数学建模试题：请你建立合理的数学模型，设计一个全面而有效的评价生物多样性 的指标。拜托大家看一下

Posted 2023-02-24

2010 年是联合国大会确定的国际生物多样性年。保护地球上的生物多
样性已经越来越被人类社会所关注，相关的大规模科研和考察计划也层出不
穷。为了更好地建立国际交流与专家间的合作，联合国还建立了生物多样性
和生态系统服务政府间科学政策平台（IPBES）。但迄今为止，几乎所有的考
察计划都面临着一个基本的困难：如何评价被考察区域的生物多样性。传统
的方法是清点物种数量，但现在有许多科学家认为这种方法具有很大的局限
性。譬如有人提出应当考虑物种的相似程度。有人则提出有一些物种的基
因多样性程度远远超过另一些物种，所以应当考虑基因的多样性等。但现在
还缺少一种能全面考虑不同因素的对生物多样性进行测定的方法。

Application of ROC curve analysis in evaluating the performance of alien
species’ potential distribution models
Yunsheng Wang1,2, Bingyan Xie1*, Fanghao Wan3, Qiming Xiao2, Liangying Dai2
1 Institute of Vegetables and Flowers, Chinese Academy of Agricultural Sciences, Beijing 100081
2 College of Bio-safety Science and Technology, Hunan Agricultural University, Changsha 410128
3 Institute of Plant Protection (South Section), Chinese Academy of Agricultural Sciences, Beijing 100081
Abstract: Ecological niche models (ENMs), which are widely employed to predict the potential geographic
distribution of species, provide an important tool to quantify the risks imposed by invasive alien species. The
problem of how to evaluate the performance of different models has attracted more and more attention. In the
present paper, we introduced the principle of the method of Receiver Operating Characteristic (ROC) curve
analysis in assessing the accuracy of different ENMs. We predicted the suitable distribution area of Radopholus
similis, an important banana toppling disease nematode, with five widely used ENMs and evaluated
the performance of different models by ROC curve analysis. The area under ROC curve (AUC) for BIOCLIM,
CLIMEX, DOMAIN, GARP, and MAXENT models was 0.810, 0.758, 0.921, 0.903, and 0.950, respectively.
Among these, the biggest value of AUC was assigned to MAXENT, indicating that the result
gained by MAXENT should be better than the other four models. According to the results of analysis of
variance (ANOVA), there was a remarkable difference in AUC between each model except for DOMAIN and
GARP.
Key words: ROC curve, alien species, model evaluation, suitable distribution area, Radopholus similis

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