A W A M O T O ET AL.

peak at intermediate temperatures, and the early oviposition peak at high temperatures. SEX RATIO The female sex ratio (female/ (male + female)) at adult emergence was estimated to be 0.57 by taking the weighted mean of 0.600 (n = 125) (Rilett, 1949) and 0.567 (n = 898) (Smith, 1966). This ratio is assumed to be constant for all adult ages. MORTALITY Mortality of eggs and immatures A common basic mortality equation was applied for the pre-adult life stages of C. ferrugineus. The change in insect density, N (number of insects/kg of wheat) from day i to day j is expressed as: N j = Ni e x p ( - U ( j - i ) )

(8)

The instantaneous mortality rate, U (day -a) is: U = UB+ UL+ UH+ UDRV+ UDEN

(9)

where UB is basic mortality rate at optimal conditions, and UL, UH, UDRV and UDEN are additional mortality rates due to low temperature, high temperature, low relative humidity, and high density, respectively. According to equation (8), the daily survival rate is e x p ( - U ) and the expected longevity of an individual is 1/U. The mortality due to high density, UDEN, is applied only for immature mortality because Smith (1966) reported no mortality of adults or eggs but significant larval mortality at high densities. The egg mortality rates, UECG, estimated from the data of Rilett (1949), Bishop (1959) and Smith (1963) varied considerably between the authors. The following equations were devised for egg mortality: UEC,~ = UEC~,B+ UL + UE~c.H + UE~,DRy UE~G'rI = UEGG'DRY =

0 PUEH(T -- TUErl) 0 PUEDR(50 -- W)

(10)

T < TUEH T > TUEH

(11)

W>_50 W < 50

(12)

where UEGO,s, basic mortality rate (0.015 day - i ) for eggs obtained by a visual fit to the data; UL is mortality due to low temperature, as described

POPULATIONDYNAMICSOF CRYPTOLESTESFERRUGINEUSIN STOREDWHEAT

147

below; TUEH, PUEH, threshold temperature (TuE H = 35.0 _+ 1.8 o C) and coefficient (PuEH = (3.44 + 1.90) × 10 -2 day -1 ° c - l ) for high-temperature mortality factor; and PUEDR, coefficient (1.74 × 10 -2 day - 1 % R H -1) for low-humidity mortality factor. The parameters TUEn and PUEH were estimated based on the mortality data at 70% RH and 35, 37.5 and 40 ° C (Smith, 1963). The mortality factor for low relative humidity was assumed to take effect at relative humidities less than 50%. The coefficient, PUEDR, was calculated by connecting U = 0.708 at 10% RH (Rilett, 1949) and UEGG,B = 0.015 at 50% RH. There was considerable variation between estimated immature mortality rates, UIMM, from the data of Rilett (1949), Bishop (1959) and Smith (1965) as there was for egg mortality. The following equations were devised for the immature mortality rate, assuming that the factors affecting mortafity are additive: UIMM = UIMM,B -~ U L + UIMM,H -4- UIMM,DRY + UIMM,DEN

0 UIMM,H =

PUIH (T - T u I H)

0 UIMM'DRY =

PUIDR(50 -- W )

UIMM'DEN =

0 PUIDENNIMM

(13)

T ~ Tui H T > Tui H

(14)

w _ 50

(15)

W<

50

T< 15°C T > 15 o C

(16)

where UIMM,B, basic mortality of immatures (0.005 day -1) obtained by visual fit; U L is mortality due to low temperature, as described below; Turn, PUIH, threshold temperature ( T u I n = 37.3 _+ 0.8 ° C) and coefficient (PuIH = (1.92 + 0.44) × 10 -2 day -1 o c - 1 ) for high-temperature mortality factor; PUIDR, coefficient (1.76 X 10 -2 day - 1 % R H -1) for low-humidity mortality factor; and PUIDEN, NIMM, coefficient of strength of density effect (PuIDEN = (8.74 __+2.64) × 10-3 density of immatures -1 day -a) and density of immatures (number of immature insects/g wheat). The parameters TUI u and PUIH were estimated based on the mortality data at 70% and 37.5, 40 and 42.5 °C (Smith, 1965). The mortality factor for low relative humidity was assumed to take effect at relative humidities less than 50% and to be equal to that for eggs at 10% RH. The coefficient, PUIDR, was calculated by connecting U = 0.708 at 10% RI-I(as described above) and UIMM,B = 0.005 at 50% RH. The coefficient PUIDEN was estimated based on Smith's (1966) data as follows. The value of P in the differential equation (dNiMM/dt = -PNI2MM) was estimated for each initial density. The initial densities ranged from 1 to 64 females per g of wheat. Then PUIDEN was calculated by taking an arithmetic mean of the P 's.

