How reliable are thermal constants for insect development when estimated from laboratory experiments?

Transcription

1 Blackwell Publishing Ltd Uncertainties in thermal constants for insects TECHNICAL NOTE How reliable are thermal constants for insect development when estimated from laboratory experiments? Klemen Bergant 1 * & Stanislav Trdan 2 1 Centre for Atmospheric Research, University of Nova Gorica, Vipavska 13, SI-5000 Nova Gorica, Slovenia and 2 Chair of Entomology and Phytopathology, Biotechnical Faculty, University of Ljubljana, Jamnikarjeva 101, SI-1111 Ljubljana, Slovenia Accepted: 29 March 2006 Key words: lower developmental threshold, sum of effective temperatures, Frankliniella occidentalis, Thysanoptera, Thripidae Introduction The concept of thermal time, where a linear relationship between developmental rate (d) and environmental temperature (T) is assumed for plants and poikilothermic animals ( = a + b T ; a is the intercept, b the slope, and the model estimate of d) (e.g., Bonhomme, 2000), has been widely used as an approximation of physiological time (Trudgill et al., 2005). This approach has been especially common in studies of insect development (e.g., Honek & Kocourek, 1990; Honek, 1996), as temperature plays a major role in the course of their life. Although a linear approximation of the generally non-linear relationship between developmental rate and temperature (e.g., Briere & Pracros, 1998) is valid only within a limited range of temperatures, the simplicity of the thermal time approach makes it very valuable in practice. Thermal constants [lower developmental threshold (LDT) and sum of effective temperatures (SET)] can be estimated from the assumed linear relationship, usually determined from laboratory observations of insect development at different constant temperatures. The LDT, which is defined as the temperature at which the development of insect ceases (d = 0) (e.g., Jaro8ík et al., 2004; Trudgill et al., 2005), can be estimated as LDT = a/b. The SET, which is defined as the temperature difference above LTD when total development (d = 1) is reached in a single day (e.g., Jaro8ík et al., 2004; Trudgill et al., 2005), can be estimated as SET = 1/b (Figure 1). Because the values d = 0 and d = 1, which determine LDT and SET, are extremes in developmental rates and therefore outside the range of values used for the development of the linear model, the estimation of thermal constants is a *Correspondence: Klemen Bergant, Centre for Atmospheric Research, University of Nova Gorica, Vipavska 13, SI-5000 Nova Gorica, Slovenia. klemen.bergant@p-ng.si typical example of extrapolation. This stimulated us to investigate how uncertain the estimates of thermal constants actually are; we base our investigation on laboratory experiments, due to the extrapolation inherent to the computational procedure. Materials and methods To investigate the reliability of thermal constants, we used an example of egg-to-adult development of western flower Figure 1 General concept of estimating thermal constants. A linear relationship between developmental rate (d) and temperature (T) is assumed (d = a + b T). LDT is estimated as a temperature where the development ceases (d = 0, LDT = a/b); cumulative SET is estimated as the temperature difference from LDT needed to complete development (d = 1, SET = 1/b); parameters of linear relationship between developmental rate and temperature can be expressed by thermal constants [d = (T LDT)/SET]. Due to uncertainty in the regression line, there is also a related uncertainty in the estimated LDT and SET values The Authors Entomologia Experimentalis et Applicata 120: , 2006 Journal compilation 2006 The Netherlands Entomological Society 251

