The changes in reproductive strategies in response to environmental change, comparing the spatial niche and neutral cases.

<p>The spatial heterogeneity is fixed at <i>k = </i>16, and the white boxplot represent the spatial niche case and the grey boxplots represent the neutral case. Panel (a) represents the case in which frequency of environmental change is high, i.e., <i>p = </i>0.1, and panel (b) represents the case of low frequency of environmental change (<i>p = </i>0.01). Within each panel, the difference of the magnitude of environmental change is illustrated: <i>q = </i>0.1 at the top, <i>q = </i>0.01 in the middle, and <i>q</i> = 0 at the bottom. When <i>q = </i>0, it is identical to <i>p = </i>0, because it means there is no environmental change.</p

The frequency distributions of reproductive strategies in both the spatial niche and the neutral cases.

<p>The frequency of environmental change is fixed at <i>q = </i>0.1. The left side panels (a–c) represent the spatial niche case and the right side panels (d–f) represent the neutral case. The three layers of panels represent the different magnitudes of change: <i>p = </i>0.1 in the top panels (a, d), <i>p = </i>0.01 in the middle panels (b, e), and <i>p = </i>0 in the bottom panels (c, f). Within each panel, habitat heterogeneity is indicated: <i>k = </i>25 for the upper boxplot and <i>k = </i>4 for the lower boxplot. White boxplots represent the spatial niche case and the grey boxplots represent the neutral case.</p

Several patterns of the frequency distribution for reproductive strategies.

<p>The horizontal axis represents the reproductive strategy (<i>P</i>) of an individual plant (0: seed reproduction only, 1: clonal reproduction only), and the vertical axis represents the frequency of each value of <i>P</i> in the plant population. This depends on the degree of environmental change in a habitat and the number of spatial niches. The number of habitats is fixed at <i>k</i> = 16. The values describing the environmental change for each line are: thick solid line corresponds to (<i>p</i>, <i>q</i>) = (0, 0), solid line with open circles corresponds to (<i>p</i>, <i>q</i>) = (0.01, 0.01), solid line with close circles corresponds to (<i>p</i>, <i>q</i>) = (0.01, 0.1), dotted line with open circles corresponds to (<i>p</i>, <i>q</i>) = (0.1, 0.01), and dashed line with close circles corresponds to (<i>p</i>, <i>q</i>) = (0.1, 0.1).</p

The visual concept of spatial heterogeneity on the habitat lattice and the plant mortality rate

<p>. The figure (a) represents the concept of spatial heterogeneity. The grey scale in the squares represents the trait value (0–1) of the habitat: the value for the pure white habitat is zero and that for the pure black habitat is one. In this case, there are 16 different habitats (<i>E</i>_1,<i>t</i>, <i>E</i>_2,<i>t</i>,…<i>E</i>_16,<i>t</i>) within the total lattice space and each habitat has 2×2 square sites. The grey scale in circles represents the plant trait value (<i>Q</i>_ij). The similarity of the grey scale between <i>E</i>_l,t and <i>Q</i>_ij determines the death rate of the individual plant inhabiting (i, j), and its relationship is illustrated in (b). The two combinations of square and circle are the example of the difference between habitat and plant trait values in (b).</p

Parameters in the model.

<p>Parameters in the model.</p

Variables in the model.

<p>Variables in the model.</p

The flow chart for the spatially explicit individual-based simulation of plant dynamics.

<p>The flow chart for the spatially explicit individual-based simulation of plant dynamics.</p