148

H. K A W A M O T O E T AL.

Mortality of adults The survivorship curves at - 9 , 0, 10, 15, 20, 25, 30, 35 and 4 0 ° C and 70% ~ observed by Kawamoto et al. (unpublished) were analysed to model the effect of temperature on adult mortality. The data of Rilett (1949), Bishop (1959) and Smith (1965) were inadequate to analyse the effect of relative humidity on mortality. The adult is known to tolerate dry conditions as low as 10% gri (Bishop, 1959; Smith, 1965; Howe, 1965, Sinha, unpublished). Thus the mortality factor due to low relative humidity was excluded. A cumulative thermal stress was introduced to explain adult mortality. Such stress was assumed to increase quickly at low and high temperatures but slowly at moderate temperatures. The adult mortality was expressed by a Weibull distribution function of the random variable represented by the cumulative thermal stress. The cumulative stress, S, is a function of absolute temperature, T' (K): d time = exp PSLA "-[-

j -~- e×p PSHA +

T t

(17)

and S = 0 at the time of adult emergence, where PSLA, PSLB, parameters for stress at low temperatures (PsLA = -- 36.1 __ 1.5, PSLB = ( 8 . 5 8 "q- 0.42) × 103);

lO0"

~4oO~O

~

v "

i 5o

v ,

v

vvvv

vv vv V v v

,

30 ° c

A A A A A A

~ ~#

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30

60

90

120

150

180

210

DAYS

Fig. 5. Survivorship curves of adults of C. ferrugineus at a wide range of temperature, simulated (lines) and observed (symbols) by Kawamoto et al. (unpublished).

P O P U L A T I O N D Y N A M I C S OF CRYPTOLESTES F E R R U G I N E U S IN S T O R E D W H E A T

149

and PSHA, PSHB, parameters for stress at high temperatures (PsHA = 101.3 + 2.0, PSLB = ( - 3 . 2 9 _ 0.06) x 1041. From day i to day j, the density, N, of an adult cohort whose stress increases from S i to Sj changes as: Nj = N~ exp(S/c'- S S )

(18.)

where C', shape parameter for the Weibull function (3.11 + 0.20). The parameters, PSLA, PSLB, PSHA, PSHB and C' were estimated simultaneously. The adult mortality over a wide range of temperature was expressed by these five parameters (Fig. 5). Mortality at low temperatures Smith (1970) and Evans (1983) indicated that acclimation at intermediate temperatures between rearing and experimental temperatures significantly improves adult survival at low temperatures. Evans (1983) reported a lower survival rate for adults at low temperatures in his experiment than did Smith (1970) and Solomon and Adamson (1955). Although Evans (1987) presented data on the survival of the immatures at low temperatures, he himself indicated that his data on C. ferrugineus are questionable due to uncontrolled experimental effects. Therefore, we did not use these data for simulation. The survival of C. ferrugineus adults at 10 to 30 ° C was 90% or higher after 2 months (Kawamoto et al., unpublished). The following equation was applied to approximate the pre-adult mortality at low temperatures: UL =

{0 0.02

T_5°C T< 5°C

(191

Population collapse at extreme temperatures Smith (1970) reported that the supercooling point of the cold-acclimated adults, at which temperature the cell fluid freezes, is - 2 1 . 2 o C. All members of the C. ferrugineus population are assumed to be killed immediately when the temperature is - 2 1 . 2 ° C or lower. Based on Smith (1980), the entire population is also assumed to be killed when the temperature is 65 °C or higher. COMPUTER SIMULATION The conceptual structure of the computer program is shown in Fig. 1. Population density is expressed with cohort-structured vectors, in which

150

H. K A W A M O T O ET AL.

individuals born in the same time step form a cohort. The surviving density per kg of wheat, developmental stage, physiological age and cumulative stress of each cohort are retained in vectors for density, stage, age and stress. For the adult stage, only female density is retained. At each time step, the development, mortality and oviposition rates are calculated using the densities at the beginning of the time step and then the cohort-structured vectors are renewed. If a cohort completes its development for one stage and commences developing for the next stage during a time step, the time step is subdivided for that cohort. The driving variables of the model are temperature and relative humidity. These variables are now arbitrarily defined but can be supplied at a later date from external data sets observed in actual grain storage. The length of a time step is an input parameter. For the simulations, a time step of one day was used. The central part of the simulation program is written in FORTRAN, and is listed in the Appendix.

