Relationship Between Temperature and Developmental Rate Of

BIOLOGICAL CONTROL Relationship Between Temperature and Developmental Rate of Stethorus punctillum (Coleoptera: Coccinellidae) and Its Prey Tetranychus mcdanieli (Acarina: Tetranychidae)

1 2 3 MICHE` LE ROY, JACQUES BRODEUR, AND CONRAD CLOUTIER

Environ. Entomol. 31(1): 177Ð187 (2002) ABSTRACT Temperature affects insect and mite development, allowing species-speciÞc traits including optimal temperature and low and high temperature thresholds to be observed. Development rate models and biological parameters estimated from them can help determining if synchrony exists between pests and natural enemies. We studied development of the coccinellid Stethorus punctillum Weise and the spider mite Tetranychus mcdanieli McGregor at 12 constant temperatures ranging 10Ð38ЊC(Ϯ0.5ЊC), and modeled their development rates as a function of temperature. This predator- prey complex is typical of red raspberry, Rubus idaeus L., in Quebec, which is characterized by a short season. Eleven published models were compared for accuracy in predicting development rate of all stages of both species, and estimating their temperature thresholds and optima. The spider mite developed to the adult stage in the 14Ð36ЊC range, compared with 14Ð34ЊC for the coccinellid. Males and females did not differ, and the development rates steadily increased from 14 to 30ЊC, leveling off in the range 34Ð36ЊC for the spider mite, or 30Ð32ЊC for its predator. Most models were rejected for failure to satisfy criteria of goodness-of-Þt and estimable temperature threshold parameters. The Lactin-2 model for T. mcdanieli and the Brie`re-1 model for S. punctillum, were superior at estimating low temperature threshold, which is critical where temperatures are frequently low in the spring, and were separately Þtted to all development stages of both organisms. Based on the predictable early spring development of S. punctillum and T. mcdanieli, the results indicate potential synchrony between them.

KEY WORDS Tetranychus mcdanieli, Stethorus punctillum, developmental rate, temperature, nonlinear models, predator-prey synchrony

KNOWLEDGE OF INSECT and mite adaptations to climatic arthropods, such that low and high temperature conditions plays an essential role in pest management, thresholds, and optimal temperature can be estimated speciÞcally in helping to predict the timing of devel- for all major life processes. Natural enemies and their opment, reproduction, and dormancy or migration host/prey may have different thermal limits and ef- (Nechols et al.1999). In biological control, details con- fective temperature range for survival, development, cerning such responses are useful to select natural reproduction, and mobility. Thermal characteristics enemies that are best adapted to conditions favoring may vary between species (Frazer and McGregor target pests (Rosen and Huffaker 1983, Obrycki and 1992, Honek 1996), populations (Campbell et al. 1974, Kring 1998). Biological control, whether using the Lee and Elliott 1998), developmental stages (Honek introduction, conservation or augmentation ap- and Kocourek 1988), and with other ecological factors proaches, is facilitated when the climatic responses of such as food source (Gilbert and Raworth 1996). biocontrol agents are known, especially temperature. Temperature also acts as a driver of arthropod life Temperature is a critical abiotic factor inßuencing processes, where within a speciÞc range, a tempera- the dynamics of mite and insect pests and their natural ture change results in a proportional increase or de- enemies (Huffaker et al. 1999 and references herein). crease of the rate of any given process (Cossins and Temperature sets the limits of biological activity in Bowler 1987). This effect of temperature can be described by speciÞc rate functions of temperature for survival, reproduction, population growth, and devel- 1 Direction des Services Technologiques, Ministe`re de lÕAgriculture, des Peˆcheries et de lÕAlimentation du Que´bec, 2700 rue opment, which are used in predicting natural enemy Einstein, Sainte-Foy, QC, Canada G1P 3W8. interactions with pests (Jervis and Copland 1996). 2 De´partement de Phytologie, Centre de Recherche en Horticul- Developmental rate, expressed as the reciprocal of ture, Universite´ Laval, Sainte-Foy, QC, Canada G1K 7P4. time taken to change from one stage to another 3 Corresponding author: De´partement de Biologie, Centre de Re- cherche en Horticulture, Universite´ Laval, Sainte-Foy, QC, Canada (Cossins and Bowler 1987), is nil at the low temper- G1K 7P4 (e-mail: [email protected]). ature threshold, increases with temperature and levels

