Peijian Shi

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.

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.

Weakening density dependence from climate change and agricultural intensification triggers pest outbreaks: a 37-year observation of cotton bollworms

Understanding drivers of population fluctuation, especially for agricultural pests, is central to the provision of agro-ecosystem services. Here, we examine the role of endogenous density dependence and exogenous factors of climate and human activity in regulating the 37-year population dynamics of an important agricultural insect pest, the cotton bollworm (Helicoverpa armigera), in North China from 1975 to 2011. Quantitative time-series analysis provided strong evidence explaining long-term population dynamics of the cotton bollworm and its driving factors. Rising temperature and declining rainfall exacerbated the effect of agricultural intensification on continuously weakening the negative density dependence in regulating the population dynamics of cotton bollworms. Consequently, ongoing climate change and agricultural intensification unleashed the tightly regulated pest population and triggered the regional outbreak of H. armigera in 1992. Although the negative density dependence can effectively regulate the population change rate to fluctuate around zero at stable equilibrium levels before and after outbreak in the 1992, the population equilibrium jumped to a higher density level with apparently larger amplitudes after the outbreak. The results highlight the possibility for exogenous factors to induce pest outbreaks and alter the population regulating mechanism of negative density dependence and, thus, the stable equilibrium of the pest population, often to a higher level, posing considerable risks to the provision of agro-ecosystem services and regional food security. Efficient and timely measures of pest management in the era of Anthropocene should target the strengthening and revival of weakening density dependence caused by climate change and human activities.

Comparison of Thermal Performance Equations in Describing Temperature-Dependent Developmental Rates of Insects: (I) Empirical Models

Abstract Temperature greatly affects the developmental duration of insects at their different stages, and many mathematical models exist for describing their temperature-dependent developmental rates. It is important to choose a suitable model to predict outbreaks of pest insects under climate change. However, previous comparisons among these models were usually based on a single species. In the present study, we compared the six nonlinear models (the Briére-1, Briére-2, Lactin, Performance-2, beta, and Ratkowsky models) based on the goodness of fit and the trade-off between the models goodness of fit and structural complexity, using 10 temperaturedependent developmental rate datasets on insects to make the conclusions general. We found that the square root model (i.e., the Ratkowsky model) fitted all datasets well, and the curve shape produced by this model also approximates the curve shape of thermodynamically based mathematical models. The square root model was originally derived to be applicable to the growth rates of bacteria, and until now it has been generally ignored in entomology. We were mainly concerned with the predicted results obtained by using this model on observations of temperature-dependent developmental rates. We found that the square root model described well the pooled developmental rates in the low-, mid-, and high-temperature ranges, and we believe that it merits wider use in entomology.

Solving the pitfalls of pitfall trapping: a two‐circle method for density estimation of ground‐dwelling arthropods

Summary Pitfall traps are widely used for investigating ground-dwelling arthropods, but have been heavily criticized due to their species-, habitat- and attractant-specific trapping radius which produces unreliable estimation of species diversity and density. We developed a two-circle method (TCM) for simultaneously estimating densities of ground-dwelling arthropods and the effective trapping radius. Multiple pairs of traps are located different distances apart, and the intersection of trapping areas can be calculated using the inverse trigonometric function. The density and effective trapping radius can be estimated from a nonlinear regression of the change in the total number of individuals caught with the distance between the paired pitfall traps. We compared the performance of TCM with the estimator based on the nested-cross array (NCA) for arranging pitfall traps, by comparing predicted densities from these two methods with the real density obtained from the suction sampling method (SSM). Simulations with known arthropod densities and effective trapping radius suggested that TCM produced accurate density estimation, while NCA significantly underestimated the known density. Pitfall trapping of ground-dwelling arthropods on two habitats (crop field and desert steppe) confirmed this conclusion when comparing estimation from TCM and NCA with densities obtained from the SSM. TCM is a promising technique for the density estimation of ground-dwelling arthropods, especially for traps with liquid attractant and areas with relatively homogenous habitat and away from habitat edges.

Testing the rate isomorphy hypothesis using five statistical methods

Abstract  Organisms are said to be in developmental rate isomorphy when the proportions of developmental stage durations are unaffected by temperature. Comprehensive stage‐specific developmental data were generated on the cabbage beetle, Colaphellus bowringi Baly (Coleoptera: Chrysomelidae), at eight temperatures ranging from 16°C to 30°C (in 2°C increments) and five analytical methods were used to test the rate isomorphy hypothesis, including: (i) direct comparison of lower developmental thresholds with standard errors based on the traditional linear equation describing developmental rate as the linear function of temperature; (ii) analysis of covariance to compare the lower developmental thresholds of different stages based on the Ikemoto‐Takai linear equation; (iii) testing the significance of the slope item in the regression line of versus temperature, where p is the ratio of the developmental duration of a particular developmental stage to the entire pre‐imaginal developmental duration for one insect or mite species; (iv) analysis of variance to test for significant differences between the ratios of developmental stage durations to that of pre‐imaginal development; and (v) checking whether there is an element less than a given level of significance in the p‐value matrix of rotating regression line. The results revealed no significant difference among the lower developmental thresholds or among the aforementioned ratios, and thus convincingly confirmed the rate isomorphy hypothesis.