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6

9

12

3

6

9

~2

MONTH

Fig. 6. Simulated dynamics of C. ferrugineus populations at constant temperatures and relative humidities at an initial density of one newly-emerged female and equivalent males per kg of wheat. Adults include females and males. Note: each temperature has its own scale.

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The population dynamics of C. ferrugineus at all combinations of three constant temperatures (20, 25, 30 o C) and three constant relative humidities (50, 70, 90%) were simulated setting the initial density at one newly emerged female and equivalent males per kg of wheat (Fig. 6). At an initial density of 100 newly emerged females and equivalent males per kg of wheat, the simulated peak densities occurred earlier but were not significantly higher than those at an initial density of one (not shown). The initial rate of increase and the peak density of the population were predominantly controlled by temperature and affected by relative humidity. Of the simulated conditions, 30°C and 90% RH had the highest initial growth rate and a peak total density of 63 000 insects/kg of wheat with 0.90 immatures per kernel was achieved in 18 weeks. When the simulated population density reached a peak, the density effects became dominant. Density-dependent mortality of immatures was so effective that more than 99% of immatures were killed during their development. Although the simulated peak density at 30 °C seems high, it is not impossible. Firstly, the data on which the oviposition equations depend were collected at optimal grain conditions, i.e. the insects were reared on whole kernel plus 5% flour (Smith, 1965). Secondly, high mortality rates of immatures and low average oviposition rates under high population densities are well simulated. Thirdly, our model does not include a resource (e.g. oviposition site and food) exploitation factor, which would inhibit population growth in response to a cumulative population density. APPLICABILITY AND LIMITATIONS OF THE MODEL The model enables the sensitivity of C. ferrugineus populations to environmental variables to be analysed. The trial simulations show a dependence of population growth-rate on temperature and relative humidity similar to that shown by Smith (1965). The model can simulate population dynamics under a changing physical environment, which may be observed or simulated (Metzger and Muir 1983). The model may also be used in conjunction with the energy budget of C. ferrugineus (Campbell and Sinha, 1978) so that the actual impact of population growth on the ecosystem in terms of food energy transfer between trophic levels can be understood. By using a modified Weibull distribution the effects of physical environment and physiological adult aging on oviposition rate have been integrated in the model. The potential fecundity is assumed to be determined by the female's physiological age, and the actual oviposition rate is assumed to be determined by this potential and environmental factors. These assumptions make the choice of equations easier and give more biological meaning to the

152

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ET AL.

equations and parameters than mechanical regression analysis with fewer biological assumptions. The immature stages from the first-instar larva to p u p a are grouped together in the current version of the model. Stage-specific treatment will be possible only when sufficient stage-specific data are available. The cohortstructured vector, instead of stage- or age-structured vector, is used in the current version of the program because it can simulate a continuous age distribution. The stage- or age-structured vector may be required when incorporating migration of insects between populations in a grain bulk. This study of modelling indicates a need for further research on the population biology of C. ferrugineus, particularly on mortality of pre-adults at low temperatures, on the relationship between oviposition and resource availability, on the migration within a bulk and between the bulk and the outside and on the initial population density in the storage. It is hoped that the present model could become a component of an integrated ecosystem model of grain storage, in which deterioration of stored grain will be explained through the activities of dynamically interacting arthropod pests and microbial species. ACKNOWLEDGEMENTS This work was supported b y Natural Sciences and Engineering Research Council of Canada. This is a joint contribution from the D e p a r t m e n t of Agricultural Engineering, University of M a n i t o b a and the Agriculture Canada Research Station, Winnipeg (Contribution No. 1313). The authors thank Drs. W.J. Turnock and R.J. Lamb for reviewing the manuscript, and Mrs. Marian Smith for providing us with the valuable unpublished data of the late Dr. L.B. Smith on the life history of C. ferrugineus. REFERENCES Bishop, G.W., 1959. The comparative bionomics of American Cryptolestes (ColeopteraCucujidae) that infest stored grain. Ann. Entomol. Soc. Am., 52: 657-665. Campbell, A. and Sinha, R.N., 1978. Bioenergetics of granivorous beetles, Cryptolestes ferrugineus and Rhyzopertha dominica (Coleoptera: Cucujidae and Bostrichidae). Can. J. Zool., 56: 624-633. Cotton, R.T., 1963. Pests of stored grain and grain products. Burgess, Minneapolis, MN, 318 PP. Cuff, W.R. and Hardman, J.M., 1980. A development of the Leslie matrix formulation for restructuring and extending an ecosystem model: the infestation of stored wheat by Sitophilus oryzae. Ecol. Modelling, 9: 281-305. Evans, D.E., 1983. The influence of relative humidity and thermal acclimation on the survival of adult grain beetles in cooled grain. J. Stored Prod. Res., 19: 173-180. Evans, D.E., 1987. The survival of immature grain beetles at low temperatures. J. Stored Prod. Res., 23: 79-83.