0046-225X/02/0177Ð0187$02.00/0 ᭧ 2002 Entomological Society of America 178 ENVIRONMENTAL ENTOMOLOGY Vol. 31, no. 1 off at the optimum, and then decreases rapidly as the related biological parameters of S. punctillum and T. high threshold is approached. This relationship is cur- mcdanieli. Although temperature is only one of the vilinear near extremes, but approximately linear at ecological factors in predator-prey dynamics, its moderate temperatures (Wagner et al. 1984). A vari- strong effects on development is particularly impor- ety of rate functions or models have been proposed to tant in affecting generation time and thus evaluating describe the relationship between temperature and the ability of a predator to track a prey population over arthropod development (Logan et al. 1976, Sharpe and several generations by its numerical response. DeMichele 1977, Wagner et al. 1984, Lamb 1992, Lac- tin et al. 1995, Briere et al. 1999). They vary with ` Materials and Methods respect to parameter number and basic assumptions about temperature effects near lower and upper limits Rearing Methods and Experimental Conditions. (see appendix). Temperature-driven rate models are Experiments were conducted in 1994 and 1995 in Con- most often used to predict the activity and seasonal viron PGR15 (Controlled Environment, Winnipeg) population dynamics of pests and natural enemies in growth chambers. Tetranychus mcdanieli and S. punc- Þeld situations (Frazer and McGregor 1992, Lamb tillum were originally collected in 1993 from a rasp- 1992, Brie`re and Pracros 1998) but they also help berry Þeld near Quebec City, Canada (46Њ 59Ј N, 71Њ determining suitable conditions for mass rearing of 29Ј W). The ensuing colonies of T. mcdanieli and S. natural enemies (Rodriguez-Saona and Miller 1999). punctillum were maintained on red raspberry, Rubus Distributed throughout North America, the Mc- idaeus L. ÔKillarneyÕ, and European cucumber, Daniel spider mite, Tetranychus mcdanieli McGregor ÔThompsonÕ at 24ЊC and a photoperiod of 16:8 (L:D) is the most important tetranychid pest of red raspberry h. Voucher specimens are preserved in the insect in Quebec (Roy et al. 1999), where it damages fruiting collection of the Ministe`re de lÕAgriculture, des Peˆch- canes in late spring to midsummer, and primocanes in eries et de lÕAlimentation du Que´bec, Sainte-Foy, late summer to early fall. Prolonged susceptibility to Que´bec. Temperature and relative humidity in each damage implies season-long spider mite control, growth chamber were recorded continuously with an which is not provided by current acaricides (Roy et al. integrated data logger. 1999). Alternative controls are needed to develop an Experimental arenas consisted of 2.0-cm-diameter integrated control program emphasizing biological raspberry leaf disks placed upside down on submerged control. In other horticultural crops including al- cotton wool in individual 5.0-cm-diameter petri monds, apples, citrus and strawberries, spider mite dishes. The dishes were covered with lids ventilated biocontrol is achieved by managing phytoseiid mite or with a 1.0 mm mesh. Spider mites and coccinellids Stethorus coccinellid predators (Tanigoshi et al. 1983, were individually handled with a small brush. Obser- Hoy 1985, McMurtry 1985, van de Vrie 1985, Kogan et vations were made with a stereomicroscope under a al. 1999). cold light source. In a recent study aiming to identify natural enemies Development and Survivorship of Immatures. To of the McDaniel spider mite, the coccinellid S. punc- obtain synchronized eggs, spider mite or coccinellid tillum Weise, a palearctic species inadvertently estab- females were incubated at 25ЊC on raspberry leaf discs lished in eastern Canada (Putnam 1955), was an im- for 5 h. Newly laid eggs of S. punctillum and T. mc- portant predator in raspberries (Roy et al. 1999). As danieli were then placed individually on leaf disks. specialist predators, Stethorus spp. can effectively con- Upon hatching, S. punctillum larvae were fed with trol spider mite populations, as shown for S. punctillum excess (Ϸ300) T. mcdanieli of various stages. Insects on cotton and vineyards in Europe (Kapur 1948) and and mites were placed in growth chambers pro- citrus in Japan (Yang et al. 1996); S. punctum punctum grammed to control temperature at 10, 12, 14, 16, 20, LeConte on apple in USA (Hull 1977); and S. punctum 24, 28, 30, 32, 34, 36, or 38 Ϯ 0.5ЊC, which covered the picipes Casey on avocado in the USA (McMurtry and full range of constant temperatures allowing complete Johnson 1966, Tanigoshi 1973). The key biological development of both species. The ambient relative attributes of S. punctillum as a spider mite predator humidity alternated between 45 and 65% during the have rarely been studied, and its potential against T. light and dark cycles, respectively. Fluorescent lamps mcdanieli is unknown. yielding 175 ␮ EsϪ1 mϪ2 within each chamber pro- The objective of this study was to develop knowl- vided a 16-h daily photophase. Sixty individuals were edge of the thermal characteristics of populations of S. tested per temperature regime. punctillum and its prey T. mcdanieli collected in Que- Progress in development and survival was assessed bec, as a prerequisite to developing a biological con- every 3 to 12 h, depending on the temperature. For trol program in raspberry. The development rate of all calculation purposes, events were assumed to have stages of both species was measured at 12 constant occurred at the midpoint between two consecutive temperatures ranging 10Ð38ЊC, thus spanning the ex- observations. Fresh leaf disks were provided every 2 or pected Þeld conditions during a typical raspberry- 3 d, until maturity was reached. The survival rate and growing season in southern Quebec. With the data at duration were obtained for all immature stages. After hand, we tested 11 temperature-driven rate models hatching, T. mcdanieli develops through larva, pro- chosen among the most commonly used, and com- tonymph and deutonymph stages, with a terminal pe- pared them not only with respect to accuracy at pre- riod of quiescence called protochrysalis, deutochrysa- dicting the development rate, but also at estimating lis, and teleiochrysalis, respectively; and S. punctillum February 2002 ROY ET AL.: T. mcdanieli AND S. punctillum DEVELOPMENT MODELS 179

