Temperature-dependent development is described by three variables termed thermal characteristics: the developmental zero temperature, below which no development is assumed to occur; the high cutoff temperature, above which development slows; and the developmental index, a measure of physiological time required for a given phase to develop. Physiological time in this study refers to number of degree-days, units that combine temperature and time. The phase of interest here is the entire larval stage. Degree-days track developmental progress more precisely than calendar days and better alert the observer for optimally timing planned interventions. Thermal characteristics are usually derived from simple Type I regressions fitted to the linear portion of plots of rate of development on rearing temperature, where rate is the reciprocal of duration. Existing thermal characteristics for 131 published datasets are revised here using an improved Type II regression proposed by Ikemoto & Takai (2000). These datasets represent species in 11 families and originated between 1927 and 2007 on six continents. Each dataset consists of ≥4 associated rates and temperatures. Revised developmental zero temperatures ranged from 3.9 to 16.0. They varied directly with mean annual temperatures at localities of dataset origin, forming a continuum of low to high values between cool and warm climates. Among other relations, the mathematical product of voltinism × the natural logarithm (ln) of developmental index, which encompasses multivoltinism, varied directly with developmental zeros. In 91% of datasets, number of degree-days for the larval phase calculated using official mean daily air temperatures agreed within ±2 calendar days with those using constant laboratory temperatures. Official temperatures were summarized from records at 18 mid-temperate North American weather stations. Thermal characteristics are found to be adapted to climatic regimes, and local weather-station temperatures are usually suitable for degree-day summations.

Differing air temperature patterns among growth seasons create differing thermal environments for most insects and other ectotherms. Development may be accelerated if weather is warmer than average, or slowed if cooler. This often makes calendar dates unreliable for forecasting temperature-dependent events such as egg hatching, pupation, or eclosion. A physiological rather than calendrical time scale may offer a more precise and more useful basis for prediction. Degree-days (or day-degrees) combine temperature with calendar days to provide such a time scale. Summing degree-days measures physiological time and tracks temperature-dependent development. It alerts the observer when pest management treatments or other time-sensitive actions are required. It is useful also in other contexts, such as risk analysis, in which thermal characteristics may indicate how successful a pest might prove where it does not yet occur (Gould et al. 2005). The method provides no formal technique for making predictions in advance, but improvisation enables short-range forecasting once a summation has begun.

The present report focuses on the larval stage of development, when capital breeding lepidopterans, including most lepidopteran pests, accumulate the bulk of their reproductive resources (Boggs 1992; Miller 1996; Tammaru & Haukioja 1996). It is typically the longest developmental stage (Honék & Kocourek 1990) and therefore the stage most representative of temperature-dependent development. ‘Development’ refers to progress through set phases of life history, while ‘growth’ refers to increase in biomass.

Practical application of temperature-dependent development consists of summing degree-days in the field to track and predict developmental mileposts in time or life history. Typical mileposts are egg hatching, adult eclosion, or completion of larval development as in this study. A beginning milepost also might be an arbitrary calendar date. Where it is not possible to introduce a temperature sensor into the larval habitat, official temperatures recorded at a nearby weather station may be substituted. Actually, weather station temperatures can be used in most situations, as in this study.

Three thermal characteristics describe temperature-dependent development: L, the developmental zero temperature, often termed lower developmental threshold, below which no development is assumed to occur; H, the high cutoff temperature above which development slows; and K, the developmental index or physiological time in accumulated degree-days required to complete a particular phase of development. H, usually >30° C, proved least important in this study because such temperatures did not occur for significant periods at mid-temperate North American weather stations used in this study. ‘Lower developmental threshold’ is somewhat misleading, as discussed further on.

Although sometimes referred to in the literature as constants and coefficients, thermal characteristics are not fixed for a species, but often differ from population to population and are subject to local adaptation and evolution, as shown here. Ikemoto & Takai (2000) pointed out that published thermal characteristics for many species, including capital-breeding lepidopterans, may be suspect because of problems with conventional linear derivation procedure. These problems are detailed further on. Before thermal characteristics were deployed in this study, a major effort was made to revise them for as many capital-breeding lepidopterans as feasible using a derivation proposed by Ikemoto & Takai (2000), here termed the improved linear model procedure.

