Cope's Rule states that the size of species tends to increase along an evolutionary lineage. A basic statistical framework is elucidated for testing Cope's Rule and some surprising complications are pointed out. If Cope's Rule is formulated in terms of mean size, then it is not invariant to the way in which size is measured. If Cope's Rule is formulated in terms of median size, then it is not i...

4.1.1 Step size selection rule Choosing the optimum step size α is desirable, but it may be computationally expensive. Hence, some other set of rules, which have good properties, e.g., convergence, are desirable. We illustrate one such rule in the following example, which is called as successive reduction rule. Example 4.1.1. Successive reduction rule: Start with an initial step size s > 0 and ...

Bergmann's and Rensch's rules describe common large-scale patterns of body size variation, but their underlying causes remain elusive. Bergmann's rule states that organisms are larger at higher latitudes (or in colder climates). Rensch's rule states that male body size varies (or evolutionarily diverges) more than female body size among species, resulting in slopes greater than one when male si...

the essential difference between hadd and ta‘zīr has long been accepted in islamic penal system. based on a study of the holy texts and the statements of the scholars it can be asserted that the rule according to which ‘the type and size of the hadd is defined by the legislator, whereas the type and amount of the ta‘zīr would only be determined by the islamic ruler’ is not comprehensive and lac...

Bergmann's rule is currently defined as a within-species tendency for increasing body size with increasing latitude or decreasing environmental temperature. This well-known ecogeographic pattern has been considered a general trend for all animals, yet support for Bergmann's rule has only been demonstrated for mammals and birds. Here we evaluate Bergmann's rule in two groups of reptiles: cheloni...

Sexual size dimorphism (SSD) is widespread within the animal kingdom. Rensch's rule describes a relationship between SSD and body size: SSD increases with body size when males are the larger sex, and decreases with body size when females are the larger sex. Rensch's rule is well supported for taxa that exhibit male-biased SSD but patterns of allometry among taxa with female-biased size dimorphi...