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Freeman, J.A., 1952. Laemophloeus spp. as major pests of stored grain. Plant Pathol., 1: 69-76. Hardman, J.M., 1978. A logistic model simulating environmental changes associated with the growth of populations of rice weevils, Sitophilus oryzae, reared in small cells of wheat. J. Appl. Ecol., 15: 65-87. Howe, R.W., 1965. A summary of estimates of optimal and minimal conditions for population increase of some stored products insects. J. Stored Prod. Res., 1: 177-184. Longstaff, B.C. and Cuff, W.R., 1984. An ecosystem model of the infestation of stored wheat by Sitophilus oryzae: a reappraisal. Ecol. Modelling, 25: 97-119. Metzger, J.F. and Muir, W.E., 1983. Computer model of two-dimensional conduction and forced convection in stored grain. Can. Agric. Eng., 25: 119-125. Rilett, R.O., 1949. The biology of Laemophloeus ferrugineus (Steph.). Can. J. Res. Sect. D Zool. Sci., 27: 112-148. SAS, 1985. SAS* User's Guide: Statistics, Version 5. SAS Institute Inc., Cary, NC, 956 pp. Schoolfield, R.M., Sharpe, P.J.H. and Magnuson, C.E., 1981. Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. J. Theor. Biol., 88: 719-731. Sharpe, P.J.H. and DeMichele, D.W., 1977. Reaction kinetics of poikilotherm development. J. Theor. Biol., 64: 649-670. Sinha, R.N., 1961. Insects and mites associated w~th hot spots in farm stored grain. Can. Entomol., 93: 609-621. Sinha, R.N., 1965. Development of Cryptolestes ferrugineus (Stephens) and Oryzaephilus mercator (Fauvel.) on seed-borne fungi. Entomol. Exp. Appl., 8: 309-313. Sinha, R.N., 1973. Ecology of storage. Ann. Technol. Agric. Paris, 22: 351-369. Sinha, R.N. and Wallace, H.A.H., 1966. Ecology of insect-induced hot spots in stored grain in Western Canada. Res. Popul. Ecol. Kyoto, 8: 107-132. Sinha, R.N. and Watters, F.L., 1985. Insect pests of flour mills, grain elevators, and feed mills and their control. Pub1. 1776. Research Branch, Agriculture Canada, Ottawa, Ont., 290 pp. Smith, L.B., 1962. Observations on the oviposition rate of the rusty grain beetle, Cryptolestes ferrugineus (Steph.) (Coleoptera: Cucujidae). Ann. Entomol. Soc. Am., 55: 77-82. Smith, L.B., 1963. The effect of temperature and humidity on the oviposition of the rusty grain beetle, Cryptolestes ferrugineus (Steph.). Proc. N. Cent. Branch Entomol. Soc. Am., 18: 74-76. Smith, L.B., 1965. The intrinsic rate of natural increase of Cryptolestes ferrugineus (Stephens) (Coleoptera, Cucujidae). J. Stored Prod. Res., 1: 35-49. Smith, L.B., 1966. Effect of crowding on oviposition, development and mortality of Cryptolestes ferrugineus (Stephens) (Coleoptera, Cucujidae). J. Stored Prod. Res., 2: 91-104. Smith, L.B., 1970. Effects of cold-acclimation on supercooling and survival of the rusty grain beetle, Cryptolestes ferrugineus (Stephens) (Coleoptera: Cucujidae), at subzero temperatures. Can. J. Zool., 48: 853-858. Smith, L.B., 1980. Relationship between grain drying and mortality of some stored grain insects. Proc. Entomol. Soc. Man., 36: 11-12. Solomon, M.E. and Adamson, B.E., 1955. The powers of survival of storage and domestic pests under winter conditions in Britain. Bull. Entomol. Res., 46: 311-355, Plates 11-12. Thorpe, G.R., Cuff, W.R. and Longstaff, B.C., 1982. Control of Sitophilus oryzae infestation of stored wheat: an ecosystem model of the use of aeration. Ecol. Modelling, 15: 331-351. Wagner, T.L., Wu, H., Sharpe, P.J.H., Schoolfield, R.M. and Coulson, R.N., 1984. Modeling insect development rates: a literature review and appfication of a biophysical model. Ann. Entomol. Soc. Am., 77: 208-225.