Table 1. Capacity of 11 developmental rate models to estimate three important biological parameters, and speciﬁc method of estimation when applicable

Model Low temp threshold Optimal temp High temp threshold Linear x at y ϭ 0 Ñ Ñ Logan-6 Ñ TLÑ⌬T TL Logan-10 Ñ TL-⌬T TL Sharpe and DeMichele Ñ x at dy/dx ϭ 0Ñ Taylor Ñ Tm Ñ a Lamb Ñ Tm Ñ Hilbert and Logan T0 TL-⌬T TL Lactin-1 Ñ TL-⌬T TL Lactin-2 x at y ϭ 0TL-⌬T TL Brie`re-1 T0 x at dy/dx ϭ 0TL Brie`re-2 T0 x at dy/dx ϭ 0TL

a Lamb (1992) proposed a replacement for low temperature threshold deÞned as the temperature at which the developmental rate is 8% of the maximum developmental rate, but this parameter does not estimate developmental threshold in absolute terms. developed through four larval stages, and the pupal model (1977), all nonlinear models have parameters stage. The sex of each adult was determined. that can be interpreted graphically, which is useful to Developmental Rate Models. Description of Models. allow initial parameter estimation (Brie`re et al. 1999). We compared the performance of one linear and 10 For the degree-day linear model, the developmental nonlinear developmental rate models, chosen because rate was regressed against temperature using a least they are the most commonly used for that purpose. squares linear regression (Draper and Smith 1998). The nonlinear models were two by Logan et al. (1976), Depending on the model, the biological parameters one by Taylor (1981), one by Sharpe and DeMichele were either directly estimated, derived from other (1977), one by Hilbert and Logan (1983), one by parameters within the model, or they were obtained Lamb (Lamb et al. 1984, Lamb 1992), two by Lactin et from the value of x at y ϭ 0 or the value of x at dy/dx ϭ al. (1995) and two by Brie`re et al. (1999). These models are described in more details in the Appendix. Criteria of Model Selection. The following criteria were used to assess the performance of each model: (1) The model should describe the data accurately. Two statistics were used to evaluate accuracy: the adjusted coefÞcient of determination (R2), and the residual sum of squares (RSS), which provide com- plementary information on goodness-of-Þt and usefulness for predicting observations (Draper and Smith 1998). (2) The model should allow estimation of parameters with biological signiÞcance (Brie`re et al. 1999). For development, the key biological parameters needed are the low temperature threshold, optimal temperature and high temperature threshold, as de- Þned previously. In the context of our study of organisms developing in cool temperate regions, a useful model preferably should provide a low temperature threshold estimate. Statistical Methods. For each species, differences among sexes for developmental times at various constant temperatures were tested for signiÞcance by analysis of variance (ANOVA) using the general linear model procedure of SAS (SAS Institute 1989). For each stage developmental time variation with temperature was conÞrmed by regression using the exponential model y ϭ a ϩ be(-T/c) (SAS Institute 1989). Then, the means of reciprocals of developmental time for each stage, and at each temperature, were used to Þt the developmental rate models. The curves were Þtted by iterative nonlinear regression based on the Mar- quardt algorithm (SAS Institute 1989) on mean developmental rates weighted by sample size (n- Fig. 1. Effect of temperature on survival from egg to weighed). Except for the Sharpe and DeMichele adult (%) of Tetranychus mcdanieli and Stethorus punctillum. 180 ENVIRONMENTAL ENTOMOLOGY Vol. 31, no. 1

Table 2. Developmental time (d ؎ SE) of immature stages of T. mcdanieli at 11 constant temperatures

Temp, ЊC Egg Larva Protonymph Deutonymph Total Immature 12 25.3 Ϯ 0.3 Ñ Ñ Ñ Ñ 14 17.1 Ϯ 0.9 8.2 Ϯ 1.7 6.7 Ϯ 1.5 7.0 Ϯ 0.6 39.0 Ϯ 3.9 16 12.0 Ϯ 0.4 6.0 Ϯ 0.7 4.8 Ϯ 0.6 6.0 Ϯ 0.7 28.8 Ϯ 1.2 20 6.9 Ϯ 0.4 3.1 Ϯ 0.5 2.8 Ϯ 0.4 3.4 Ϯ 0.5 16.3 Ϯ 1.0 24 4.0 Ϯ 0.2 2.4 Ϯ 0.4 2.0 Ϯ 0.4 2.3 Ϯ 0.3 11.1 Ϯ 0.8 28 3.1 Ϯ 0.1 1.5 Ϯ 0.3 1.3 Ϯ 0.3 1.7 Ϯ 0.4 7.6 Ϯ 0.9 30 2.7 Ϯ 0.1 1.2 Ϯ 0.2 0.9 Ϯ 0.1 1.4 Ϯ 0.2 6.3 Ϯ 0.4 32 2.5 Ϯ 0.1 1.2 Ϯ 0.3 1.2 Ϯ 0.3 1.6 Ϯ 0.4 6.5 Ϯ 0.8 34 2.3 Ϯ 0.1 1.1 Ϯ 0.2 0.9 Ϯ 0.1 1.2 Ϯ 0.2 5.5 Ϯ 0.3 36 2.3 Ϯ 0.1 1.2 Ϯ 0.2 0.9 Ϯ 0.2 1.1 Ϯ 0.2 5.5 Ϯ 0.3 38 2.6 Ϯ 0.2 1.7 Ϯ 0.0 Ñ Ñ Ñ

n ϭ 60 at experiment initiation; a dash indicates mortality or arrested development; the exponential regression y ϭ a ϩ be(ϪT/c) was Þtted to each stage (r2 ϭ 0.99 and P Ͻ 0.0001 in all cases).

