栖息地永久性破坏的比例对物种多度稳定值影响的迭代算法
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973资助项目(2009CB119200); 国家科技支撑计划资助项目(2006BAD19B0102); 国家自然科学基金资助项目(30970510,31030012);中国科学院知识创新工程重要方向资助项目(KSCX2-EW-Z-6)


Iterative algorithm for analyzing the influence of the proportion of permanently destroyed sites on the equilibrium abundances of species
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    摘要:

    为了分析栖息地破坏程度对集合群落中物种多度稳定值的影响,基于Tilman等提出的多物种竞争的集合群落模型,设计了一种通用的迭代算法用以分析栖息地永久性破坏的比例对物种多度稳定值的影响。针对Tilman等提出的物种多度与其扩散能力或者与其竞争能力相互关系的4种模型,也即:(1)物种竞争力越强则其多度稳定值越大,所有物种死亡率相同;(2)所有物种不论竞争力如何,其多度稳定值相同、死亡率也相同;(3)物种竞争力越弱则其多度稳定值越大,所有物种死亡率相同;(4)物种多度的稳定值相同,但物种竞争力越弱其死亡率越高。先前的研究已经阐明了在前2种模型中栖息地永久性破坏的比例对物种多度稳定值的影响;而对于模型3,因为其数学表达式较为复杂,先前的研究者不得不使用模型3的简化式来考察栖息地永久性破坏的比例对物种多度稳定值的影响;而对于模型4,由于其数学表达式更为复杂,栖息地永久性破坏的比例对物种多度稳定值的影响未能被以往的研究所阐明。本文所使用的迭代算法可以阐明四种模型中任何一种模型条件下栖息地永久性破坏的比例对物种多度稳定值的影响。我们发现对于模型1和2迭代算法所得到的物种多度稳定值与通过数学解析式分析的结果完全一致,同时通过使用迭代算法还阐明了模型4中栖息地永久性破坏的比例对物种多度稳定值的影响。假设栖息地永久性破坏的比例达到了能够导致第s个物种灭绝的水平,起初幸存物种竞争力的排序为s+1~s+3~s+5~…~s+6~s+4~s+2,但是随着栖息地永久性破坏的比例不断增大,当其快达到(但还未达到)能够导致第s+1个物种灭绝的水平,物种竞争力的排序将变为s+2~s+4 ~ s+6~…~s+5~s+3~s+1。模型4中栖息地永久性破坏的比例对物种多度稳定值的影响与模型2中栖息地永久性破坏程度对物种多度稳定值的影响几乎一致,唯一不同是模型2中所有物种栖息地稳定值的曲线有一个共同的交点,而模型4中所有物种栖息地稳定值的曲线交点不唯一。此外,还使用迭代算法考对比了模型3原始数学表达式和简化式两种情况下栖息地永久性破坏的比例对物种多度稳定值的影响,发现结果略有不同。

    Abstract:

    We developed a general iterative algorithm for analyzing the influence of habitat destruction on the equilibrium abundances of species in a competitive metacommunity exposed to habitat destruction, based on the multi-species competitive model proposed by Tilman et al. We focus on the four cases put forward by Tilman et al. that reflect different relationships between the equilibrium abundances of species in an intact habitat and their dispersal or competitive abilities: (1) best competitors most abundant and equal mortality; (2) equally abundant species and equal mortality; (3) poorer competitors more abundant and equal mortality; (4) equally abundant but poorer competitors with higher mortality. For cases 1 and 2, the previous studies have clearly elucidated the impacts of habitat destruction on the equilibrium abundances of species under these two cases. Case 3 has a complex mathematical formulation. Thus, the pervious investigators had to replace case 3 by a simplified formulation during exploring the impact of habitat destruction on the equilibrium abundances of species. For case 4, the influence of habitat destruction on the equilibrium abundances of species was not analyzed because the mathematical formulation of case 4 is more complex. The iterative algorithm of the current study can be used to analyze the impacts of habitat destruction on the equilibrium abundances of species for all four cases. We find that the relationship between habitat destruction and equilibrium abundance of any species is linear between two adjacent proportions of permanently destroyed sites which can drive one species to extinction. Our results by using the iterative program accord with the conclusions by analytical methods for cases 1 and 2. We also find the effect of habitat destruction on the equilibrium abundances of species for case 4, which has not been reported by previous research. Let s be the number of extinct species for case 4. If s is an odd number, species s+1 is the best competitor and occupies the most sites around the critical proportion of permanently destroyed sites, which drives species s to extinction. However, the abundance of species s+1 will gradually descend with the proportion of permanently destroyed sites increasing. When the proportion of permanently destroyed sites approximates to (but less than) the level which can drive species s+1 to extinction, species s+2 is the best competitor and species s+1 is the worst competitor. The order of the equilibrium abundances is s+2~s+4 ~ s+6~…~s+5~s+3 ~ s+1. This conclusion still holds for case 4 when s is an even number. We find that the impact of habitat destruction on the equilibrium abundances of species for case 4 is very similar to that of case 2. For case 2, the equilibrium abundance lines of species between two adjacent critical proportions of permanently destroyed sites, which can drive one species to extinction, have a common intersection; however, for case 4, the equilibrium lines do not have a common intersection. In addition, we compare the results using the original and simplified formulations of case 3. We find that there is a slight difference in the impacts of habitat destruction on the equilibrium abundances of species between using the original and simplified formulations.

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时培建,戈峰,杨清培.栖息地永久性破坏的比例对物种多度稳定值影响的迭代算法.生态学报,2011,31(15):4327~4333

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