作业帮数学建模试题：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.
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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.
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.
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
Allouche O, Tsoar A, Kadmon R (2006) Assessing the accuracy
of species distribution models: prevalence, kappa and
the true skill statistic (TSS). Journal of Ecology, 43,
1223–1232.
Andersen MC, Adams H, Hope B, Powell M (2004) Risk assessment
for invasive species. Risk Analysis, 24, 787–793.
Brotons L, Thuiller W, Araújo MB, Hirzel AH (2004) Presence-
absence versus presence-only modelling methods for
predicting bird habitat suitability. Ecography, 27,
437–448.
Busby JR (1991) BIOCLIM―a bioclimate analysis and prediction
system. In: Nature Conservation: Cost Effective Biological
Surveys and Data Analysis (eds Margules CR,
Austin MP), pp. 64–68. CSIRO, Melbourne.
Carpenter G, Gillison AN, Winter J (1993) DOMAIN: a flexible
modelling procedure for mapping potential distributions
of plants and animals. Biodiversity and Conservation,
2, 667–680.
Cohen J (1960) A coefficient of agreement for nominal scales.
Educational and Psychological Measurement, 20, 37–46.
Elith J, Graham HC, Anderson PR, Dudik M, Ferrier S, Guisan
A, Hijmans JR, Huettmann F, Leathwick RJ, Lehmann A,
Li J, Lohmann GL, Loiselle AB, Manion G, Moritz C,
Nakamura M, Nakazawa Y, Overton MJ, Peterson AT,
Phillips JS, Richardson K, Scachetti-Pereira R, Schapire
ER, Soberon J, Williams S, Wisz SM, Zimmermann EN
(2006) Novel methods improve prediction of species' distributions
from occurrence data. Ecography, 29, 129–151.
Friedman JH, Hastie T, Tibshirani R (2000) Additive logistic
regression: a statistical view of boosting. Annals of Statistics,
28, 337–407.
Goodenough DJ, Rossmann K, Lusted LB (1974) Radiographic
applications of receiver operating characteristic (ROC)
curves. Radiology, 110, 89–95.
Guisan A, Thuiller W (2005) Predicting species distribution:
offering more than simple habitat models. Ecology Letters,
8, 993–1009.
Hanley JA, McNeil BJ (1982) The meaning and use of the area
under a receiver operating characteristic (ROC) curve.
Radiology, 143, 29–36.
Hijmans RJ, Cameron SE, Parra JL, Jones PG, Jarvis A (2005)
Very high resolution interpolated climate surfaces for
global land areas. International Journal of Climatology,
25, 1965–1978.
Hirzel AH, Hausser J, Chessel D, Perrin N (2002) Ecological-
niche factor analysis: how to compute habitat-
suitability maps without absence data. Ecology, 83,2027–2036.
Lantz CA, Nebenzahl E (1996) Behavior and interpretation of
factors affecting the performance of climatic envelope
models. Journal of Clinical Epidemiology, 49, 431–434.
Lehmann A, Overton JM, Leathwick JR (2002) GRASP: generalized
regression analysis and spatial prediction. Ecological
Modelling, 157, 189–207.
Leshowitz B (1969) Comparison of ROC curves from one- and
two-interval rating-scale procedures. The Journal of
Acoustical Society of America, 46, 399–402.
Manel S, Williams HC, Ormerod SJ (2001) Evaluating presence-
absence models in ecology: the need to account for
prevalence. Journal of Applied Ecology, 38, 921–931.
McPherson JM, Jetz W, Rogers DJ (2004) The effects of species'
range sizes on the accuracy of distribution models:
ecological phenomenon or statistical artefact? Journal of
Applied Ecology, 41, 811–823.
Metz CE (1978) Basic principles of ROC analysis. Seminars in
Nuclear Medicine, 8, 283–298.
Peng DL (彭德良), Xie BY (谢丙炎)(2005) Burrowing nematode,
Radopholus similis (Cobb) Thorne. In: Biology and
Management of Invasive Alien Species in Agriculture and
Forestry (重要农林外来入侵物种的生物学与控制) (eds
Wang FH (万方浩), Zheng XB (郑小波), Guo JY (郭建
英)), pp. 640–649. Science Press, Beijing. (in Chinese)
Phillips SJ, Anderson RP, Schapire RE (2006) Maximum entropy
modeling of species geographic distributions. Ecological
Modelling, 190, 231–259.
