Takaya Ikemoto

A New Linearized Formula for the Law of Total Effective Temperature and the Evaluation of Line-Fitting Methods with Both Variables Subject to Error

Abstract In the quantitative analysis of experimental data regarding temperature-dependent development, the so-called law of total effective temperature is sometimes expressed in the linearized equation 1,: 1/D = −(t/k) + (1/k)T. D indicates the duration of development; T, temperature; t, the estimated developmental zero temperature; and k, the effective cumulative temperature. The method of fitting usually involves the regression of y = 1/D on x = T. Although the degree of fitting of equation 1, to data within optimum temperature ranges is fairly satisfactory, we have in the current study addressed three problems regarding the use of equation 1, and methods of fitting involving the regression of y on x. First, we found that the detection of optimum temperature ranges is frequently difficult with equation 1,. Second, in applying the method of regression of y on x with equation 1, the weights of the data points are disproportionate between those in the upper and lower parts of the line and they are not homogeneous along the temperature axis. The lower the temperature, the more disproportionate weight is burdened and the less weight is loaded. Third, in most of the data, errors in the x-variable are ignored. The second and third problems would in most cases result in a reduction in the slope of the line, a smaller t, and a larger k. Therefore, we proposed a new linearized formula: (DT) = k + tD. We further propose the use of the reduced major axis, obtained as the solution of the functional model among bivariate errors-in-variables models, in the method of fitting to data. We demonstrated that the majority of the problems raised above could be unraveled under this new approach based on statistical analysis.

Intrinsic Optimum Temperature for Development of Insects and Mites

Abstract The law of total effective temperature, which has been conventionally used by many researchers, and the thermodynamic model based on enzymatic reaction, which was presented by previously, are representative models used to express a relationship between temperature and the development rate of poikilotherms. The former is a very simple and highly descriptive linear model. In contrast, the latter is very complex because it is a nonlinear model, but it has fine descriptive power. In a previous paper, I discovered the existence of a common temperature (Tc) and a common duration (Dc) of development among closely related members of arthropods during the course of comparatively analyzing many estimated values of constants of the linear model and succeeded in explaining the significance of Tc−Dc in an evolutionary process. This study was focused on an extended application of Tc−Dc to the nonlinear thermodynamic model. One of the practical difficulties in using the nonlinear thermodynamic model results from the vexatious complication of estimating simultaneously the values of seven unknown constants. In particular, there were no means to estimate the values of the constants of reference temperature (T0) and development rate (ρ) at T0, which are defined in the nonlinear thermodynamic model. Here, I determine a suitable replacement of the constants T0 and ρ by the common temperature (Tc) and inverse of the common duration (1/Dc), respectively, resulting in reasonably successful curve fitting for data. Therefore, Tc (=T0) could be considered in principle to be common in the two models. I suggest that Tc and T0 be conferred a new definitive concept, that is, the intrinsic optimum temperature for development that tends to be fixed for a taxon, and that they exhibit the minimum effects on enzyme inactivation at low and high temperatures.

Tropical malaria does not mean hot environments.

Abstract If global warming progresses, many consider that malaria in presently malaria-endemic areas will become more serious, with increasing development rates of the vector mosquito and malaria parasites. However, the correlation coefficients between the monthly malaria cases and the monthly mean of daily maximum temperature were negative, showing that the number of malaria cases in tropical areas of Africa decreases during the season when temperature was higher than normal. Moreover, an analysis of temperature and development rate using a thermodynamic model showed that the estimated intrinsic optimum temperatures for the development of the malaria parasites, Plasmodium falciparum and P. vivax, in the adult mosquito stage and that of the vector mosquito Anopheles gambiae s.s. were all ≈23–24°C. Here, the intrinsic optimum temperature is defined in the thermodynamic model as the temperature at which it is assumed that there are no or negligible adverse effects for development. Therefore, this study indicates that the development of malaria parasites in their mosquito hosts and the development of their vector mosquitoes are inhibited at temperatures higher than 23–24°C. If global warming progresses further, the present center of malarial endemicity in sub-Saharan Africa will move to an area with an optimum temperature for both the vector and the parasite, migrating to avoid the hot environment.

A Modified Program for Estimating the Parameters of the SSI Model

ABSTRACT Temperature has a significant influence on the development rates of poikilotherms. There are many nonlinear mathematical models for describing temperature-dependent development rates. Among these models, the Sharpe-Schoolfield (SS) model with six parameters may be the most popular one. The reciprocal of the denominator in the SS model represents the probability of enzyme being in the active state. There is a reference temperature, 25°C, which was defined as a temperature at which the probability of enzyme being in the active state reaches its maximum. However, several examples of using the SS model to fit experimental data display that the probability of enzyme being in the active state does not reach its maximum at 25°C. For different taxonomic groups, the temperatures at which the probability of enzyme being in the active state reaches its maximum might be different. Thus, Ikemoto modified the SS model to a new model (i.e., the SSI model) which can meet the condition that at a particular temperature the probability of enzyme being in the active state can reach its maximum. In addition, Ikemoto related the SSI model to the linear model and devised an algorithm to estimate model parameters; however, that original program of Ikemoto is so timeconsuming that it limits the use of the SSI model. We provide a new program for a faster estimation of the parameters in the SSI model. One complete run of the new program takes less than 1 min (using R 2.10.1). This new program allows investigators to use the SSI model more readily. In addition, we test the linear approximation of the SSI model over three temperature ranges: low, middle, and high temperatures. We also provide a method for calculating the tangent at any point in the SSI model.

