Statistical analysis of spatial patterns of the heliozoanActinophrys sol

Cell-to-cell interaction and spatial distribution of the heliozoanActinophrys sol was analyzed with computer-aided video microscopy. By means of goodness-of-fit statistics (χ2 analysis) and a quadrat-count analysis (Iδ-curve analysis), the spatial point pattern of the cells was shown to be of regular distribution, which implies that a regulating mechanism is operating to encourage an even spatial distribution of the cell centers ofActinophrys. An attempt was further made to define a unified model which fitsActinophrys cell distribution observed at different cell densities. For this purpose, the fitting of a parameterized potential function φ (r)=(σ/r)12 was carried out, wherer is the distance between cell centers of two neighboring cells. The scaling parameter a was estimated from the maximum likelihood procedure for obtaining the best fit for the data, which was found to be a decreasing function of the cell density; we obtained σ = 0.44 mm at a low cell density (0.5 cell/mm2) and σ=0.10 mm at the highest cell density (6.5 cells/mm2). These results suggest that (1) the possible nearest distance between two neighboring cells is primarily defined by the axopodial length, and (2) at lower cell densities,Actinophrys can recognize the presence of distant neighboring cells by some unknown means.