0 (Table 1). In the latter two cases the variance of off, following the exponential model. In the range these parameters was obtained by the Delta method 14Ð36ЊC, the length of the egg stage averaged 42% of (Agresti 1990). The maximum likelihood ratio test total. (Lehmann 1994) was applied to determine whether or The development time of all stages of S. punctillum not the biological parameters differed among growth at eight constant temperatures is presented in Table 3. stages, and if observed values (midpoint between the General trends noted above for T. mcdanieli also apply two closest experimental temperatures) signiÞcantly to S. punctillum. In the range 14Ð34ЊC, the length of departed from model estimates. the egg stage was 28%, and the pupal stage was 23% of total development. Model Accuracy and Precision. For T. mcdanieli, the Results adjusted R2 varied between 0.76 and 0.98 (Table 4, Survival of Immatures. T. mcdanieli successfully because the R2 and RSS trends were similar to those developed to adult between 14 and 36ЊC, but failed at observed for total immature development, only the 10, 12, and 38ЊC. (Fig. 1). The optimal temperature for latter are presented). The linear, Taylor, Brie`re-1, immature survival ranged between 16 and 36ЊC. The Lactin-1 and Logan-6 models do not accurately pre- highest mortality occurred during the egg stage at dict the developmental rate of T. mcdanieli at tem- extreme temperatures (data not shown). Survival for peratures Ͻ 20 and Ͼ 30ЊC. Adding one parameter to all other stages between 14 and 36ЊC ranged from 71.4 the Logan-6, Lactin-1 and Brie`re-1 models, provides to 100%. for more accurate prediction. For example, the R2 Stethorus punctillum successfully developed to the value of the four-parameter Brie`re-2 model (0.98) is adult stage between 14ЊC and 34ЊC, but survival was substantially higher than the three-parameter Brie`re-1 low at both ends of the temperature range (Fig. 1). model (0.83). The optimal range for immature survival was between The Brie`re-2, Hilbert and Logan, Lactin-2, Logan- 16 and 32ЊC. Eggs failed to hatch at 12 and 36ЊC. Similar 10, and Lamb models all have adjusted R2 higher than to T. mcdanieli, S. punctillum mortality occurred 0.96 (Table 4), and also had the smallest RSS. There- mainly during the egg stage (data not shown). fore, with T. mcdanieli, the linear, Taylor, Sharpe and Development Time. ANOVA on development time DeMichele, Logan-6, Lactin-1, and Brie`re-1 models of both species at all temperatures revealed no differ- are rejected because they failed to meet the criterion ence between males and females (data not shown; P Ͼ for high model accuracy. 0.05), hence averages were computed using pooled For S. punctillum, the adjusted R2 ranged 0.84Ð0.99 data. Table 2 presents the average development times (Table 4). With R2 values below 0.97, the linear, Tay- of all stages of T. mcdanieli at 11 constant tempera- lor and Sharpe and DeMichele models were rejected. tures. The length of each stage decreased and levelled Contrary to T. mcdanieli, the addition of one param-

Table 3. Developmental time (d ؎ SE) of immature stages of S. punctillum fed on T. mcdanieli at eight constant temperatures

Temp, ЊC Egg 1st Instar 2nd Instar 3rd Instar 4th Instar Pupa Total immature 14 21.1 Ϯ 0.0 8.4 Ϯ 0.0 7.0 Ϯ 0.0 6.0 Ϯ 0.0 11.1 Ϯ 0.0 15.0 Ϯ 0.0 68.5 Ϯ 0.0 16 14.4 Ϯ 0.9 6.4 Ϯ 1.0 4.2 Ϯ 0.9 4.9 Ϯ 0.7 8.4 Ϯ 0.9 10.7 Ϯ 0.8 48.9 Ϯ 3.0 20 7.8 Ϯ 0.5 3.4 Ϯ 0.4 2.1 Ϯ 0.4 2.4 Ϯ 0.5 4.3 Ϯ 0.5 6.1 Ϯ 0.3 26.1 Ϯ 0.9 24 4.8 Ϯ 0.3 2.0 Ϯ 0.2 1.6 Ϯ 0.2 1.7 Ϯ 0.3 3.0 Ϯ 0.3 4.1 Ϯ 0.3 17.1 Ϯ 0.6 28 3.6 Ϯ 0.2 1.5 Ϯ 0.4 1.1 Ϯ 0.3 1.3 Ϯ 0.2 2.3 Ϯ 0.3 2.9 Ϯ 0.1 12.7 Ϯ 0.6 30 3.4 Ϯ 0.2 1.2 Ϯ 0.2 1.0 Ϯ 0.1 1.2 Ϯ 0.2 2.0 Ϯ 0.2 2.8 Ϯ 0.2 11.5 Ϯ 0.2 32 3.2 Ϯ 0.2 1.4 Ϯ 0.2 1.0 Ϯ 0.2 1.3 Ϯ 0.3 2.2 Ϯ 0.4 2.7 Ϯ 0.2 11.8 Ϯ 0.6 34 3.1 Ϯ 0.2 1.6 Ϯ 0.2 1.0 Ϯ 0.0 1.4 Ϯ 0.0 2.1 Ϯ 0.7 3.0 Ϯ 0.0 12.1 Ϯ 0.7

n ϭ 60 at experiment initiation; the exponential regression y ϭ aϩbe(ϪT/c) was Þtted to each stage (r2 ϭ 0.99 and P Ͻ 0.0001 in all cases). February 2002 ROY ET AL.: T. mcdanieli AND S. punctillum DEVELOPMENT MODELS 181

