Character displacement is an ecological process by which, theoretically, co-existing species diverge in size to reduce competition. A closely allied concept is deletion, in which species are excluded from a habitat because they do not differ sufficiently from other species living there. Character displacement has been a controversial topic in recent years, largely due to a lack of statistical procedures for testing its existence. We propose herein a variety of approaches for testing displacement and deletion hypotheses. The applicability of the methods extends beyond the motivating ecological problem to other fields. / Consider the model / X(,ij) = (mu)(,i) + (epsilon)(,ij), i = 1, ..., k; j = 1, ..., n(,i), / where X(,ij) is the j('th) observation on species i with population mean (mu)(,i). The (epsilon)(,ij)'s are independent normally distributed error terms with mean zero and common variance. / Traditionally ecologists have regarded species sizes as randomly distributed. We develop tests for displacement and deletion by considering uniform, lognormal and loguniform distributions for species sizes. (A random variable Y has a loguniform distribution if log Y has a uniform distribution.) / Most claimed manifestations of character displacement concern the ratios of each species size to the next smallest one (contiguous ratios). All but one of the test statistics are functions of spacings (logarithms of contiguous ratios). We prove a useful characterization of distributions in terms of spacings, and show that the loguniform distribution produces constant expected contiguous ratios--an important property in character displacement studies. The random effects approaches generally lack power in detecting the suspected patterns. / We develop further tests for the model in which the (mu)(,i)'s are regarded as fixed. This fixed effects approach, which may be more realistic ecologically, produces considerably more powerful tests. Displacement hypotheses in the fixed effects framework are expressed naturally in terms of the ordered means (mu)(,(1)) < (mu)(,(2)) < ... < (mu)(,(k)). We develop a general theory by which a particular class of linear hypotheses about any number of sets of ordered means may be tested. / Finally a functional relation is used to model the movement of species means from one environment to another. Existing asymptotic tests are shown to perform remarkably well for small samples. / Source: Dissertation Abstracts International, Volume: 43-05, Section: B, page: 1543. / Thesis (Ph.D.)--The Florida State University, 1982.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74827 |
| Contributors | SINCLAIR, DENNIS FRANKLIN., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 144 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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