2 252 Bergant & Trdan thrips [Frankliniella occidentalis Pergande (Thysanoptera: Thripidae)] (WFT). Several experiments, in which developmental time t of WFT has been observed at different constant temperatures T, are reported in the literature. In reported studies, WFT were reared on radish leaves (Bryan & Smith, 1956), green bean and French bean leaves and pods (Brødsgaard, 1994; Gerin et al., 1994; Lublinkof & Foster, 1977; Stacey & Fellowes, 2002), chrysanthemum florets and leaves (Robb & Parrella, 1991; Katayama, 1997; McDonald et al., 1998), peanut leaves (Lowry et al., 1992), or cucumber leaves (Grassely et al., 1988; Gaum et al., 1994; van Rijn et al., 1995; Jaro8ík et al., 1997). Also, various photoperiods were used in the different experiments: L18:D6 (Katayama, 1997), L16:D8 (Gerin et al., 1994; Brødsgaard, 1994; Jaro8ík et al., 1997; Stacey & Fellowes, 2002), L15:D9 (Lublinkof & Foster, 1977), L14:D10 (Lowry et al., 1992), L12:D12 (Giotonga et al., 2002), or L8:D16 and L4:D20 (Brødsgaard, 1994). The above-mentioned authors determined the duration of consecutive developmental stages (see the references for details on the experiments), but only data for total development from egg-to-adult were used in our study. The data were used to investigate the reliability of thermal constants of insects that are commonly estimated on the basis of laboratory experiments. A simple linear regression (e.g., Krzanowski, 1998) was used to relate developmental rate d (reciprocal of time t) with temperature T and to reconstruct thermal constants LDT and SET reported in the literature = a + b T with a = intercept, b = slope, and = model estimate of d. (1) Only data where WFT had been reared at least at three different temperatures (Table 1) were used for the reconstruction of reported LDT and SET values. As mentioned, the thermal constants can be estimated from the coefficients of the linear regression model (e.g., Jaro8ík et al., 2004), using LDT = a/b and SET = 1/b. (2) Because the pairs of observed values (T, d) do not lie exactly on the regression line, some uncertainty is related to the coefficients a and b (Equation 1), which are estimated with the least squares regression method (e.g., Krzanowski, 1998). The coefficients a and b are not estimated independently, and therefore they have coupled confidence region that can be expressed by the confidence ellipse (e.g., Johnson & Wichern, 1998) α 2 ( a) + 2T a b + T ( b) 2F2, n 2s, (3) where a and b represent the uncertainty in the estimates for regression coefficients a and b at α significance level, F represents the F-distribution (e.g., Krzanowski, 1998), n the number of observations, the bracket denotes an average over n observations, and s 2 the variance of the residuals, with n s = ( di i). (4) n 2 i= 1 Due to the uncertainty in regression coefficients, there is also an uncertainty in the regression line and in the estimates of LDT and SET. A confidence (Working-Hotelling) band for the regression line at α significance level (e.g., Johnson & Wichern, 1998) can be defined as ( T T) α ( d) 2F2, n 2s +, (5) n Q TT where d is the uncertainty of an average estimate for developmental rate d at temperature T, and Q TT is the sum of squared deviations of temperatures T from their average n 2 value, Q TT = (T T). Additionally, the elliptic i = i 1 confidence range for regression coefficients can be transformed to the elliptic-like confidence range for LDT and SET using their relationship with the coefficients (Equation 2). Reference Reported Estimated LDT ( C) SET ( C) n T LDT ( C) SET ( C) Bryan & Smith (1956) Robb & Parrella (1991) Gaum et al. (1994) Katayama (1997) Jaro8ík et al. (1997) McDonald et al. (1998) Stacey & Fellowes (2002) Gitonga et al. (2002) All available data Table 1 Reported and estimated values of LDT (in C) and SET (in C) needed for egg-to-adult development of WFT (Frankliniella occidentalis) together with the number of different temperatures (n T ) applied in the individual experiments

3 Uncertainties in thermal constants for insects 253 In our study, a 10% significance level (α = 0.10) was used for the estimation of uncertainty in the regression line and regression coefficients, and consequently the uncertainty in LDT and SET estimates. Determination coefficient (r 2 in %), which describes the percentage of variability explained by the linear model, was used as a measure of the quality of the fit of the regression line to the reported pairs of (T, d) values (e.g., Krzanowski, 1998). Results and discussion As our estimates for the thermal constants are close to the values reported in the literature (Table 1), it is likely that the calculation procedure for their estimation was the same or at least similar to those applied in the original studies. We are concerned about the large uncertainty in the regression coefficients (a and b) and consequently in the estimated LDT and SET values (Figure 2) for some Figure 2 Estimated coefficients (a and b; upper plot) of the linear relationship between developmental rate (d) and temperature (T) together with the derived thermal constants (LDT and SET; lower plot) for egg-to-adult development of WFT (Frankliniella occidentalis). Ellipses, representing joint confidence region at 10% significance level, are added to the estimates based on data from various studies (see figure legends for references). values in the literature (e.g., Bryan & Smith, 1956; Robb & Parrella, 1991; Jaro8ík et al., 1997), especially as the uncertainty is not commonly included in study reports. The confidence regions for coefficients a and b, and thus for the estimates of LDT and SET, overlap in many cases, which means that their estimates cannot be distinguished with 90% confidence. There are different sources of the uncertainty, mostly related to the experimental setup and quality of experimental results (Figure 3). Fewer pairs of (T, d) values available for linear model development makes the estimation of LDT and SET values more uncertain, although the same percentage of variability is explained by the linear model (e.g., Bryan & Smith, 1956 vs. Gitonga et al., 2002). Higher dissipation of (T, d) pairs around the fitted regression line also increases the uncertainty of estimated thermal constants (e.g., Robb & Parrella, 1991 and Jaro8ík et al., 1997 vs. McDonald et al., 1998). Another important source of uncertainty is the proximity of available data to the d = 0 value, which influences mostly the uncertainty of the LDT estimate (e.g., Gaum et al., 1994 vs. McDonald et al., 1998) as we are in every case far from the value of d = 1 that determines the SET value. The uncertainty decreases if the experiment includes temperatures at which the developmental rate d approaches 0, but on the other hand we still need to stay inside the range of the linear response of d to T. Additionally, the larger range of T used in the study makes the estimates of LDT and SET less uncertain even in the case of similar r 2 values (e.g., Katayama, 1997 and Gitonga et al., 2002 vs. McDonald et al., 1998). Due to these facts, it is obvious that the experimental setup plays an important role in the estimation of thermal constants of insects, especially in their uncertainties, and can be one of the reasons for relatively big differences in the values reported in the literature. These differences could be to a large extent caused by artefacts due to the extrapolation from the uncertain regression line that describes the relationship between developmental range and temperature. Due to the uncertainty in the estimated LDT and SET values and the orientation of confidence ellipses, some doubts arise with regard to trade-offs between SET and LDT (e.g., Trudgill et al., 2005). The negative relationship between SET and LDT, well known when comparing different insect species (Honek, 1996, 1999) adapted to different environmental (climatic) conditions, indicates that species living in warmer environments have a higher LDT and need a lower SET for completing their development than species living in colder environments. Such a tradeoff, indicating the capability for local adaptation even within the same species, supposedly occurs for WFT as well (Stacey & Fellowes, 2002). Considering only the LDT and SET pairs, this negative relationship can be also seen in