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Weibull, W., 1951. A statistical distribution function of wide applicability. J. Appl. Mech., 18: 293-297. Yaciuk, G., Muir, W.E. and Sinha, R.N., 1975. A simulation model of temperatures in stored grain. J. Agric. Eng. Res., 20: 245-258. Yang, R.C., Kozak, A. and Smith, J.H.G., 1978. The potential of Weibull-type functions as flexible growth curves. Can. J. For. Res., 8: 424-431. APPENDIX C FILE

F E R R U G . F O R -- R U S T Y GRAIN B E E T L E M O D E L C C S I M U L A T I O N M O D E L OF R U S T Y G R A I N BEETLE, C R Y P T O L E S T E S F E R R U G I N E U S (STEPHENS) C (COLEOPTERA, CUCUJIDAE), P O P U L A T I O N IN S T O R E D WHEAT. C C P R O G R A M M E D BY: S. WOODS, D E C E M B E R 1987, R E V I S E D D E C E M B E R 1988. C LANGUAGE: VAX F O R T R A N V4.6 C C THE F O L L O W I N G ARE R E Q U I R E D FOR R U N N I N G T H I S PROGRAM: C C SUBROUTINES: SETUP (TO SET I N I T I A L CONDITIONS, P A R A M E T E R S FOR R U N N I N G THE MODEL, A N D O U T P U T OPTIONS) C (TO INPUT T E M P E R A T U R E S A N D R E L A T I V E H U M I D I T I E S ) C ENVIN C PSTEP (TO P R I N T OUTPUT) C FUNCTIONS: Y ( D E V E L O P M E N T RATE) (MORTALITY -- P A R T I A L M O R T A L I T Y FOR ADULTS) C UMORT C OVIMOD ( A G E - I N D E P E N D E N T O V I P O S I T I O N FACTOR) C OVIP (ACTUAL O V I P O S I T I O N P E R FEMALE) C ADSURV (ADULT S U R V I V A L RATE) C P A R A M E T E R FILE: FERRUG.PAR C C C O N T E N T S OF FILE F E R R U G . P A R -- P A R A M E T E R S FOR F E R R U G . F O R C P A R A M E T E R (MAXCOH=2000) C P A R A M E T E R (MAXTIMI2000) C PARAMETER (IEGG=I,IIMMAT=2,IADULT=3) C P A R A M E T E R (NSTAGE=3) C P A R A M E T E R (PCOLL=-21.2D0) C P A R A M E T E R (PCOLH=65.0D0) C PARAMETER (PROPF=0.57087D0) C PARAMETER (PROPFINV=I.0D0/PROPF) C ******************************************************************************* IMPLICIT DOUBLE PRECISION INCLUDE 'FERRUG.PAR/LIST' C C C C C C C C C C

(A-H,O-Z)

FIRST 4 A R R A Y S H O L D C O U N T (INSECT C O U N T PER A F F E C T S A D U L T M O R T A L I T Y ) , A N D STAGE OF E A C H O V I P O S I T I O N RATE. NEXT 2 ARRAYS HOLD TEMPERATURE AND HUMIDITY LAST 2 A R R A Y S H O L D M O R T A L I T Y A N D D E V E L O P M E N T IMMATURE OR ADULT), C A L C U L A T E D AT E A C H T I M E

KG OF WHEAT), AGE, STRESS (WHICH COHORT. A D U L T AGE A F F E C T S VALUES RATES STEP.

FOR E A C H T I M E INTERVAL. FOR E A C H STAGE (EGG,

FOR THE A D U L T STAGE, FEMALE COUNTS A R E U S E D INTERNALLY. BY P R O P F I N V TO GET T O T A L A D U L T COUNT F O R P R I N T I N G ONLY. DIMENSION COUNTS(MAXCOH),AGES(MAXCOH),STRESS(MAXCOH) DIMENSION ISTAGE(MAXCOH) DIMENSION TEMP(MAXTIM),HUMID(MAXTIM) DIMENSION STMORT(NSTAGE),STY(NSTAGE)

THEY ARE MULTIPLIED

C C INPUT INITIAL CONDITIONS, O U T P U T O P T I O N S A N D E N V I R O N M E N T A L F A C T O R S CALL SETUP(NDAYS,STEP,NSTEP,NCOH,COUNTS,AGES,STRESS,ISTAGE, 1 NPSTEP,IOPT) CALL E N V I N ( N S T E P , S T E P , T E M P , H U M I D ) T=TEMP(1) W=HUMID(1) CALL PSTEP(0,STEP,NCOH,COUNTS,AGES,STRESS,ISTAGE,0,0,0,T,W,IOPT) C C M A I N L O O P I T E R A T E D O N C E FOR E A C H T I M E STEP DO I S T E P = I , N S T E P

A N D PRINT.

