tailieunhanh - Niche Modeling: Predictions From Statistical Distributions - Chapter 9

Trong toán học, hệ thống phi tuyến, rõ ràng, không tuyến tính. Hệ thống tuyến tính và một số hệ thống phi tuyến tính có thể dễ dàng giải quyết được như họ có thể trình bày như một tổng hợp của các bộ phận của họ. Giả định mong muốn và lưu lượng xấp xỉ từ các hình thức mô hình cụ thể, như tuyến tính và sự phân chia, cho phép tính toán dễ dàng hơn kết quả. Trong bối cảnh của mô hình thích hợp, một phương trình mô tả phản ứng của một loài y x1. | Chapter 9 Non-linearity In mathematics non-linear systems are obviously not linear. Linear system and some non-linear systems are easily solvable as they are expressible as a sum of their parts. Desirable assumptions and approximations flow from particular model forms like linearity and separability allowing for easier computation of results. In the context of niche modeling an equation describing the response of a species y given descriptors Xi .xn is obviously linear y ai Xi . an Xn However this form of equation is unsuitable for niche modeling as it cannot represent the inverted U response that is a minimal requirement for representing environmental preferences. The second order polynomial can represent the curved response appropriately and is also linear and easily solvable y aiiXi a12X2 . an2xn However our concern here is not with solvability. Our concerns are the errors that occur when non-linear . curved systems such as equation above are modeled as linear systems like equation . Specifically we would like to apply niche modeling methods and determine how types of non-linearity affect reliability of models for reconstructing past temperatures over the last thousand years from measurements of tree ring width. This will demonstrate another potential application of niche modeling to dendroclimatology. Response of an individual and species as a whole to their environment is basic to climate reconstructions from proxies. Simulation first in one and then two dimensions can help to understand the potential errors in this methodology from non-linearity. 143 2007 by Taylor and Francis Group LLC 144 Niche Modeling Growth niches While we use a one dimension example of reconstructions of temperatures for simplicity the results are equally applicable in two dimensions. However we initially use actual reconstructions of past temperature. Reconstructions of past climates using tree-rings have been used in many fields including climate change and .