A method for analysing spatio‐temporal pattern in plant establishment, tested on a Populus balsamifera clone

Abstract

1 Ecological patterns in space and time have been well documented using interval variables such as plant density. In this paper, we use join Page: 1Is the text OK: join count statistics to examine spatio‐temporal patterns in a binary variable, plant establishment. 2 Establishment along a belt transect is represented as a grid or lattice in which each cell denotes a particular quadrat in a particular year. A cell is ‘black’ if a plant established at that particular time and place; otherwise it is ‘white’. 3 Each pair of black cells is connected by a ‘join’ that represents the association between stems established at two different places and times. Join ‘length’ is the pair of factors (s,t) that describes the distance between stems in space and in time, respectively. Spatio‐temporal pattern is detected by comparing the number of joins of each ‘length’ in a particular lattice with the expected number calculated from lattices generated by three different random models. Colonization rates can be estimated if there are particular join classes that occur more frequently than expected. 4 Artificially generated lattices were used to examine the effect of background noise on the ability to detect underlying pattern. 5 Field data were obtained from a Populus balsamifera clone that was colonizing a grassland. Three belt transects, 1 m wide and up to 13 m in length, were established, and ramets in each 0.5‐m interval were aged by tree ring counts. Position and age were used to construct a lattice of stem establishment. 6 We were able to discern a pattern both in artificial lattices and in the colonization of P. balsamifera ramets. Ramets took between 1 and 2 years to advance 1 m into the grassland (equivalent to a rate of 0.5–1 m per year). 7 Describing plant establishment in space and time with two‐factor join count statistics provides a way of measuring the rate of species movement at the scale of the individual.