P O P U L A T I O N D Y N A M I C S O F CRYPTOLESTES F E R R U G I N E U S IN STORED W H E A T

1

T=TEMP(ISTEP) W=HUMID(ISTEP) IF ( ( T . L E . P C O L L ) . O R . ( T . G E . P C O L H ) ) THEN NCOH=0 ! P O P U L A T I O N C O L L A P S E AT E X T R E M E T E M P E R A T U R E S . CALL P S T E P ( 0 , S T E P , N C O H , C O U N T S , A G E S , S T R E S S , I S T A G E , 0 , 0 , 0 , T , W , IOPT) STOP END IF CEGG=0. ! COUNT N E W EGGS P R O D U C E D IN T I M E STEP

C C C O M P U T E F E M A L E D E N S I T Y (DENS) A N D L A R V A L D E N S I T Y (DLARV) FOR TIME STEP DENS=0. DLARV=0. DO I C O H = I , N C O H IF ( I S T A G E ( I C O H ) . E Q . I A D U L T ) THEN DENS=DENS+COUNTS(ICOH) ELSE IF ( I S T A G E ( I C O H ) . E Q . I I M M A T ) THEN DLARV=DLARV+COUNTS(ICOH) END IF END DO DENS=DENS*.001D0 ! DENS = F E M A L E D E N S I T Y / G R A M OF W H E A T DLARV=DLARV*.001D0 ! D L A R V = I M M A T U R E D E N S I T Y / G R A M OF W H E A T C C C O M P U T E D E A T H RATE (STMORT) A N D D E V E L O P M E N T (STY) BY STAGE, A N D C M O D I F I C A T I O N FACTOR (OMOD) FOR O V I P O S I T I O N , FOR THE TIME STEP DO J S T A G E = I , N S T A G E STMORT(JSTAGE)=UMORT(JSTAGE,T,W,DLARV) STY(JSTAGE)=Y(JSTAGE,T,W) END DO OMOD=OVIMOD(T,W,DENS) C C INNER L O O P I T E R A T E D ONCE FOR E A C H COHORT: GET OLD I N F O R M A T I O N F R O M THE C ARRAYS, C O M P U T E N E W V A L U E S A N D U P D A T E THE ARRAYS. FALL T H R O U G H THE L O O P C IF THE COUNT IS 0. DO I C O H = I , N C O H COUNT=COUNTS(ICOH) ! GET OLD I N F O R M A T I O N FOR THIS C O H O R T IF (COUNT.GT.0.D0) T H E N AGEOLD=AGES(ICOH) JSTAGE=ISTAGE(ICOH) C AGENEW=AGEOLD+STEP*STY(JSTAGE) ! COMPUTE NEW VALUES C C S U B D I V I D E STEP IF STAGE C H A N G E S (EGG TO I M M A T U R E OR I M M A T U R E TO ADULT) IF ( ( A G E N E W . G E . I . D 0 ) . A N D . ( J S T A G E . L T . I A D U L T ) ) THEN STEPI=STEP*(I.D0-AGEOLD)/(AGENEW-AGEOLD) COUNT=COUNT*EXP(-STMORT(JSTAGE)*STEPI) STEPI=STEP-STEPI JSTAGE=JSTAGE+I IF ( J S T A G E . E Q . I A D U L T ) T H E N COUNT=PROPF*COUNT STRESS(ICOH)=0.D0 END IF AGEOLD=0.D0 AGENEW=STEPI*STY(JSTAGE) ELSE STEPI=STEP END IF ISTAGE(ICOH)=JSTAGE AGES(ICOH)=AGENEW IF ( J S T A G E . N E . I A D U L T ) T H E N COUNTS(ICOH)=COUNT*EXP(-STMORT(JSTAGE)*STEPI) ELSE C C U P D A T E N E W EGG COUNT A N D C O H O R T C O U N T FOR A D U L T S CEGG=CEGG+COUNT*OVIP(AGEOLD,AGENEW,OMOD) STRESSOLD=STRESS(ICOH) STRESS(ICOH)=STRESSOLD+STEPI*STMORT(IADULT) COUNTS(ICOH)=COUNT* 1 ADSURV(STRESSOLD,STRESS(ICOH)) END IF END IF END DO ! END OF INNER L O O P IF (CEGG.GT.0.) T H E N

