Competitive Networks and Measures of Intransitivity
Competitive Networks and Measures of Intransitivity
复制标题
竞争网络和不及物性测量
DOI：
10.1086/283539
复制
发表时间：
1979
期刊：
影响因子：
--
通讯作者：
P. Petraitis
中科院分区：
文献类型：
--
作者：
P. Petraitis
虽然关于不传递竞争关系的重要性的论述并不新鲜（Lewontin 1968），但最近几个人的工作（Gilpin 1975;杰克逊and Buss 1975;杰克逊1977; May and伦纳德1975）已经引起了生态学家的注意。然而，如果不对竞争者之间的不及物性的相对水平进行某种测量，就无法对竞争性社区中的不及物性进行研究。两种措施，一种是肯德尔和史密斯（1940）提出的，另一种是朗道（1951）提出的，已被用于这一目的。然而，这些措施并不适合这个问题。肯德尔和史密斯把注意力集中在不及物三和弦上（A击败B，B击败C，但C击败A）。对于奇数个物体，朗道的测度与肯德尔和史密斯的测度相同。然而，不及物关系的数量不是不及物三元组数量的简单函数。表1给出了一个例子。在前两种情况下，有八个不及物三和弦。然而，情况1需要四个反转，而情况2需要三个反转，才能转化为一个层次结构。在竞争系统中，一个更理想的不传递性度量将基于将网络转化为层次结构所需的最小反转次数，并将由可能的最大不传递关系数标准化。对于这样的测度，令t= 1-sIM，其中s是所需反转的最小数量，M是可能的不传递关系的最大数量。t的范围是从0到1;当t= 1时，没有不传递关系。
While conjectures about the importance of intransitive competitive relationships are not new (Lewontin 1968), recent work by several people (Gilpin 1975; Jackson and Buss 1975; Jackson 1977; May and Leonard 1975) has brought he problem to the attention of ecologists. Yet, intransitivity in competitive communities cannot be examined without some measure of the relative level of intransitivity among competitors. Two measures, one proposed by Kendall and Smith (1940) and the other by Landau (1951), have been used for this purpose. These measures, however, are not appropriate for this problem. Kendall and Smith confine their attention to intransitive triads (A beats B, B beats C, but C beats A). Landau's measure is the same as Kendall and Smith's measure for an odd number of objects. However, the number of intransitive relationships is not a simple function of the number of intransitive triads. An example is given in table 1. In the first wo cases there are eight intransitive triads. Yet case 1 requires four reversals, while case 2 requires three reversals, to be transformed into a hierarchy.A more desirable measure of intransitivity in competitive systems would be based on the minimum number of reversals required to transform a network into a hierarchy and would be standardized by the maximum number of intransitive relationships possible. For such a measure, let t= 1-sIM where s is the minimum number of required reversals and M is the maximum number of possible intransitive relationships. The range of t is from zero to one; when t= 1 there are no intransitive relationships.