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Computational Ecology and Software, 2011, 1(3):125-137<br />

127<br />

compet<strong>it</strong>ive mechan<strong>is</strong>ms <strong>in</strong> natural <strong>plant</strong> <strong>commun<strong>it</strong>ies</strong> have been <strong>in</strong>ferred from compar<strong>in</strong>g <strong>plant</strong> <strong>commun<strong>it</strong>ies</strong><br />

at different successional stages, the so-called “space for time subst<strong>it</strong>ution” (Barclay-Estrup and Gim<strong>in</strong>gham,<br />

1969; Bakker et al., 1996). F<strong>in</strong>ally, for test<strong>in</strong>g specific ecological hypotheses, <strong>it</strong> may be <strong>difficult</strong> <strong>to</strong> f<strong>in</strong>d natural<br />

<strong>plant</strong> <strong>commun<strong>it</strong>ies</strong> w<strong>it</strong>h the required variation <strong>in</strong> the <strong>in</strong><strong>it</strong>ial cond<strong>it</strong>ions and <strong>it</strong> has, therefore, become<br />

<strong>in</strong>creas<strong>in</strong>gly popular <strong>to</strong> study the mechan<strong>is</strong>m of <strong>compet<strong>it</strong>ion</strong> <strong>in</strong>directly by observ<strong>in</strong>g changes <strong>in</strong> synthetic or<br />

experimental <strong>plant</strong> <strong>commun<strong>it</strong>ies</strong> (Fukami et al., 2005; Ejrnæs et al., 2006; Fridley et al., 2007).<br />

The development of <strong>in</strong>direct methods for <strong>in</strong>ferr<strong>in</strong>g <strong>in</strong>terspecific compet<strong>it</strong>ive relationships has had a central<br />

role <strong>in</strong> the <strong>in</strong>creas<strong>in</strong>g awareness of the importance of l<strong>in</strong>k<strong>in</strong>g ecological data w<strong>it</strong>h quant<strong>it</strong>ative population<br />

models by means of advanced stat<strong>is</strong>tical approaches (Rees et al., 1996; Clark, 2007). However, <strong>in</strong> order <strong>to</strong> test<br />

specific hypotheses on the role of <strong>plant</strong> <strong>compet<strong>it</strong>ion</strong> <strong>in</strong> determ<strong>in</strong><strong>in</strong>g <strong>plant</strong> commun<strong>it</strong>y structures, <strong>it</strong> <strong>is</strong> necessary<br />

<strong>to</strong> make a direct l<strong>in</strong>k between the spatial arrangement of neighbour<strong>in</strong>g <strong>plant</strong>s and <strong>plant</strong> performance. Such<br />

direct studies of the importance of <strong>compet<strong>it</strong>ion</strong> have been performed under the head<strong>in</strong>g of neighbourhood<br />

analyses, <strong>where</strong> the effect of the d<strong>is</strong>tance between neighbour<strong>in</strong>g <strong>plant</strong>s on <strong>plant</strong> performance <strong>is</strong> quantified.<br />

Pacala and Silander (1990) described the commun<strong>it</strong>y dynamics between two annual <strong>plant</strong> species <strong>in</strong> a<br />

neighbourhood analys<strong>is</strong>, and Turnbull et al. (2004) estimated the <strong>in</strong>dividual-level <strong>compet<strong>it</strong>ion</strong> coefficients for<br />

seven annuals grow<strong>in</strong>g <strong>in</strong> limes<strong>to</strong>ne grassland over 2 years. However, the method of neighbourhood analys<strong>is</strong> <strong>is</strong><br />

only feasible <strong>in</strong> <strong>plant</strong> <strong>commun<strong>it</strong>ies</strong> that are dom<strong>in</strong>ated by <strong>plant</strong> species <strong>where</strong> <strong>it</strong> <strong>is</strong> easy <strong>to</strong> d<strong>is</strong>t<strong>in</strong>gu<strong>is</strong>h<br />