Table 4. Comparison of 11 developmental rate models based on the number of parameters (NPAR), the adjusted coefﬁcient of determination (R2), and the residual sum of squares (RSS) for predicting total immature development of T. mcdanieli and S. punctillum

Tetranychus mcdanieli Stethorus punctillum Model NPAR R2 RSS R2 RSS Linear 2 0.76643 0.00619 0.84468 0.00067 Logan-6 4 0.88410 0.00230 0.97173 0.00009 Logan-10 5 0.97744 0.00037 0.99215 0.00002 Sharpe and DeMichele 4a 0.93536 0.00124 0.93503 0.00020 Taylor 3 0.81881 0.00420 0.93337 0.00025 Lamb 4 0.98044 0.00039 0.98971 0.00003 Hilbert and Logan 5 0.96906 0.00051 0.98928 0.00003 Lactin-1 3 0.89344 0.00247 0.97625 0.00090 Lactin-2 4 0.96580 0.00068 0.98936 0.00003 Brie`re-1 3 0.83545 0.00382 0.97649 0.00009 Brie`re-2 4 0.98001 0.00040 0.98328 0.00005

a Wagner et al. (1984) identiÞed the four parameter-reduced model, as the most appropriate. eter to the Logan-6, Lactin-1 and Brie`re-1 models only ature threshold are best predicted with the Brie`re-1 slightly improved their Þtting for S. punctillum devel- model (Fig. 3). Again, this parameter differed signif- opment. For example, with the four-parameter Bri- icantly (P Ͻ 0.01) among stages, but with no consistent e`re-2 model R2 (0.983) is Ͻ1% better than the three- trend. parameter Brie`re-1 version (0.976), whereas R2 With these four models, differences between pre- increased by 15% with T. mcdanieli. For S. punctillum, dicted and observed values of optimal temperature the models retained using the RSS criterion also were and high temperature threshold for S. punctillum are the same as using the R2. not as large as for the low temperature threshold (data Biological Parameters. The Logan-6, Logan-10, not shown). The observed optimal temperature for Sharpe and DeMichele, Taylor, and Lactin-1 models fast development of S. punctillum ranged 34Ð36ЊC, do not estimate a low temperature threshold; and with signiÞcant variation among stages (P Ͻ 0.01) but although the Lamb model proposed a replacement for without any speciÞc trend. The observed high tem- the low temperature threshold, it did not estimate it as perature threshold of 36.0ЊC did not vary among stages deÞned earlier. Also, the linear model does not pro- (P Ͼ 0.05). vide either the optimal temperature or the high temperature threshold (Table 1). Therefore, all these models fail to satisfy our second criterion. In contrast, the Hilbert and Logan, Lactin-2, Brie`re-1, and Brie`re-2 models, all provide estimates for low and high temperature thresholds, and optimal temperature. Predicted low temperature threshold estimates of the three models meeting both selection criteria were compared with predicted values in Fig. 2 for T. mcdanieli. The observed values are within the 95% con- Þdence interval of the model estimate for all stages, except the egg for the Hilbert and Logan and Brie`re-2 models. Still, the low thresholds seem to be best predicted by the Lactin-2 model. They differed signiÞ- cantly among stages (maximum likelihood ratio test, P Ͻ 0.01), but these differences did not translate into any clear trend or pattern. The estimates of the optimal temperature and high temperature threshold of T. mcdanieli are similar to observed values for the three models (data not shown). The observed optimal temperatures for fast development of T. mcdanieli ranged within 34Ð36ЊC and did not differ among growth stages (P Ͼ 0.05). The observed high temperature thresholds ranged 38Ð40ЊC. For all three models the predicted value of the high temperature threshold of the egg stage was Fig. 2. Observed ( ) and predicted values (bars es- signiÞcantly higher than values predicted for the other F ϭ timate ϩ 95% conÞdence interval) of low temperature stages (P Ͻ 0.01). threshold of Tetranychus mcdanieli based on three develop- For S. punctillum, both criteria were met by four mental rate models. Within models, estimates with the same models, i.e., the Hilbert and Logan, Lactin-2, Brie`re-1, letter do not differ signiÞcantly according to the maximum and Brie`re-2. The observed values of the low temper- likelihood ratio test (␣ ϭ 0.05). 182 ENVIRONMENTAL ENTOMOLOGY Vol. 31, no. 1

