Mathematical elucidation of the Kaufmann effect based on the thermodynamic SSI model

Ikemoto, Takaya; Egami, Chikahiro

doi:10.1007/s13355-013-0190-6

Cited by 16 publications

(14 citation statements)

References 21 publications

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“…Second, given that we found temperature dynamics to affect development, we tested whether the effect of temperature dynamics can be predicted by Jensen's inequality (Keen and Parker 1979;Ikemoto and Egami 2013), considering that r(T) is the developmental rate under static temperature T. The effect of Jensen's inequality on the development of organisms is termed Kaufmann effect (Kaufmann 1932). The model predicts that when temperature changes at discrete levels, the developmental rate under the temperature dynamics, r dyn , is as follows,…”

Section: The Model and Statistical Analysismentioning

confidence: 99%

“…In specific, we tested whether it is possible to describe the effect of temperature dynamics using the simple model described below. This is important because most existing studies have focused on documenting the presence of the effect of temperature dynamics (but see Keen and Parker ; Ikemoto and Egami ), but little is known about how to predict the development of organisms when temperature is not constant. Predictions of the model were also contrasted to published studies when appropriate.…”

Section: Introductionmentioning

confidence: 99%

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Development of insects under fluctuating temperature: a review and case study

Shiao

Okuyama

2014

J Applied Entomology

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The relationship between temperature and the developmental rate of organisms is crucial for understanding a variety of biological processes. It is common to use an average‐based index of temperature, for example degree‐days, for examining the relationship; and relatively little attention has been given to the variance of temperature. In this study, we examined the importance of temperature fluctuation on the development of organisms by compiling published studies. Published studies have shown highly variable results where the developmental rate was sometimes higher and sometimes lower under static temperature compared with variable temperature. A laboratory experiment on Megaselia scalaris showed that M. scalaris developed faster under fluctuating temperature than static temperature. We tested an additive model to predict the effect of fluctuating temperature on development and found that the model was inadequate for making quantitative predictions. However, some qualitative predictions, for example temperature fluctuation has a positive or negative effect, can be successfully predicted by the additive model. Our results show that the effect of temperature on developmental rate is not completely additive and average‐based indices such as degree‐days cannot be used when quantitative predictions are required.

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Section: The Model and Statistical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Development of insects under fluctuating temperature: a review and case study

Shiao

Okuyama

2014

J Applied Entomology

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“…Such a thermal developmental curve over these three thermal regions is usually assessed in controlled environments with a constant temperature. The curve can be used for predicting, for instance, the occurrence date of a particular phenological event of arthropods by accumulating the daily developmental rates for full development from a starting date (Wagner et al 1984;Ungerer et al 1999;Ikemoto and Egami 2013;Shi et al 2017a). If the temperaturedependent developmental rate curve is also applicable to plants, we can predict the occurrence date of a particular phenological event in plants.…”

Section: Introductionmentioning

confidence: 99%

The effect of temperature on the developmental rates of seedling emergence and leaf-unfolding in two dwarf bamboo species

Lin

Shao

Hui

et al. 2018

Trees

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Key messageThe mean and variance of developmental rates of bamboos at different temperatures follow a power law. The rate isomorphy hypothesis, demonstrated in insects and mites, does not hold in bamboos. Abstract The developmental time of plants and poikilotherms can be significantly affected by temperature. Developmental rate (i.e. the reciprocal of developmental time) of arthropods and germination rate of some plant seeds have been demonstrated to follow a linear function with temperature. The rate isomorphy hypothesis in entomology suggests a lower developmental threshold below which development of all life stages terminates. If this hypothesis also holds for plants, the estimated lower threshold for one development stage could be used for predicting thresholds of other stages. Here, we tested this hypothesis to compare the developmental time of seedling emergence and the time from seedling emergence to the unfolding of the third leaf in two bamboo species. We used five constant thermal environments from 18.5 to 28.5 °C with an increment of 2.5 °C. Both species showed a linear relationship between temperature and developmental rate, with the mean and variance of developmental rates following a power law. Using the bootstrap percentile method, we showed that the isomorphy hypothesis does not hold for both species. The effect of temperature on the survival rate at the time of seedling emergence differed significantly between the two species.

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“…Ungerer et al (1999) have applied the ADP model to estimate the number of generations per year for the southern pine beetle (Dendroctonus frontalis Zimmermann) by integrating a nonlinear temperature-dependent developmental rate model proposed by Schoolfield et al (1981). Ikemoto and Egami (2013) proposed a revision to the Schoolfield model and calculated developmental rates in a natural thermal environment from a controlled thermal experiment. However, to date, no studies have compared these methods in describing the phenological events of plants in early spring.…”

Section: Introductionmentioning

confidence: 99%

Timing of cherry tree blooming: Contrasting effects of rising winter low temperatures and early spring temperatures

Shi

Chen

Reddy

et al. 2017

Agricultural and Forest Meteorology

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Phenology reflects the interplay of climate and biological development. Early spring phenological phenomena are particularly important because the end of diapause or dormancy is related not only to heat accumulation in the early spring but also probably to winter low temperatures. Although a warmer winter can reduce overwintering mortality in many insects and plants, it also reduces the accumulation of chilling time that often triggers the end of diapause or dormancy. We examined a continuous 67-year time series of the first flowering date of cherry trees and compared three phenological models based on the temperature-dependent developmental rate: (i) the accumulated degree days (ADD) method, (ii) the number of days transferred to a standardized temperature (DTS) method, and (iii) the accumulated developmental progress (ADP) method. The ADP method performed the best but only slightly better than the DTS method. We further explained the residuals from the ADP method by an additive model using the mean winter minimum daily temperatures, the number of days with low temperatures (represented by daily minimum temperature) below a critical low temperature, and the minimum annual extreme temperature. These three temperature variables explained more than 57.5% deviance of the ADP model residuals. Increased mean winter low temperatures can delay the blooming of cherry trees by reducing the accumulation of chilling time, whereas reduced numbers of cold days can shift the blooming to become earlier. Overall, rising winter low temperatures will delay the flowering time, while rising early spring temperatures directly shift earlier the flowering time. The flowering time has been shifted to earlier, and the balance from the opposing effects of rising winter low temperatures and early spring temperatures explains this shift.

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Mathematical elucidation of the Kaufmann effect based on the thermodynamic SSI model

Cited by 16 publications

References 21 publications

Development of insects under fluctuating temperature: a review and case study

Development of insects under fluctuating temperature: a review and case study

The effect of temperature on the developmental rates of seedling emergence and leaf-unfolding in two dwarf bamboo species

Timing of cherry tree blooming: Contrasting effects of rising winter low temperatures and early spring temperatures

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