<strong>in</strong>dividual <strong>plant</strong>s, and many open natural herbal and grassland <strong>commun<strong>it</strong>ies</strong> are dom<strong>in</strong>ated by perennial species<br />

that form dense vegetation <strong>where</strong> <strong>it</strong> <strong>is</strong> <strong>difficult</strong> <strong>to</strong> d<strong>is</strong>t<strong>in</strong>gu<strong>is</strong>h <strong>in</strong>dividual <strong>plant</strong>s and, consequently, <strong>to</strong> determ<strong>in</strong>e<br />

dens<strong>it</strong>y. Furthermore, if <strong>in</strong>dividual <strong>plant</strong>s may be d<strong>is</strong>t<strong>in</strong>gu<strong>is</strong>hed, they almost always vary markedly <strong>in</strong> size, so<br />

that the number of neighbour<strong>in</strong>g <strong>in</strong>dividuals w<strong>it</strong>h<strong>in</strong> a certa<strong>in</strong> d<strong>is</strong>tance <strong>is</strong> of lim<strong>it</strong>ed value for describ<strong>in</strong>g the<br />

amount of <strong>compet<strong>it</strong>ion</strong> experienced by the target <strong>plant</strong>. More generally, the degree of <strong>compet<strong>it</strong>ion</strong> experienced<br />

by the target <strong>plant</strong> <strong>is</strong> expected <strong>to</strong> be species-specific spatial functions (<strong>compet<strong>it</strong>ion</strong> kernels or field-ofneighbourhoods)<br />

that depend cr<strong>it</strong>ically on the size and d<strong>is</strong>tances of the neighbour<strong>in</strong>g <strong>plant</strong>s (Berger and<br />

Hildenbrandt, 2000), and such field-of-neighbourhoods are not easily estimated <strong>in</strong> <strong>plant</strong> <strong>commun<strong>it</strong>ies</strong> w<strong>it</strong>h<br />

several species.<br />

In th<strong>is</strong> paper a novel method for measur<strong>in</strong>g <strong>compet<strong>it</strong>ion</strong> <strong>in</strong> und<strong>is</strong>turbed natural <strong>plant</strong> <strong>commun<strong>it</strong>ies</strong> <strong>is</strong><br />

d<strong>is</strong>cussed. The method allows direct measurements of the compet<strong>it</strong>ive effects of neighbour<strong>in</strong>g <strong>plant</strong>s on <strong>plant</strong><br />

performance and the estimation of parameters that describe the ecological processes of <strong>plant</strong>-<strong>plant</strong> <strong>in</strong>teractions<br />

dur<strong>in</strong>g the grow<strong>in</strong>g season as well as the process of survival and recru<strong>it</strong>ment between grow<strong>in</strong>g seasons us<strong>in</strong>g<br />

data from a standard p<strong>in</strong>-po<strong>in</strong>t analys<strong>is</strong> (Damgaard et al., 2009). In a p<strong>in</strong>-po<strong>in</strong>t analys<strong>is</strong>, a frame w<strong>it</strong>h a fixed<br />

grid pattern <strong>is</strong> placed above the vegetation. At each grid po<strong>in</strong>t, a p<strong>in</strong> <strong>is</strong> <strong>in</strong>serted vertically <strong>in</strong><strong>to</strong> the vegetation<br />

and the number of times the p<strong>in</strong> <strong>to</strong>uches different <strong>plant</strong> species <strong>is</strong> recorded (Levy and Madden, 1933; Kent and<br />

Coker, 1992). A p<strong>in</strong>-po<strong>in</strong>t measurement provides estimates of two important <strong>plant</strong> ecological variables: cover<br />

and vertical dens<strong>it</strong>y. The species cover <strong>is</strong> the relative area that a species “covers” when projected on<strong>to</strong> the twodimensional<br />

ground surface and, <strong>in</strong> a p<strong>in</strong>-po<strong>in</strong>t analys<strong>is</strong>, cover <strong>is</strong> estimated by the relative number of p<strong>in</strong>s that<br />

<strong>to</strong>uch the species. It <strong>is</strong> argued that cover <strong>in</strong> many open perennial <strong>plant</strong> <strong>commun<strong>it</strong>ies</strong> will be a more su<strong>it</strong>able<br />

predic<strong>to</strong>r of the compet<strong>it</strong>ive <strong>in</strong>teractions than local <strong>plant</strong> dens<strong>it</strong>y. The vertical dens<strong>it</strong>y <strong>is</strong> def<strong>in</strong>ed as the number<br />

of times a s<strong>in</strong>gle p<strong>in</strong> h<strong>it</strong>s a specific species (for a d<strong>is</strong>cussion on term<strong>in</strong>ology see Wilson, 2011), th<strong>is</strong> measure <strong>is</strong><br />

pos<strong>it</strong>ively related <strong>to</strong> the 3-dimensional space occupancy (or volume) of the species and has been shown <strong>to</strong> be a<br />

non-l<strong>in</strong>ear function of <strong>plant</strong> biomass (Jonasson, 1983, 1988). For most <strong>plant</strong> species, both the cover and the<br />

vertical dens<strong>it</strong>y will be relevant measures of the ecological success of the species (Damgaard et al., 2009).<br />

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