reported development data for S. punctillum at a single temperature. T. mcdanieli survival and development data reported here partially agree with Tanigoshi et al. (1975) results on PaciÞc Northwest populations on apple. They reported development at 10 and 38ЊC, whereas we did not obtain any development under 14ЊC and over 36ЊC, suggesting differing temperature adaptations between the two populations. The effect of temperature on S. punctillum development has been studied in Europe by Bravenboer (1959) at 21Ð23ЊC; and Berker (1958) in the 15Ð35ЊC interval, which does not extend sufÞciently low to fully cover the climatic conditions prevailing in Quebec. Numerous studies show that the egg stage of Tet- ranychus spp. lasts longer, by a factor of approximately two, than any active stage (Crooker 1985), similar to our results (Table 2). This implies a long window of opportunity for S. punctillum adults, which preferen- tially feed on spider mite eggs. As was expected, S. punctillum had a much longer development than its T. mcdanieli prey: for example 26.1 d at 20ЊC is 10 d longer than T. mcdanieli (Tables 2 and 3). This major differ- ence plus the temperature range for high survival to maturity being markedly wider for the prey (16Ð36ЊC) than the predator (20Ð32ЊC) (Fig. 1), suggest that, in the long-term over a number of generations, the prey should have numerical advantage over the predator. The curvilinear developmental rate-temperature relation for both species is typical of many other in- Fig. 3. Observed (F) and predicted values (bars ϭ es- sects and mites (Brie`re and Pracros 1998). It can be timate ϩ 95% conÞdence interval) of low temperature adequately described by several nonlinear rate models threshold of Stethorus punctillum based on four developmen- for each species, but only one was retained in each tal rate models. Within models, estimates with the same letter case based on goodness-of-Þt, and estimable temper- do not differ signiÞcantly according to the maximum likeli- ature-related biological parameters. For T. mcdanieli, hood ratio test (␣ ϭ 0.05). six of the 11 models tested did not Þt the data well. Surprisingly, the Logan-6 model, which was Þtted by Given similar estimation of the optimal temperature Logan et al. (1976) to data from a Washington State and high temperature thresholds by three models for population of T. mcdanieli, did not provide a good Þt. T. mcdanieli and four for S. punctillum, accuracy at Among the Þve other models, the Lamb and the Lo- predicting the low temperature threshold was re- gan-10 models provided good Þt, but predicted devel- ferred to for Þnal selection. This threshold was more opment rate approaches zero asymptotically and no closely predicted by the Lactin-2 model for T. mc- low temperature threshold can be estimated (Brie`re danieli and the Brie`re-1 model for S. punctillum, hence and Pracros 1998). In contrast, the Brie`re-2, Hilbert they were chosen and their Þt to data are presented in and Logan and Lactin-2 models enabled the develop- Figs. 4 and 5, respectively. They were separately Þtted ment rate curve to intersect the temperature axis. The to all stages as the maximum likelihood ratio test in- low temperature threshold estimates for speciÞc dicated that the value of the parameters do, in some stages were most accurate using the Lactin-2 model instances (see above), vary among stages. (Fig. 2). All in all, we conclude that the Lactin-2 model best describes the relationship of development rate to temperature for this T. mcdanieli population. Lactin et Discussion al. (1995) stated that this model is preferable when No other study has covered the full range of tem- temperatures are frequently near the low threshold, peratures that are suitable to the development and which is the case early in the season in Quebec. This survival of T. mcdanieli and S. punctillum in North model also was found highly efÞcient in modeling the America. Tanigoshi et al. (1975) studied the effects of rice root aphid, Rhopalosiphum ruﬁabdominalis temperature on development, reproduction, and pop- (Sasaki) (Tsai and Liu 1998). ulation growth of T. mcdanieli from Washington State For S. punctillum, eight models Þtted the data well, on lima beans. Concerning Stethorus coccinellids, tem- and adequately predicted developmental rates. The perature effects on development are available for S. Lamb, Logan-6, Logan-10, and Lactin-1 models were madecassus Chazeau (Chazeau 1974), S. loxtoni Brit- rejected for failure to estimate a low temperature ton and Lee (Richardson 1977), and S. punctum picipes threshold as generally deÞned. The low temperature (Tanigoshi 1973). In North America, Putnam (1955) thresholds estimates of the Lactin-2, Brie`re-1 and Bri- February 2002 ROY ET AL.: T. mcdanieli AND S. punctillum DEVELOPMENT MODELS 183

