By Arora S., Karakostas G.
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Additional info for A 2 + approximation algorithm for the k-MST problem
In many locations its spread has been correlated with a decrease in the abundance of wading birds due to its occupation of feeding sites (Goss-Custard & Moser, 1988), and it has also threatened to colonise amenity beaches (Truscott, 1984). Both of these examples are human-aided invasions and illustrate the speed with which range expansion may occur. Whilst they have occurred in recent history, charting their spread on a geographic scale and identifying phases in the invasion process remain impractical because of the lack of records.
As a result of dispersal, propagules (seeds or plant fragments) arrive at a site beyond their previous geographic range and establish populations of adult plants. 2. Colonisation. The plants in the founding population reproduce and increase in number to form a colony which is self-perpetuating. 3. Naturalisation. The species establishes new self-perpetuating populations, undergoes widespread dispersal and becomes incorporated within the resident flora. It is only once the third stage is reached that the species is likely to be considered a nuisance and classed as a weed.
Such frequency distributions can be summarised by regression modelling; Auld et al. 1) where n is frequency, rfis distance from nearest previous location, and c and s are parameters. Auld et al. (1982) refer to s as the 'spread gradient'. The lower the value of s, the more the species will tend to spread by isolated outbreaks, rather than as an advancing front. There are problems with interpreting these regression curves. When a species is just beginning to spread outwards from a single source, the relationship will represent the true frequency distribution of distances How can we measure rate of spreadfrom available data?