How to compare the lower developmental thresholds.

ABSTRACT According to the hypothesis of isomorphy rate, all the lower developmental thresholds of different developmental stages of an insect are equal. However, there is lack of a formal statistical method for testing whether there is a significant difference among the lower developmental thresholds on the basis of the traditional linear model describing developmental rate as a linear function of temperature. For comparing the lower developmental thresholds of different developmental stages, a new method based on the Chow test is proposed in the current study. Another feasible way based on the linear model proposed by Ikemoto and Takai is also proposed. The lower developmental thresholds can be compared by the analysis of covariance on this linear model. The current study can be used to test the hypothesis of isomorphy rate. When comparing the lower developmental thresholds of different geographical populations for one insect species, the two methods proposed here are also applicable.

Capturing spiral radial growth of conifers using the superellipse to model tree-ring geometric shape.

Tree-rings are often assumed to approximate a circular shape when estimating forest productivity and carbon dynamics. However, tree rings are rarely, if ever, circular, thereby possibly resulting in under- or over-estimation in forest productivity and carbon sequestration. Given the crucial role played by tree ring data in assessing forest productivity and carbon storage within a context of global change, it is particularly important that mathematical models adequately render cross-sectional area increment derived from tree rings. We modeled the geometric shape of tree rings using the superellipse equation and checked its validation based on the theoretical simulation and six actual cross sections collected from three conifers. We found that the superellipse better describes the geometric shape of tree rings than the circle commonly used. We showed that a spiral growth trend exists on the radial section over time, which might be closely related to spiral grain along the longitudinal axis. The superellipse generally had higher accuracy than the circle in predicting the basal area increment, resulting in an improved estimate for the basal area. The superellipse may allow better assessing forest productivity and carbon storage in terrestrial forest ecosystems.

Effects of crop species richness on pest-natural enemy systems based on an experimental model system using a microlandscape.

The relationship between crop richness and predator-prey interactions as they relate to pest-natural enemy systems is a very important topic in ecology and greatly affects biological control services. The effects of crop arrangement on predator-prey interactions have received much attention as the basis for pest population management. To explore the internal mechanisms and factors driving the relationship between crop richness and pest population management, we designed an experimental model system of a microlandscape that included 50 plots and five treatments. Each treatment had 10 repetitions in each year from 2007 to 2010. The results showed that the biomass of pests and their natural enemies increased with increasing crop biomass and decreased with decreasing crop biomass; however, the effects of plant biomass on the pest and natural enemy biomass were not significant. The relationship between adjacent trophic levels was significant (such as pests and their natural enemies or crops and pests), whereas non-adjacent trophic levels (crops and natural enemies) did not significantly interact with each other. The ratio of natural enemy/pest biomass was the highest in the areas of four crop species that had the best biological control service. Having either low or high crop species richness did not enhance the pest population management service and lead to loss of biological control. Although the resource concentration hypothesis was not well supported by our results, high crop species richness could suppress the pest population, indicating that crop species richness could enhance biological control services. These results could be applied in habitat management aimed at biological control, provide the theoretical basis for agricultural landscape design, and also suggest new methods for integrated pest management.

Applications of the Bootstrap to Insect Physiology

ABSTRACT The effect of temperature on development and the effect of photoperiod on diapause incidence of insects are common topics in insect physiology. Related to these topics, are 3 important concepts: the lower and upper developmental thresholds, which represent the lower and upper limits of thermal range for insects to develop, and the critical photoperiod, which causes diapause in 50% of a population. To compare lower or upper developmental thresholds of 2 different developmental stages or of 2 populations at the same developmental stage is difficult because of the lack of a suitable statistical method. Shi et al. (2010) proposed 2 methods for testing whether there is a significant difference between 2 lower developmental thresholds. However, these 2 methods are only applicable to the linear relationship between developmental rate and temperature. There are also many studies on the geographic variation in the critical photoperiods for different populations of an insect species. Also, a method is lacking for testing whether there is a significant difference between 2 critical photoperiods. In this study, we test bootstrap to determine if there is a significant difference between different parameters. Bootstrap can then be used to compare any 2 lower or upper developmental thresholds, or to compare 2 critical photoperiods. It can also provide the confidence interval of a critical photoperiod.