Estimation of Carrying Capacity of Recreational Grassland using a Mathematical Model of Turf Cover Growth

Abstract

(1) The growth of a hybrid Bermuda grass turf without trampling and the reduction of turf coverage due to the different levels of trampling stress under experimental condition were studied in the field of University of Osaka Prefectur.
(2) The increase of turf coverage without the trampling agreed with the logistic growth curve, 1/C dc/di=λ(1-C/C)
in which c is the coverage at a given time, C the upper limit of cover, which is 100%, and the intrinsic relative growth rate of turf cover.
(3) The percentage reduction of turf cover, 100 (c_a-c_b)/c_b, due to the stress of trampling can be approximated by c_a=c_bexp (-hν), in which c_a and c_b are the coverage of turf after and before the trampling, ν the intensity of trampling and h is a constant.
(4) The change of turf coverage due to increasing or decreasing stress of trampling were simulated assuming different values of intrinsic relative growth rate of turf growth. Though theoretically the change is exponential to changing trampling stress (ν), it could be approximated fairly well by a linear equation, c=100-aν, in which a is a constant.
(5) If we prepare a map of existing turf coverage, we can draw the areal change of turf cover by simulation. When the recreational intensity is reduced to 1 / n of actual trampling level, the coverage will recover to c/n-100/ n+100% of total ground surface, in which c is the the actual turf coverage under actual intensity of recreational use.
Thus we can estimate the level of trampling stress under which a desired level of turf coverage, can be maintained.