Surprisingly, degree-day summation from field temperatures, although basic to tracking field development, has been inadequately investigated. Published thermal characteristics for only 22% of the 108 species here were accompanied by field-testing or other evaluation. Moreover, most of the reported testing was based on existing, unrevised thermal characteristics. Field-testing is essential because of the potential for summation errors posed by certain effects to be described.

The three aims of this report are (1) to revise existing thermal characteristics as already noted; (2) to examine how revised thermal characteristics relate to climate, geography, voltinism, and to one another; and (3) to ascertain how well phase durations based on fluctuating field temperatures agree with those based on constant laboratory temperatures. The report also touches on how rate of degree-day accumulation might affect fecundity, a fitness factor influenced by temperature (Miller 2005).

Notable overviews of temperature-dependent development are given by Uvarov (1931), Allee et al. (1949), Andrewartha & Birch (1954), Wilson & Barnett (1983), Wagner et al. (1984), Ratte (1984), Delahaut (2003), Régnière & Logan (2003), and Herms (2007). Taylor (1981) specifically treats physiological time. Baskerville & Emin (1969), Pruess (1983), Higley et al. (1986), and Worner (1992) deal with issues of methodology, and Wang (1960) and Baker (1980) offer methodological critiques. Additional reports are cited later in relevant contexts.

## Materials and Methods

**Degree-day terminology and computation.** Symbols and definitions used are shown in Table 1. All temperatures in this report refer to °C. By definition, one DD accumulates when T for all 24 h of one calendar day is one degree higher than L. During any calendar day, number of DDs accumulated is T - L, assuming T > L. Thus, if T for a calendar day averages 20°, and L is 12°, then 20 minus 12, or 8 DDs, accumulate that day. For n calendar days, number of DDs accumulate as

The progression of natural temperatures through daily lows and highs resembles a sine wave, and a sine function (Allen 1976) is built into the summation algorithm used here, as described later. Hourly temperatures can be used, but the 24-h calendar day used here is most common. In the absence of an accurately estimated developmental zero temperature, an arbitrary approximation or ‘base temperature’ is used.

When DDs have accumulated in field summation to an ending milepost, that number is designated W, the field version of the laboratory developmental index, K (Table 1). Ideally, median-to-median or mean-to-mean individuals in the population should be used when developmental intervals defined by phenological mileposts are attained. Because plant development is also temperature dependent, phenological events such as bud-break or blooming in particular plants can serve as DD indicators if they correspond to mileposts in insect development (Herms 2007).

Thermal characteristics are components of phenological models, which range from the conventional linear type with two parameters to more complex nonlinear, multiparameter types. Linear and nonlinear refer to the straight or curved shape of the line that relates developmental rate to temperature. This study used only linear models—conventional or improved—fitted to datasets with ≥4 successive graphed points that formed a reasonably straight line. Most published models for capital-breeding lepidopterans are linear and of the conventional simple Model I regression type. The conventional model, which is the source of ‘unrevised’ thermal characteristics, is discussed more fully further on.

Phenological models are based on experimental data obtained when D is recorded for an insect at different Ts, usually in the laboratory, but in the field if the subject insect is not amenable to laboratory rearing. Laboratory Ts are usually constant, and were so in nearly all datasets here, but the methodology can accommodate laboratory Ts programmed to fluctuate diurnally . In the event that a field rather than a laboratory study is used to create a model, mean temperatures during the phase of interest in different years or locations, or in manipulated habitats, serve as Ts (Legg et al. 1998b). One dataset here for *Pthorimaea operculella* (Saunders) (Gelechiidae) is of this type (Langford & Cory 1932). The rest used constant laboratory Ts.

In laboratory or field, other environmental factors may influence thermal characteristics, as shown later, and should be monitored or controlled.

## Table 1.

Symbols and definitions used in this study.

