生物多样性 ›› 2011, Vol. 19 ›› Issue (4): 404-413. DOI: 10.3724/SP.J.1003.2011.10020
王宜成
收稿日期:
2011-01-26
接受日期:
2011-05-25
出版日期:
2011-07-20
发布日期:
2011-07-29
基金资助:
Yicheng Wang
Received:
2011-01-26
Accepted:
2011-05-25
Online:
2011-07-20
Published:
2011-07-29
摘要:
生境破碎是导致生物多样性损失的重要原因之一, 在设计自然保护区时设法减少生境破碎是提高保护区有效性的重要方法。由于经济资源或地理因素制约不可能把连续的大片土地都划为保护区时, 设计一个由相互分离的几部分组成的保护区是更为现实的做法。选择地块组成内部间隔最小的保护区是减少破碎化的一个重要途径, 但结合空间特征的保护区地块选择模型求最优解时容易遇到计算困难。Williams(2002)基于原图和对偶图概念, 提出一个线性整数规划模型, 主要用于规划连续的土地。本文对他的模型进行改进, 以确定一个保护一组目标物种、间隔最小的自然保护区。改进后的模型对每个备选地块定义两个变量, 用两个变量的取值差异表示保护区内部间隔。模型的计算效率检验结果显示, 该模型可在合理时间内解决包含100个备选地块的间隔最小保护区设计问题。用美国Illinois州部分地区濒危鸟类保护区设计为例, 设计了多种情形下间隔最小的保护区。线性整数规划模型的计算效率仍需提高, 以解决大型保护区最优化设计问题。模型的实际应用需要完整和准确的数据包括物种分布、选择费用等。
王宜成 (2011) 用原图-对偶图法设计内部间隔最小的自然保护区. 生物多样性, 19, 404-413. DOI: 10.3724/SP.J.1003.2011.10020.
Yicheng Wang (2011) A model for designing nature reserves with minimal fragmentation using a primal-dual graph approach. Biodiversity Science, 19, 404-413. DOI: 10.3724/SP.J.1003.2011.10020.
图2 分别包含9个原点和5个对偶点的原图和对偶图以及它们的关系
Fig. 2 Primal and dual graphs consisting of 9 primal nodes and 5 dual nodes, respectively, and their intersecting relation
图3 原图和对偶图的互补结构(黑点和粗线组成原图, 圆圈和细线组成对偶图)
Fig. 3 Interwoven structure of primal and dual trees (primal tree consists of black dots and bold lines, and dual tree blank circles and thin lines)
α | SCP解 SCP solution | r | 模型大小 Model sizea | 目标值 Objective valueb | 时间(秒) Time (s)c | 迭代 Iterationsd | 节点 Nodese |
---|---|---|---|---|---|---|---|
0.8 | 2 | 3 | 0.0 | 3.9 | 11,084 | 61 | |
0.7 | 2 | 3 | 0.1 | 10.0 | 34,150 | 238 | |
0.6 | 3 | 3 | 952 | 1.6 | 36.2 | 183,910 | 1,810 |
0.5 | 3 | 4 | 1,241 | 0.9 | 36.4 | 170,883 | 1,313 |
0.4 | 4 | 6 | 200 | 0.1 | 54.6 | 245,866 | 1,308 |
0.3 | 5 | 7 | 1.0 | 98.1 | 480,861 | 3,207 | |
0.2 | 7 | 9 | 2.8 | 194.0 | 1,056,830 | 8,873 |
表1 间隔最小模型的计算结果(备选地块数量=100, 物种数量=30)
Table 1 Computational results of the minimal fragmentation model (No. of sites = 100, No. of species = 30)
α | SCP解 SCP solution | r | 模型大小 Model sizea | 目标值 Objective valueb | 时间(秒) Time (s)c | 迭代 Iterationsd | 节点 Nodese |
---|---|---|---|---|---|---|---|
0.8 | 2 | 3 | 0.0 | 3.9 | 11,084 | 61 | |
0.7 | 2 | 3 | 0.1 | 10.0 | 34,150 | 238 | |
0.6 | 3 | 3 | 952 | 1.6 | 36.2 | 183,910 | 1,810 |
0.5 | 3 | 4 | 1,241 | 0.9 | 36.4 | 170,883 | 1,313 |
0.4 | 4 | 6 | 200 | 0.1 | 54.6 | 245,866 | 1,308 |
0.3 | 5 | 7 | 1.0 | 98.1 | 480,861 | 3,207 | |
0.2 | 7 | 9 | 2.8 | 194.0 | 1,056,830 | 8,873 |
图5 模型的部分运行结果。深灰色地块组成保护区, 浅灰色是间隔。α是可共存于同一地块的物种占物种总数的最大比例, r是选中地块的最大数量。
Fig. 5 Selected solutions of the model. Dark grey cells consist of the reserve, shallow grey cells are fragmentation. α, Ratio of species that can coexist in any potential site to total number of species; r, Maximal number of selected sites.
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