Fig. 4. Fitting the Lactin-2 model to developmental rate data for the egg, larva, protonymph and deutonymph stages of Tetranychus mcdanieli as a function of temperature (ЊC). Dots represent observed rates. e`re-2 models were close (Fig. 3), however, the Bri- a single model. However, in practice using a single e`re-1 model requires three parameters versus four for model is preferable, which may justify compromising the other two models. A model should meet the gen- to some degree. Our criteria resulted in choosing dif- eral criterion of parsimony (see e.g., Lamb et al. 1984), ferent best models for T. mcdanieli and S. punctillum and contain as few parameters as possible given that but these criteria could include the requirement for a goodness-of-Þt and other (e.g., biological) criteria are unique model for both species. met. Our results indicate potential synchrony between Although the Lactin-2 model for T. mcdanieli and the two organisms based on their predictable early the Brie`re-1 model for S. punctillum seem to be the spring development, so long as overwintered adults best and satisfactorily estimated the optimal temper- emerge from postdiapause and start reproducing si- atures and the high temperature thresholds, they multaneously. The low threshold estimate of T. mc- sometimes provided inaccurate estimation of the low danieli eggs is 11.35ЊC (Figs. 2 and 4). At a daily temperature threshold. Development may be ob- average of 12ЊC, the Þrst eggs laid would hatch in 25 d served at the estimated low temperature threshold (Table 2), but unless average temperature increases (e.g., T. mcdanieli eggs, Fig. 4; and S. punctillum Þrst by a few degrees, the spider mite would not develop instar, Fig. 5). In other instances, no development was further. At 14ЊC, T. mcdanieli eggs would hatch in 17 d, observed over several degrees above the estimated and the larvae would then become protonymphs low temperature threshold (e.g., T. mcdanieli (Crooker 1985). The low threshold estimate ofS. punc- deutonymph, Fig. 4; and S. punctillum fourth instar, tillum is 12.0ЊC (Figs. 3 and 5) and the Þrst eggs could Fig. 5). reach the Þrst instar in 22 d at 14ЊC if prey are available. Problems in estimating low temperature thresholds Thus, at 14ЊC, by the time T. mcdanieli would reach the may be due to intrinsic model weaknesses in Þtting protonymph stage, the Þrst instar of S. punctillum data across such broad temperature ranges. The pro- would have developed and be able to feed on mite cesses that cause heat stress and death at high tem- eggs and protonymphs, the preferred prey stages of perature may be basically different from those that the closely related S. punctum (Houck 1980). Our data affect development and chilling injury at low temper- suggest that these relationships would hold at higher ature. Inaccuracies might also be due to experimental average temperatures as well (Tables 2 and 3). Thus, error, or greater variability of individuals within a a raspberry system with S. punctillum should be less population, when exposed to extreme conditions. Ad- exposed to unrepressed early feeding by spider mite ditional sampling at the left-hand side of the curve, by protonymphs and deutonymphs, as predatory stages of including more experimental temperatures and more the coccinellid should be active simultaneously. individuals might provide more precise estimation of This work described the development-temperature the low temperature threshold. relationships of Quebec populations T. mcdanieli and In addition, the dual objective of selecting a useful S. punctillum under the broad range of temperatures model for predicting development rate and estimating generally prevailing in this region, and estimated their life history parameters may not be met efÞciently by key bioclimatic parameters. Nevertheless, more 184 ENVIRONMENTAL ENTOMOLOGY Vol. 31, no. 1

Fig. 5. Fitting the Brie`re-1 model to developmental rate data for the egg, Þrst, second, third, fourth larval and pupal stages of Stethorus punctillum as a function of temperature (ЊC). Dots represent observed rates.

knowledge of their adaptations at temperatures close red raspberry production system under cool climatic to the low threshold would be important. Poikilo- conditions. therms often are well adapted to survive and even develop to some extent during long periods of cold temperatures (Brie`re et al. 1999, Liu and Meng 1999). Acknowledgments Also, although it appears that early synchrony be- We thank Annie Saint-Louis, Marie-Claude Pe´pin, and tween the two organisms would allow the coccinellid Lucie Laverdie`re for technical assistance; Gae´tan Daigle for to impact the spider mite protonymphs and statistical assistance; and Claudel Lemieux for editorial help. deutonymphs, the assumption that S. punctillum We express special thanks to Robert J. Lamb for helpful would prey on these T. mcdanieli stages like S. punctum comments. This project was funded by the Green Plan of on T. urticae Koch remains to be veriÞed. Knowledge Agriculture and Agri-Food Canada and by the Quebec Min- istry of Agriculture, Fisheries and Food. of the predatory behavior of S. punctillum is very limited (e.g., Rott and Ponsonby 2000). Finally, T. mcdanieli and S. punctillum are multivol- References Cited tine, implying that the effect of temperature on re- productive potential and especially their intrinsic rate Agresti, A. 1990. Categorical data analysis. Wiley, New York. of natural increase (rm) would be most useful for predicting their long-term interactions over several Berker, V. J. 1958. Die naturlichen Feinde der Tetranychi- den. Zeitschrift Fu¨ r Angewandte Entomol. 43: 115Ð72. generations. A better set of key ecological parameters Bravenboer, L. 1959. De Chemische en biologische bes- would then be available to determine the potential trijding van de spintmijt Tetranychus urticae Koch. Ph.D. usefulness and role of S. punctillum in an integrated dissertation, Landbouwhogeschool, Wagenigen. February 2002 ROY ET AL.: T. mcdanieli AND S. punctillum DEVELOPMENT MODELS 185