**Revision of thermal characteristics**. An extensive search yielded 223 published datasets that met the following criteria for admission to the study: ≥4 associated D and T values for larval cohorts reared throughout development at the same Ts, same photoperiods, and on the same food. If results were reported by gender, female data were used here; otherwise the combined sexes were used. Humidities were generally uncontrolled. Datasets for which nonlinear models originally had been fitted were admitted if they otherwise met the above criteria. In several datasets multiple observations of D at one T were averaged to obtain a single value to avoid pseudoreplication. The assembled datasets were subjected to additional requirements such as more stringent testing for linearity, as described later. Ultimately, L' and K' were calculated for 131 of the original 223 datasets using the improved linear model of Ikemoto & Takai (2000) (Table 2). Species nomenclature, although updated in a few cases, generally follows that used in dataset sources.

**
Conventional model.
** This model begins with the hyperbola, or reverse-J shaped curve, formed when D is plotted on T. It is illustrated here for

*Mamestra configurata*Walker (Noctuidae) (Fig. 1: curve D). Next, the reciprocal of D, 1/D, is plotted on T (Fig. 1: line R), an operation that usually transforms at least part of any hyperbola into a straight line (Sokal & Rohlf 1981; Ikemoto & Takai 2000). Finally, simple Model I regression—y = a + bx—is fitted to the straight-line portion of the R—T plot (Fig. 1). The temperature where the reverse-extrapolated regression line intersects the T axis is taken as L (Fig. 1: circle on horizontal axis). L can be estimated visually, or more exactly from model parameters as -a/b. It should be noted for future discussion that L is technically a theoretical value; in practice it cannot be estimated experimentally. The reciprocal 1/b is taken as K. For

*Mamestra configurata*, the conventional model gives L as 6.8° and K as 376 (Table 2: No. 36). Unrevised thermal characteristics were recomputed using the conventional model and included in Table 2 for reference. They sometimes diverged from those in original sources because of different rounding, differing interpretations of linearity, or other reasons. Methods of estimating L and K are discussed by Arnold (1959), Pruess (1983), Legg et al. (1998b), and others.

Requisite linearity is based on inspection of the graphed R–T data. Data points are often too scanty for useful statistical evaluation of linearity. Data interpreted as linear in conventional model procedure may not be so interpreted in improved linear model procedure (Figs. 1, 2). As discussed in the next section, the range of effective developmental temperatures usually is defined as those from L to H, and not based on temperatures selected to define it. Curiously, the temperature of fastest development—illustrated here by point No. 6 in Fig. 1—is sometimes wrongly termed ‘optimum temperature’ (Martin & Huey 2008). Points that depart from linearity are deleted before regression computation.

Problems with the conventional model alluded to earlier are that (1) linear portions of plotted data can be difficult to delimit; (2) variances are not constant along the regression line so that lower and upper y-values are disproportionately weighted; and (3) x is untenably treated as error-free, which may depress the slope parameter b. The latter two problems result from usual assumptions of Model I regression (Sokal & Rohlf 1981). Improved linear model procedure addresses these problems, as discussed below.

**
Improved linear model.
** The form of this model is the same as that of the conventional model, y = a + bx, but assumptions are those of Model II reduced major axis (RMA) regression in which both y and x are treated as subject to error instead of y alone (Sokal & Rohlf 1981; Ikemoto & Takai 2000). The same experimental values of D and T are used to create the model, but y becomes the mathematical product T × D instead of R (1/D), and x becomes D instead of T (Fig. 2). The order of plotted data points relative to T is reversed from that of the conventional model (Figs. 1, 2). Linearity is again ascertained subjectively from the graphed (T × D)—D data, but because of model linearizing, departures stand out and a more stringent test of linearity results. Points excluded due to nonlinearity were mostly in the tails of distributions. The ‘confirmed effective temperature range’ as defined here and displayed in Table 2 does not begin with L' and end with H. It is instead defined by the Ts of the highest and lowest values of T × D on the straight line, 818.4 and 504.0 (Fig. 2), which yield a range of 12–28°. Although not ideal, this definition seems more realistic because little development occurs in the several degrees between L' and the beginning of the straight line.

