Population modeling for pesticide risk assessment of threatened species-A case study of a terrestrial plant,Boltonia decurrens : Assessing risk of pesticides to threatened plant populations

During the past 50 years, the human population has more than doubled and global agricultural production has similarly risen. However, the productive arable area has increased by just 10%; thus the increased use of pesticides has been a consequence of the demands of human population growth, and its impact has reached global significance. Although we often know a pesticide's mode of action in the target species, we still largely do not understand the full impact of unintended side effects on wildlife, particularly at higher levels of biological organization: populations, communities, and ecosystems. In these times of regional and global species declines, we are challenged with the task of causally linking knowledge about the molecular actions of pesticides to their possible interference with biological processes, in order to develop reliable predictions about the consequences of pesticide use, and misuse, in a rapidly changing world.

A new empirical equation for the sigmoid pattern of determinate growth, 'the beta growth function', is presented. It calculates weight (w) in dependence of time, using the following three parameters: t(m), the time at which the maximum growth rate is obtained; t(e), the time at the end of growth; and w(max), the maximal value for w, which is achieved at t(e). The beta growth function was compared with four classical (logistic, Richards, Gompertz and Weibull) growth equations, and two expolinear equations. All equations described successfully the sigmoid dynamics of seed filling, plant growth and crop biomass production. However, differences were found in estimating w(max). Features of the beta function are: (1) like the Richards equation it is flexible in describing various asymmetrical sigmoid patterns (its symmetrical form is a cubic polynomial); (2) like the logistic and the Gompertz equations its parameters are numerically stable in statistical estimation; (3) like the Weibull function it predicts zero mass at time zero, but its extension to deal with various initial conditions can be easily obtained; (4) relative to the truncated expolinear equation it provides more reasonable estimates of final quantity and duration of a growth process. In addition, the new function predicts a zero growth rate at both the start and end of a precisely defined growth period. Therefore, it is unique for dealing with determinate growth, and is more suitable than other functions for embedding in process-based crop simulation models to describe the dynamics of organs as sinks to absorb assimilates. Because its parameters correspond to growth traits of interest to crop scientists, the beta growth function is suitable for characterization of environmental and genotypic influences on growth processes. However, it is not suitable for estimating maximum relative growth rate to characterize early growth that is expected to be close to exponential.

Ecological models are important for environmental decision support because they allow the consequences of alternative policies and management scenarios to be explored. However, current modeling practice is unsatisfactory. A literature review shows that the elements of good modeling practice have long been identified but are widely ignored. The reasons for this might include lack of involvement of decision makers, lack of incentives for modelers to follow good practice, and the use of inconsistent terminologies. As a strategy for the future, we propose a standard format for documenting models and their analyses: transparent and comprehensive ecological modeling (TRACE) documentation. This standard format will disclose all parts of the modeling process to scrutiny and make modeling itself more efficient and coherent. Copyright (c) 2010 Elsevier Ltd. All rights reserved.