155

156

H. I~,WAMOTO ET A L

NCOH=NCOH+I COUNTS(NCOH)=CEGG AGES(NCOH)=0.D0 ISTAGE(NCOH)=IEGG END IF C C PRINT O U T P U T FOR T H I S STEP IF R E Q U E S T E D IF ( M O D ( I S T E P , N P S T E P ) . E Q . 0 . O R . I S T E P . E Q . N S T E P ) i CALL P S T E P ( I S T E P , S T E P , N C O H , C O U N T S , A G E S , S T R E S S , I S T A G E , S T M O R T , 2 STY,OMOD,T,W,IOPT) END DO ! END OF M A I N L O O P STOP END C C FUNCTION Y(STAGE,TEMPERATURE,HUMIDITY) R E T U R N S D E V E L O P M E N T RATE. FUNCTION Y(JSTAGE,T,W) I M P L I C I T D O U B L E P R E C I S I O N (A-H,O-Z) INCLUDE 'FERRUG.PAR/NOLIST' PARAMETER (PEGG=.016875149D0,TTEGG=I5.2854176D0) P A R A M E T E R (TTAD=I6.5717D0) C P A R A M E T E R S FOR D E V E L O P M E N T AT I M M A T U R E S T A G E S P A R A M E T E R (TK0=273.15D0) ! 0 D E G C = 273.15 D E G K PARAMETER (TA=25.D0,TL=I9.82D0,TH=30.5D0) ! T H R E S H O L D T E M P S (C) PARAMETER (PA=24959.D0/I.987D0,PL=-47324.D0/I.987D0) PARAMETER PH=34960.D0/I.987D0 P A R A M E T E R (PT=.04128D0) PARAMETER (PW=-.01397D0,WD=75.D0) PARAMETER (TKA=TK0+TA,TKL=TK0+TL,TKH=TK0+TH) ! T H R E S H O L D T E M P S (K) PARAMETER (PTKA=PA/TKA,PTKL=PL/TKL,PTKH=PH/TKH) C IF ( J S T A G E . E Q . I I M M A T ) T H E N TK=T+TK0 ! KELVIN TEMPERATURE TKINV=I.D0/TK FA=EXP(PTKA*(T-TA)*TKINV) ! FA=EXP(PA*(I/TKA-I/TK)) FL=EXP(PTKL*(T-TL)*TKINV) FH=EXP(PTKH*(T-TH)*TKINV)

Y=PT*(TK/TKA)*FA/(I.DO+FL+FH) IF (W.LT.WD) Y = Y * E X P ( P W * ( W D - W ) ) ELSE Y=0.D0 IF (JSTAGE.EQ.IEGG) T H E N IF (T.GT.35.D0) T H E N Y=PEGG*(35.D0-TTEGG) ELSE IF (T.GT.TTEGG) T H E N Y=PEGG*(T-TTEGG) END IF ELSE IF (T.GT.TTAD) Y = T - T T A D END IF END IF RETURN END C C F U N C T I O N UMORT R E T U R N S THE D A I L Y M O R T A L I T Y R A T E FOR E G G A N D I M M A T U R E C FOR ADULTS, IT R E T U R N S O N L Y THE M O R T A L I T Y R A T E DUE TO T E M P E R A T U R E . FUNCTION UMORT(JSTAGE,T,W,DLARV) I M P L I C I T D O U B L E P R E C I S I O N (A-H,O-Z) INCLUDE 'FERRUG.PAR/NOLIST' PARAMETER (BE=.015D0,BI=.005D0) PARAMETER (UHE=.0344D0,UHI=.0192D0) PAP~AMETER ( T H E = 3 4 . 9 7 D 0 , T H I = 3 7 . 2 6 D 0 ) PARAMETER (UDE=.0174D0,UDI=.01758D0) PARAMETER (WDE=50.D0,WDI=50.D0) PARAMETER (UL=.02D0,TL=5.D0) PARAMETER (TDENSI=I5.D0,ADENSI=.008741D0) PARAMETER (BIA=-36.09842D0,B2A=8579.987581D0) PARAMETER (B3A=I01.29999D0,B4A=-32867.09380D0) IF (JSTAGE.EQ.IEGG) T H E N UMORT=BE IF (T.GT.THE) T H E N UMORT=UMORT+UHE*(T-THE)

STAGES.