Although linear in form, Model II RMA regression was computed by nonlinear methods (Fleury 1991). First, a Model I regression of T × D on D was fitted, and its parameters a and b then used as start values for iterative computation of final parameter values by means of the nonlinear SYSTAT option (SYSTAT 1992). The final a becomes K', and the final b becomes L'. For *Mamestra configurata,* L' is 6.19° (rounded to 6.2) and K' is 404 (Table 2: No.36). Not surprisingly, these values differ from their counterparts of 6.8° and 376 obtained with the conventional model. In this report, some variables, notably K', are sometimes transformed to natural logarithms (ln) before analysis to improve linearity. Thus far, it seems that only Liu et al. (2002) have used the improved linear model for a capital-breeding lepidopteran.

**Summation with official temperatures**. Field developmental index, W, was obtained as the mathematical product DA × D, where DA is mean number of DDs accumulating/day at a given mean monthly field temperature, and D is the median developmental duration at constant T values in the laboratory (Table 1). Thus W is equivalent to K' except that the Ts underlying W are weather-station daily minima and maxima. Number of calendar days represented by W and K' were compared, and how closely the number based on W agreed with that based on K' (Table 2) indicates the usefulness of W.

To readily estimate W for the field-based part of the study, Table 3 was prepared to provide DAs necessary for the DA × D computation. This table gives DAs for mean field Ts of 8–31° in 0.5° increments, and for L' of 5.0, 8.0, 11.0, and 14.0°. Only datasets with values of T and L' in the tabulated ranges were used to prepare Table 3, a restriction that excluded 37 datasets with uncommonly large or small values of L' or T (Table 2: Nos. 3, 14–17, 19, 22, 24–29, 43–45, 47–49, 54–56, 79, 80, 82–86, 93, 99, 100, 105–107, 109, 111, and 113). Also excluded were datasets for stored-product capital breeders (Table 2: Nos. 118–124), as W was not estimated for them because they typically develop under artificial storage rather than natural conditions. Table 3 provided expected DAs not only for this study but also for anticipated future studies. Its use often required linear interpolation to obtain a desired DA because input values of T and L' were often intermediate between tabulated values.

Table 3 was generated in four steps as follows: (1) Accumulated DDs for each of the four selected months (May–August) of each included year were computed from temperature records of the 18 weather stations using a spreadsheet devised by R. D. Moon, Department of Entomology, University of Minnesota. The selected months encompass the period of most larval development. Spreadsheet inputs were daily temperature maxima (daytime) and minima (nighttime) as well as each of the four L' values. The spreadsheet computed DDs between a specified L' and the sine curve of temperatures for that day (Allen 1976). (2) Resulting number of DDs accumulating above each L' for each month were divided by number of days in the month to obtain mean number of DDs accumulating per day per month (DA). (3) Mean DAs for each month of each year for each L' at each weather station were plotted on corresponding mean monthly field T values, to which third-order polynomial regressions were fitted (Fig. 3). (4) Overall mean DAs were estimated with the regression equations in Fig. 3 for each 0.5° T-step and L', and then assembled as Table 3.

## Table 2.

Thermal characteristics and related values for datasets used in this study. Dash signifies undetermined or unknown value.

## Continued.

## Continued.

## Continued.

## Continued.

## Continued.

## Table 3.

Mean DD accumulations per day (DA) at weather-station mean monthly temperatures from 8–31° C (T) and L' from 5–14° C based on equations in Fig. 3.

As the calendar day is usually the ultimate currency in DD applications, how closely W approximated K' was compared in terms of calendar days (Table 2), which were computed as (K'-W)/DA.

*Mamestra configurator* can again serve to illustrate how W was estimated and how Table 3 assisted. In laboratory rearing of this species, the four surviving values of T and D yielded an L' of 6.19° (rounded to 6.2) (Fig. 2, Table 2: No. 36) and T and D medians of 18.0° and 36.4, respectively. Turning to Table 3, T of 18.0° and L' of 6.19° indicates a DA intermediate between 12.59 for L' = 5 and 9.77 for L' = 8, which after interpolation is 11.5. The mathematical product of 11.5 × 36.4 (DA × D) yields W of 418.6 (rounded to 419) (Table 2: No. 36). Then K' of 404 less W of 419 equals -15 DDs, which, when divided by 11.5 DDs per calendar day (DA), gives a difference of -1.3 calendar days between W and K' (Table 2: No. 36).