Phillips SJ, Dudik M, Schapire RE (2004) A maximum entropy
approach to species distribution modeling. In: Proceedings
of 21st International Conference on Machine Learning
(eds Brodley C, Cavazos J, Chan P, Jacob N, Kak A,
Lippman R, Moss E, Pavlopoulou C, Precup D, Scheeff D,
Stefanovic D, Utgoff P, Yurcik B), pp. 655–662. ACM
Press, New York.
Segurado P, Araujo MB (2004) An evaluation of methods for
modelling species' distributions. Journal of Biogeography,
31, 1555–1568.
Shao G, Halpin PN (1995) Climatic controls of eastern North
American coastal tree and shrub distributions. Journal of
Biogeography, 22, 1083–1089.
Stockwell D, Peters D (1999) The GARP modelling system:
problems and solutions to automated spatial prediction.
International Journal of Geographical Information Systems,
13, 143–158.
Sutherst RW, Maywald GF, Skarratt DB (1995) Predicting
insect distributions in a changed climate. In: Insects in
Changing Environment (eds Harrington R, Stork NE), pp.
59–91. Academic Press, London.
Vanagas G (2004) Receiver operating characteristic curves and
comparison of cardiac surgery risk stratification systems.
Interactive Cardiovascular and Thoracic Surgery, 3,
319–322.
Wiley EO, McNyset KM, Peterson AT, Robins CR, Stewart
AM (2003) Niche modeling and geographic range predictions
in the marine environment using a machine-learning
algorithm. Oceanography, 16, 120–127.
Wittenberg R, Cock MJW (2001) Invasive Alien Species: A
Toolkit of Best Prevention and Management Practices.
CAB International, Wallingford.
Yee TW, Mitchell ND (1991) Generalized additive models in
plant ecology. Journal of Vegetation Science, 2, 587–602.
Yu CH (余传华) (2002) Evaluation on diagnostic test. In:
Medical Statistics (医学统计学) (ed. Yu SL (余松林)),
pp. 164–178. People’s Medical Publishing House, Beijing.
(in Chinese)
Zweig MH, Cambell G (1993) Receiver operating characteristic
(ROC) plots: a fundamental evaluation tool in clinical
medicine. Clinical Chemistry, 39, 561–577.
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
Allouche O, Tsoar A, Kadmon R (2006) Assessing the accuracy
of species distribution models: prevalence, kappa and
the true skill statistic (TSS). Journal of Ecology, 43,
1223–1232.
Andersen MC, Adams H, Hope B, Powell M (2004) Risk assessment
for invasive species. Risk Analysis, 24, 787–793.
Brotons L, Thuiller W, Araújo MB, Hirzel AH (2004) Presence-
absence versus presence-only modelling methods for
predicting bird habitat suitability. Ecography, 27,
437–448.
Busby JR (1991) BIOCLIM―a bioclimate analysis and prediction
system. In: Nature Conservation: Cost Effective Biological
Surveys and Data Analysis (eds Margules CR,
Austin MP), pp. 64–68. CSIRO, Melbourne.
Carpenter G, Gillison AN, Winter J (1993) DOMAIN: a flexible
modelling procedure for mapping potential distributions
of plants and animals. Biodiversity and Conservation,
2, 667–680.
Cohen J (1960) A coefficient of agreement for nominal scales.
Educational and Psychological Measurement, 20, 37–46.
Elith J, Graham HC, Anderson PR, Dudik M, Ferrier S, Guisan
A, Hijmans JR, Huettmann F, Leathwick RJ, Lehmann A,
Li J, Lohmann GL, Loiselle AB, Manion G, Moritz C,
Nakamura M, Nakazawa Y, Overton MJ, Peterson AT,
Phillips JS, Richardson K, Scachetti-Pereira R, Schapire
ER, Soberon J, Williams S, Wisz SM, Zimmermann EN
(2006) Novel methods improve prediction of species' distributions
from occurrence data. Ecography, 29, 129–151.
Friedman JH, Hastie T, Tibshirani R (2000) Additive logistic
regression: a statistical view of boosting. Annals of Statistics,
28, 337–407.
Goodenough DJ, Rossmann K, Lusted LB (1974) Radiographic
applications of receiver operating characteristic (ROC)
curves. Radiology, 110, 89–95.
Guisan A, Thuiller W (2005) Predicting species distribution:
offering more than simple habitat models. Ecology Letters,
8, 993–1009.