Insecticidal compounds against mosquito larvae fromOscillatoria agardhii strain 27

It was found that Oscillatoria agardhii strain 27 produced compounds toxic against mosquito larvae (Aedes albopictus), therefore, these compounds were extracted and separated for insecticide development. Structural characterization of the toxic fraction by 1H‐NMR and GC‐MS showed that these compounds are not the neurotoxins or hepatotoxins conventionally produced by Oscillatoria, but it contained a mixture of unsaturated fatty acids, oleic, linoleic, and γ‐linolenic acids, as well as saturated fatty acids, myristic, palmitic, and stearic acids. In a bioassay developed for these hydrophobic compounds using mosquito larvae, authentic unsaturated fatty acids were shown to be toxic, whereas saturated ones were not active. The results suggested that it might be possible to use unsaturated fatty acids as environmentally safe and effective insecticides without the side effects of the chemically synthesized insecticides. © 2000 John Wiley & Sons, Inc. Environ Toxicol 15: 114–119, 2000

Confidence interval of intrinsic optimum temperature estimated using thermodynamic SSI model

The intrinsic optimum temperature for the development of ectotherms is one of the most important factors not only for their physiological processes but also for ecological and evolutional processes. The Sharpe–Schoolfield–Ikemoto (SSI) model succeeded in defining the temperature that can thermodynamically meet the condition that at a particular temperature the probability of an active enzyme reaching its maximum activity is realized. Previously, an algorithm was developed by Ikemoto (Tropical malaria does not mean hot environments. Journal of Medical Entomology, 45, 963–969) to estimate model parameters, but that program was computationally very time consuming. Now, investigators can use the SSI model more easily because a full automatic computer program was designed by Shi et al. (A modified program for estimating the parameters of the SSI model. Environmental Entomology, 40, 462–469). However, the statistical significance of the point estimate of the intrinsic optimum temperature for each ectotherm has not yet been determined. Here, we provided a new method for calculating the confidence interval of the estimated intrinsic optimum temperature by modifying the approximate bootstrap confidence intervals method. For this purpose, it was necessary to develop a new program for a faster estimation of the parameters in the SSI model, which we have also done.

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

The development rate of insects at hourly fluctuating temperatures is not infrequently different from that at constant temperatures even when the averages of these temperatures are the same. This temperature-dependent development phenomenon has been known as the Kaufmann effect. However, its theoretical analysis has not yet been successfully carried out owing to the insufficiency of mathematical insight especially into quantitative expressions. In insect development, the interrelationships among the three environmental temperatures, namely, the constant and alternating temperatures controlled in the laboratory and the hourly fluctuating temperatures in the natural environment, have not been clarified. Here, we completely succeeded in analyzing this phenomenon and in elucidating the interrelationships by introducing the components of the nonlinear SSI development model, the second derivative, the cosine-wave model of hourly fluctuating temperatures and their variance, and Taylor series. As a result, it has been possible to predict the development rate at fluctuating temperatures in the natural environment using prospective daily maximum, minimum and average temperatures and the development rate at constant temperatures without conducting experiments at alternating temperatures.

Studies on the spatial distribution pattern of larvae of the mosquito,Anopheles sinensis, in rice fields

The spatial distribution patterns of the population ofAnopheles sinensis larvae were studied in the rice field area in the suburb of Urawa city in Japan, during the summer seasons in 1973 and 1974. The distribution pattern of the larval population within the field, analysed by the m−m regression method, indicated that the basic component of larval distribution was not a group of individuals but a single individual and such components were distributed contagiously over the field. This basic pattern did not change significantly according to developmental stage, census date or field. Therefore, we could describe the distribution pattern of the population in a rice field by the single linear regression, x=0.021+1.339x(r2−0.912). Also, the relation for the whole population in the field area including the five fields could be shown by the linear regression, x=0.049+1.749x(r2−0.959). The value of α remained to be nearly equal to zero, but the value of β became larger than the value for the single-field relation. Such a change in distribution pattern seemed to reflect the greater heterogeneity in conditions among the fields than within individual field. Using the information on the distribution patterns mentioned above, some considerations were given on the sampling plans for mosquito larvae, including samplesize determination and application of sequential methods to estimate population size as well as to classify population level.