Field temperatures used in this study originated from 1920–2000, and the 18 official weather stations providing them were believed representative of temperatures where more than 25 North American datasets originated (Fig. 4, Appendix 1). U. S. temperature records, except those for Minnesota, were obtained at http://cdo.ncdc.noaa.gov/CDO/cdo; temperatures for the one Minnesota station were obtained at http://climate.umn.edu/MnlocMS/MNlocNEW.asp. Official Canadian temperature records were obtained at http://climate.weatheroffice.ec.go.ca/climateData/canada_e.html.

Mean annual temperatures, latitudes, and voltinism were compiled from dataset source publications, maps, and on-line resources. These variables as well as others appear in or are derivable from Table 2. Temperatures originally reported in °F were converted to °C before use. Statistics were generated with SYSTAT software (SYSTAT 1992), and SE refers to standard error.

**Kaufmann and related effects.** A fundamental problem with all linear phenological models is that the full range of any R–T relation is actually curvilinear at its lower and upper ends (Ruel & Ayres 1999; Worner 1992; Liu et al. 1995). At the lower end, the curve is accelerating or concave-upward, and at the upper end, decelerating or concave-downward (Fig. 5). Nonlinear models can be fitted to the full range of data, but linear model simplicity is thereby lost, and more parameters must be estimated—their number often approaching the number of observations in small datasets. Temperatures that fluctuate beyond the effective temperature range (Fig. 5: shaded areas) create summing errors. These errors constitute the Kaufmann or rate-summation effect (Kaufmann 1932). The straight line underestimates developmental rate in the lower shaded area, and overestimates it in the upper shaded area. Total summation error will depend on how often unusually low and high temperatures occur. The possibility of such occurrences underscores the importance of generating adequate numbers of T-D points for modeling to ensure that removal of points that later prove to depart from linearity does not reduce model accuracy.

The Kaufmann effect is encompassed by Jensen's Inequality (Ruel & Ayres 1999), a broader phenomenon involving more than the tails of the rate response distribution. The inequality refers to the difference between actual and predicted DDs when the rate response to temperature is nonlinear. In such cases, field temperature variance acts independently of average field temperature. As discussed further on, these potential effects appear to have had minimal impact in this study.

## Results and Discussion

**Revision of thermal characteristics**. Among the 223 datasets originally meeting study criteria, 16 (7%) were convincingly curvilinear and therefore dropped. Most of the dropped datasets had been fitted with nonlinear models. One or more of these were published by Bari & Lange (1980), Butler et al. (1975), Butturini & De Berardinis (1992), Chen & Su (1982), Daoud et al. (1999), Gould et al. (2005), Johansen (1997), Jones (2005), Legaspi & Legaspi (2007), Madge (1962), Miner (1947), Snyder (1954), and Tiso et al. (1991–92).

More significantly, 207 (93%) of the 223 datasets had ≥4 linear points. However, application of the improved linear model during thermal characteristic revision resulted in reductions to <4 linear points in more than 70 of the 207 datasets, causing them also to be dropped (Appendix 2). Such wholesale exclusion of datasets again underscores the importance of generating sufficient numbers of T–R points for modeling—at least six, preferably eight or more (Legg et al. 2002)—in case points must be removed because of nonlinearity.

The 131 surviving datasets (Table 2) originated from 1927–2007 on six continents, and represent species in 11 families. Across all families, L' ranged 3.9 ± SE 0.58–16.0 ± SE 0.62. The statistical distribution of revised thermal characteristics shifted only slightly: L and L' medians were 10.8 and 10.9, respectively, L' exceeding L in 62 (47%) of datasets, and medians of K and K', each 280, K' exceeding K in 55 (42%) (Table 2). Lack of greater overall differences is of little consequence, however, as the focus of thermal characteristic revision was the individual dataset and its purpose the improvement of dataset quality and reliability.