Hanley JA, McNeil BJ (1982) The meaning and use of the area
under a receiver operating characteristic (ROC) curve.
Radiology, 143, 29–36.
Hijmans RJ, Cameron SE, Parra JL, Jones PG, Jarvis A (2005)
Very high resolution interpolated climate surfaces for
global land areas. International Journal of Climatology,
25, 1965–1978.
Hirzel AH, Hausser J, Chessel D, Perrin N (2002) Ecological-
niche factor analysis: how to compute habitat-
suitability maps without absence data. Ecology, 83,2027–2036.
Lantz CA, Nebenzahl E (1996) Behavior and interpretation of
factors affecting the performance of climatic envelope
models. Journal of Clinical Epidemiology, 49, 431–434.
Lehmann A, Overton JM, Leathwick JR (2002) GRASP: generalized
regression analysis and spatial prediction. Ecological
Modelling, 157, 189–207.
Leshowitz B (1969) Comparison of ROC curves from one- and
two-interval rating-scale procedures. The Journal of
Acoustical Society of America, 46, 399–402.
Manel S, Williams HC, Ormerod SJ (2001) Evaluating presence-
absence models in ecology: the need to account for
prevalence. Journal of Applied Ecology, 38, 921–931.
McPherson JM, Jetz W, Rogers DJ (2004) The effects of species'
range sizes on the accuracy of distribution models:
ecological phenomenon or statistical artefact? Journal of
Applied Ecology, 41, 811–823.
Metz CE (1978) Basic principles of ROC analysis. Seminars in
Nuclear Medicine, 8, 283–298.
Peng DL (彭德良), Xie BY (谢丙炎)(2005) Burrowing nematode,
Radopholus similis (Cobb) Thorne. In: Biology and
Management of Invasive Alien Species in Agriculture and
Forestry (重要农林外来入侵物种的生物学与控制) (eds
Wang FH (万方浩), Zheng XB (郑小波), Guo JY (郭建
英)), pp. 640–649. Science Press, Beijing. (in Chinese)
Phillips SJ, Anderson RP, Schapire RE (2006) Maximum entropy
modeling of species geographic distributions. Ecological
Modelling, 190, 231–259.
Phillips SJ, Dudik M, Schapire RE (2004) A maximum entropy
approach to species distribution modeling. In: Proceedings
of 21st International Conference on Machine Learning
(eds Brodley C, Cavazos J, Chan P, Jacob N, Kak A,
Lippman R, Moss E, Pavlopoulou C, Precup D, Scheeff D,
Stefanovic D, Utgoff P, Yurcik B), pp. 655–662. ACM
Press, New York.
Segurado P, Araujo MB (2004) An evaluation of methods for
modelling species' distributions. Journal of Biogeography,
31, 1555–1568.
Shao G, Halpin PN (1995) Climatic controls of eastern North
American coastal tree and shrub distributions. Journal of
Biogeography, 22, 1083–1089.
Stockwell D, Peters D (1999) The GARP modelling system:
problems and solutions to automated spatial prediction.
International Journal of Geographical Information Systems,
13, 143–158.
Sutherst RW, Maywald GF, Skarratt DB (1995) Predicting
insect distributions in a changed climate. In: Insects in
Changing Environment (eds Harrington R, Stork NE), pp.
59–91. Academic Press, London.
Vanagas G (2004) Receiver operating characteristic curves and
comparison of cardiac surgery risk stratification systems.
Interactive Cardiovascular and Thoracic Surgery, 3,
319–322.
Wiley EO, McNyset KM, Peterson AT, Robins CR, Stewart
AM (2003) Niche modeling and geographic range predictions
in the marine environment using a machine-learning
algorithm. Oceanography, 16, 120–127.
Wittenberg R, Cock MJW (2001) Invasive Alien Species: A
Toolkit of Best Prevention and Management Practices.
CAB International, Wallingford.
Yee TW, Mitchell ND (1991) Generalized additive models in
plant ecology. Journal of Vegetation Science, 2, 587–602.
Yu CH (余传华) (2002) Evaluation on diagnostic test. In:
Medical Statistics (医学统计学) (ed. Yu SL (余松林)),
pp. 164–178. People’s Medical Publishing House, Beijing.
(in Chinese)
Zweig MH, Cambell G (1993) Receiver operating characteristic
(ROC) plots: a fundamental evaluation tool in clinical
medicine. Clinical Chemistry, 39, 561–577.