POPULATION

DYNAMICS

OF CRYPTOLESTES

FERRUGINEUS

IN STORED WHEAT

157

E L S E IF (T.LT.TL) T H E N UMORT=UMORT+UL END IF IF (W.LT.WDE) U M O R T = U M O R T + U D E * ( W D E - W ) E L S E IF ( J S T A G E . E Q . I I M M A T ) T H E N UMORT=BI IF (T.GT.THI) T H E N UMORT=UMORT+UHI*(T-THI) ELSE IF (T.LT.TL) T H E N UMORT=UMORT+UL END IF IF (W.LT.WDI) U M O R T = U M O R T + U D I * ( W D I - W ) IF (T.GT.TDENSI) U M O R T = U M O R T + A D E N S I * D L A R V ELSE TKI=I.D0/(273.15D0+T) UMORT=EXP(BIA+B2A*TKI)+EXP(B3A+B4A*TKI) E N D IF RETURN END C C FUNCTION ADSURV(STRESSOLD,STRESSNEW) R E T U R N S A D U L T S U R V I V A L FOR STEP. FUNCTION ADSURV(STRESSOLD,STRESSNEW) I M P L I C I T D O U B L E P R E C I S I O N (A-H,O-Z) INCLUDE 'FERRUG.PAR/NOLIST' PARAMETER CC=3.106985449D0 X=STRESSOLD**CC-STRESSNEW**CC ADSURV=EXP(X) RETURN END C C F U N C T I O N O V I P R E T U R N S A C T U A L O V I P O S I T I O N P E R FEMALE. FUNCTION OVIP(AGEOLD,AGENEW,OMOD) I M P L I C I T D O U B L E P R E C I S I O N (A-H,O-Z) INCLUDE 'FERRUG.PAR/NOLIST' PARAMETER(POINV=I.D0/980.6912D0,CO=I.25674D0) OVIP=OMOD*(EXP(-(POINV*AGEOLD)**CO)-EXP(-(POINV*AGENEW)**CO)) RETURN END C C FUNCTION OVIMOD(TEMPERATURE,HUMIDITY,FEMALE DENSITY) R E T U R N S THE C A G E - I N D E P E N D E N T O V I P O S I T I O N F A C T O R PER FEMALE. FUNCTION 0VIMOD(T,W,DENS) I M P L I C I T D O U B L E P R E C I S I O N (A-H,O-Z) INCLUDE 'FERRUG.PAR/NOLIST' PARAMETER(TEGG=686.923D0) PARAMETER(PL=0.229167D0,TL=29.4D0) PARAMETER(PH=0.286331D0,TH=35.0D0) PARAMETER(PD=I.815D-3,TD=22.5D0) PARAMETER(PC=0.519738D0) XMOD=0. IF (T.LT.TL) X M O D = X M O D + P L * ( T - T L ) IF (T.GT.TH) X M O D = X M O D + P H * ( T H - T ) IF (T.GT.TD) X M O D = X M O D + P D * ( 1 0 0 . D 0 - W ) * ( T D - T ) XOVIP=TEGG*EXP(XMOD) IF (DENS.GT.I.D0) X O V I P = X O V I P * D E N S * * ( - P C ) OVIMOD=XOVIP RETURN END C THE F O L L O W I N G S U B R O U T I N E S H A V E B E E N M O V E D TO A S E P A R A T E FILE F E R R U G S U B S . F O R . C (LISTING HAS B E E N O M I T T E D B E C A U S E T H E Y W I L L C H A N G E D E P E N D I N G ON H O W C E N V I R O N M E N T A L F A C T O R S ARE TO BE M O D E L L E D A N D W H A T O U T P U T IS REQUIRED.) C C S U B R O U T I N E SETUP SETS I N I T I A L C O N D I T I O N S , P A R A M E T E R S FOR R U N N I N G THE M O D E L C (STEP, NDAYS) A N D O U T P U T O P T I O N S C C S U B R O U T I N E E N V I N INPUTS T E M P E R A T U R E S A N D R E L A T I V E H U M I D I T I E S C C S U B R O U T I N E PSTEP P R I N T S O U T P U T AT S E L E C T E D T I M E I N T E R V A L S C INCLUDE ' F E R R U G S U B S . F O R / L I S T '