L' tended to reflect local climates, values changing by nearly 1° for each 3° change in mean annual temperature at the site of data collection, forming a continuum of low to high values from cool to warm conditions (Fig. 6). Low L' values enable earlier development in short, cool growth seasons. K' appeared uninfluenced by mean annual temperature (Fig. 7), but it assumed more importance when combined with other variables, as shown further on.

Noctuidae was the best-represented family among surviving datasets. Although many noctuids are capable of feeding as adults, and a few may approach butterfly income breeding in amount of adult feeding, all were considered capital breeders here because not enough is known at present to classify them more accurately. Mean values of L' and K' for Noctuidae (56 n) were 9.9 and 336 (ln = 5.817), and for the next three best represented families were Tortricidae (25 n), 8.6 and 341 (ln = 5.832), Crambidae (17 n) 12.4 and 320 (ln = 5.768), and Gelechiidae (15 n) 12.0 and 220 (ln = 5.394).

Trudgill & Perry (1994) suggested that high L values serve to delay development until lethal spring frosts have mostly passed. Theoretical and empirical studies of unrevised thermal characteristics have further suggested that tropical ectotherms would have higher L and lower K values than temperate ones (Honék 1996b; Trudgill & Perry 1994; Trudgill 1995). The revised thermal characteristics strongly support these suggestions.

Not surprisingly, L' declined with increasing north latitude (Fig. 8) as it did with decreasing mean annual temperature, the former also noted for unrevised values of L by Honék (1999). The trend in L' relative to increasing south latitude was positive but not statistically significant. The south latitude sample was small (14 n), but a different trend is perhaps to be expected because of the larger ratio of ocean to landmass in the southern hemisphere. Response of one species to differing geography is well illustrated by *Agrotis ipsilon* (Hufnagel) (Noctuidae) with L's ranging 5.8–11.6 among three continents (Table 2: Nos. 1–5), although for reasons thus far unclear, relations between L' and climatic variables in this example do not mirror statistical outcomes across families.

Voltinism across all families ranged from 1–12 (Table 2). It declined like L' with declining mean annual temperature (Fig. 9), but increased with decreasing K' (Fig. 10). Joint relations among voltinism, V, ln K', and L' are readily understandable at high values of L' where multiple generations develop in one growth season (Fig. 11). It is assumed in Fig. 11 that L' for a species at a given locality does not change appreciably between generations during the same growth season.

As emphasized by Honék (1996a) for unrevised thermal characteristics L and K, revised thermal characteristics L' and K' were themselves inversely correlated among species (Fig. 12). For a 1° change in L' near its median, K' changed by ∼31 DDs.

Body size is not addressed in the present study, but it is noteworthy in passing that Honék (1999) showed that body mass and unrevised K are directly correlated. Honék concluded that, other things being equal, larger bodied species require longer developmental durations than smaller ones and thus have larger Ks.

Examples of environmental factors other than temperature influencing thermal characteristics include humidity where at 90–60% R. H. K' at the same Ts ranged 390–512 (Table 2: Nos. 120–122); photoperiod where K' among photophases of 10–14 h of daylight ranged 161–197 (Table 2: Nos. 25–27); and food quality where L' and K' were, respectively, 8.5° and 416 on cotton, and 14.0° and 245 on corn (Table 2: Nos. 14 and 15).

In summary, thermal-characteristic revision does not appear to have overturned any broad conclusions based earlier on unrevised values, but instead strengthens such conclusions with higher quality surviving datasets. For instance, the inverse correlation of L' and mean annual temperature (Fig. 6) confirms that thermal characteristics of populations are adaptive and subject to evolution.

**Summation with official temperatures**. Agreement of calendar-day differences between W and K' here for a period as long as the entire larval phase exceeded expectations. Some 91%—all but 9—agreed within ±2 calendar days (Table 2). Agreement was doubtless enhanced by the exclusion of datasets that were weak or had extreme values. Most divergences of >2 calendar days were from coastal or near coastal oceanic and lacustrine environments in Japan, Australia, Taiwan, (Table 2: Nos. 8, 20, 38, 61, 69, 75, 96,129), the U. S. and Canada (Table 2: Nos. 38, 75, 96), Brazil, and Spain (Table 2: Nos. 69, 131). Association of divergences with these environments may be coincidental, however, as other datasets from similar environments did not diverge excessively (Table 2: Nos. 2, 9–10, 18, 50, 57, 62, 66, 108, 115, 125–127).

