MODELING MARKOVIAN DEPENDENCE IN POPULATIONS OF ARALIA-NUDICAULIS

I examined spatial patterns of two populations of the clonal herb Aralia nudicaulis for evidence of spatial inhibition among neighboring ramets. Second-order spatial analysis revealed that ramet patterns of both populations were regular at local spatial scales, a result consistent with the proposition that localized, inter-ramet interactions are important in reducing spatial overlap. Localized ramet interactions suggest Markovian dependence, which is defined when an event (e.g., occurrence of a ramet) at X is dependent solely on the existence or otherwise of an event within a distance delta of X. Evidence of Markovian dependence in the populations was tested by fitting Markov point-process models to the observed ramet patterns. The populations conformed well to the Markov model, the results indicating that both ramet spatial patterns were Markov of range delta = 18 cm. This inhibition distance corresponds closely to the mean horizontal radius of an A. nudicaulis ramet, indicating that interactions occur at the spatial scale of the individual. I suggest that a likely mechanism for the development of locally regular spatial patterns in these populations is inter-ramet competition for a limiting resource, probably light.