4 254 Bergant & Trdan Figure 3 Linear relationship between mean developmental rate (d) and temperature (T) for egg-to-adult development of WFT (Frankliniella occidentalis), together with the 90% confidence band for the regression line, based on results from eight different experiments from the literature (see the titles of subplots for references).

5 Uncertainties in thermal constants for insects 255 data for WFT used in our study (Figure 2) and it is similar to the one reported in Stacey & Fellowes (2002). If such a relationship exists, the adaptation to local climate would take place not only between different species but also between different populations within the same species. But adding the confidence ellipses for LDT and SET shows that such a relationship could be to a large extent caused artificially by the interdependency in the calculation between SET and LDT values. The estimates of SET and LDT are both derived from the slope of the regression line (SET = 1/b, LDT = a/b = T d/b), and an overestimate of the slope of the regression line (b) results in an over-estimate of LDT and a corresponding underestimate of SET and vice versa (Trudgill et al., 2005). It is also well known that the development of WFT is further fine-tuned by many other factors besides T, such as photoperiod (Brødsgaard, 1994) and food quality (Hulshof et al., 2003), which consequently impact the estimation of thermal constants. This could be another reason for the differences in reported LDT and SET values for WFT. To separate the impact of variations in food and photoperiod from the impact of temperature only, we used all available data for the estimation of a linear model and related thermal constants (Figure 4). The resulting thermal constants are LDT = 8.9 and SET = Such an approach could be useful if local adaptation within the WFT species is not an important issue, but we have actually no guarantee that these thermal constants are more realistic than any values reported in the literature. If the differences in reported thermal constants are significantly related to the local adaptation of WFT, the common thermal constants have practically no value. Unfortunately, it is difficult, if not impossible, to separate the impact of possible sources that could contribute to the differences in reported values for thermal constants of WFT, although a major part is probably related to the experimental setup and related uncertainty in the calculation procedure. Conclusions We argue that thermal constants, based on laboratory experiments, commonly suffer from a great amount of uncertainty and should be used with caution in practice. More attention should be given in the future to a proper experimental setup that could decrease the uncertainty in thermal constants and reveal some important factors that are really affecting the constants. This includes observation of insect development at several (at least five) temperatures within the range of linear response of the developmental rate to the temperature. Additionally, a sufficient temperature range should be covered in the experiment to approach the borders of the linear response as closely as possible. A sufficient number of individuals should be included in the experiment at a single temperature to average out individual differences, which could be, for example, related to body mass that also plays an important role in the thermal requirements for development (Charnov & Gillooly, 2003). The thermal constants for insects should be reported together with their uncertainties, and we need to be aware of them when using degree-day models in practice. Additionally, we should not disregard the fact that a linear relationship is an approximation of the real dependence of insect development on temperature and that other factors can significantly influence development besides temperature. To get a better understanding of the impact of various factors on development, more complex experiments are needed. They should include rearing the insects at different temperatures and photoperiods, feeding with foods of different nutritional quality, and, if possible, collecting the insects at locations with a different climate. Acknowledgements The authors would like to thank the two anonymous reviewers for their comments that helped us to improve the manuscript. Figure 4 Linear relationship between mean developmental rate (d) and temperature (T) for egg-to-adult development of WFT (Frankliniella occidentalis) estimated with all data available in the literature. References Bonhomme R (2000) Bases and limits to using degree.day units. European Journal of Agronomy 13: Briere JF & Pracros P (1998) Comparison of temperature dependent growth models with the development of Lobesia botrana (Lepidoptera: Tortricidae). Environmental Entomology 27:

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