Methods of estimating W gave values that agreed reasonably well with K' even in warm-climate species. Most W estimates involved temperatures in the confirmed effective range of ∼15–28°; only 32 datasets (26%) had upper values >31° (stored product lepidopterans excluded) (Table 2). During the May–August period of official temperatures used to estimate DA and W, field temperatures averaged ∼20°. In 64 datasets that included a T of 20°, resulting D values ranged 11.9–173.6, with a median of 29.2 days, or ∼1 month. Mean monthly temperatures ≥29° were never observed in the North American weather-station records used (Fig. 3). For instance, the 30-yr July ‘normal’ (longterm average) temperature at Sioux Falls, SD, was 23.5 ± SD 1.7°, with 99 percent confidence limits of 19.1–27.9°. This makes a warmer average July temperature unlikely to occur there oftener than once a century. Of course, very warm temperatures may occur for less than monthly durations, and even regularly in the Torrid Zone (<24° latitude on either side of the equator). Six surviving datasets originated in the Torrid Zone, and in all four for which W was calculated (Table 2: Nos. 21, 52, 53, 87), agreement of W with K' proved to be well within ±2 calendar days. As emphasized by Ruel & Ayres (1999), however, hourly or other less than half-day field temperatures would provide more accurate results. The degree of agreement between W and K' suggests that Jensen's Inequality had little adverse impact on DAs in Table 3 and thus on W.

Lack of attention to egg and pupal development probably detracts little from the uses of this study, as previous surveys found that unrevised thermal characteristics were similar for egg, larval, and pupal stages of Lepidoptera (Honék 1996a, b).

Interestingly, Podolsky (1984) has written at length about a forecasting method that bypasses thermal characteristics. This method first assembles phase durations at different habitat temperatures. As the temperatures in this first step are uncontrolled, many more observations may be required than with a thermal-characteristic approach. Next, mean temperatures at the location of interest are assembled by successive 10-day or other intervals. Finally, the two assemblies are combined into a nomogram allowing phase durations to be predicted starting on any of a range of dates. Perhaps because of the large amount of data required and uncertainty whether results are transferable between localities, Podolsky's method has not been widely adopted.

Finally, agreement of W with K' seems sufficient to warrant exploration of weather-station temperatures for new developmental applications. One topic for study is the effect of temperature on growth-related population fitness factors such as fecundity. Capital-breeding Lepidoptera reared at different temperatures differ in maternal body size and fecundity (Honék 1993; Miller 2005) with, surprisingly, cooler rather than warmer temperatures having the greater positive impact (Atkinson 1994; Miller 2005) (Fig. 13). Martin & Huey (2008) explained why cool, seemingly suboptimal temperatures are actually optimal. What may have been overlooked in past work on capital-breeding Lepidoptera is that rate of development also may affect fecundity. For instance, fecundity in *Adoxophyes honmai* Yasuda (Tortricidae) peaked at a rather slow developmental rate of ∼0.042 (Fig. 13: b) and midrange T of 20° (Fig. 13: a). Because developmental rate, R, is the reciprocal 1/D, peak fecundity occurred at a larval duration of 24 calendar days, which is protracted compared with the shortest D of 14 days at a T of 30°. This suggests that DD summation, in so far as it indicates developmental rate, might predict fecundity. In future work, fecundity and other fitness factors relative to temperature-dependent developmental rates and associated population indices such as capacity for increase should be explored.

## Acknowledgements

I thank the following for generous assistance: M. P. Ayres, whose review of an earlier manuscript on temperature-dependent development inspired this study; R. D. Moon for making available his degree-day calculator, and for statistical guidance; R. D. Moon, M. A Roberts, Peijian Shi, and an anonymous reader for very constructive reviews of the manuscript; J. L. Moe and C. W. Muggli-Miller for computer support and figure transcriptions; C. W. Muggli-Miller for Japanese translations; and M. A. Borg for bibliographic help.

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