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Appendix: Models where T is the rearing temperature (ЊC), ⌿ is the maximum developmental rate, ␳ is a constant deÞning The linear model or degree-day model is commonly the rate at optimal temperature, T is the lethal max- used to determine thermal constants (degree-days) L imum temperature, and ⌬T is the temperature range and lower development thresholds from developmen- over which physiological breakdown becomes the tal rate of arthropod stages (Campbell et al. 1974, overriding inßuence. The Logan-10 model is deÞned Frazer and McGregor 1992, Rencken and Pringle 1998, as follow, Lopez-Arroyo et al. 1999). The linear model is deÞned as follows: D(T) ϭ ␣ ((1/(1 ϩ ke(Ϫ␳T))) Ϫ e(-(TL - T)/ ⌬T)), where ␣, and k are empirical constants, and T, ␳,T , D(T) ϭ a ϩ bT, L and ⌬T are as in the Logan-6 model. where T is the rearing temperature (ЊC), a is the The Sharpe and DeMichele (1977) biophysical developmental rate at T ϭ 0ЊC, and b is the slope of the model, reparametrized by SchoolÞeld et al. (1981) is regression line. based on enzyme reaction rate theory, and all six The two models developed by Logan et al. (1976) parameters are assumed to have a thermodynamic are deÞned by combining two functions with matched biochemical interpretation (Wagner et al. 1984). This asymptotes, and are usually referred to as Logan mod- model has been used to predict development of ar- els six and 10. These empirical models have been thropod preys and predators (Orr and Obrycki 1990, widely used in biological control studies (Cloutier et Sta¨ubli Dreyer et al. 1997). The Sharpe and DeMichele al. 1995, van Rijn et al. 1995). The Logan-6 model is model is deÞned by the equation, deÞned by the equation D(T) Ϫ (␳T/298.15 e(⌬HA/1.987 (1/298.15 Ϫ 1/T)))/ D(T) ϭ ␺ (e(␳T) Ϫ e(␳TL Ϫ (TL Ϫ T)/⌬T)) (1 ϩ (e(⌬HL/1.987(1/ T1/2L Ϫ 1/T))) ϩ (e(⌬HH/1.987 (1/T1/2H - 1/T)))), February 2002 ROY ET AL.: T. mcdanieli AND S. punctillum DEVELOPMENT MODELS 187

2 2 2 where T is the rearing temperature (ЊK), ␳ is the D(T) ϭ⌿((T Ϫ T0) /((T Ϫ T0) ϩ d ) developmental rate at 25ЊC, ⌬HA is the enthalpy of Ϫ e (Ϫ(TL Ϫ (T Ϫ T0))/ ⌬T)), activation of reaction, ⌬HL is the change in enthalpy at low temperature, T is the temperature at 1/2L where T, ⌿,TL, and ⌬T are as in the Logan-6 model, which the enzyme for the low temperature portion T0 and d are empirical parameters. is 1/2 active, ⌬HH is the change in enthalpy at high In 1995, Lactin et al. proposed two modiÞcations of temperature, T1/2 H is the temperature at which the the Logan-6 model. First, they eliminated a redundant enzyme for the high temperature portion is 1/2 parameter to obtain the Lactin-1 model. Second, they active. incorporated an intercept parameter, which allows The Taylor model (1981) is a simple normal func- estimation of a low temperature threshold for devel- tion written as follows: opment, resulting in Lactin-2 model. These models 2 D(T) ϭ R e (Ϫ.5((T Ϫ Tm)/T␴) ), have recently been used by Brie`re and Pracros (1998) m and by Tsai and Liu (1998). The Lactin-1 model is where T is the rearing temperature (ЊC), Rm is the deÞned as follows: maximum development rate at temperature T, T is m (␳T) (␳T Ϫ (T - T)/ ⌬T) the temperature where the development rate is high- D(T) ϭ e Ϫ e L L , est, and T␴ is a shape parameter giving the spread of and the Lactin-2 model is, the curve. (␳T) (␳TL Ϫ (TL Ϫ T)/ ⌬T) The Lamb model (Lamb et al.1984, Lamb 1992) is D(T) ϭ e Ϫ e ϩ ␭. an asymmetrical normal function modiÞed from Tay- In both LactinÕs models, T, ␳,TL, and ⌬T are as in lor (1981) and is deÞned as follows: the Logan-6 model, and in the Lactin-2 model ␭ forces 2 the curve to intercept the y-axis at a value below zero D(T) ϭ R e(Ϫ.5((T Ϫ Tm)/T␴L) ) for T Յ T m m and thus allows estimation of a low temperature and threshold. ( .5((T T )/T )2) More recently, Brie`re et al. (1999) have proposed D(T) ϭ R e Ϫ Ϫ m ␴H for T Ͼ T , m m two more models with a nonlinear part at low and high where T, Rm, and Tm are as in TaylorÕs equation. T␴L temperatures and a linear portion at intermediate tem- is a shape parameter giving the spread of the curve for peratures. The Brie`re-1 model is deÞned as follows: T Յ Tm, and, T␴H is a shape parameter giving the 1/2 D(T) ϭ a T (T Ϫ T0) (TL Ϫ T) spread of the curve for T Ͼ Tm. The Hilbert and Logan model (1983), a combina- and the Brie`re-2 model is as follows: tion of sigmoid and exponential equations, was for- (1/d) mulated to improve the Logan model by providing a D(T) ϭ a T (T Ϫ T0) (TL Ϫ T) . lower threshold of development. This model has been In both models T is the rearing temperature (ЊC), a used recently by Scott and Yeoh (1999) to predict the is an empirical constant, T0 is the low temperature development of an aphid with biocontrol potential development threshold, TL is the lethal temperature against a weed. The Hilbert and Logan model is de- threshold, and in the Brie`re-2 model d is an empirical Þned as follows: constant.