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Magurran & Henderson (2003) argued that all communities can be divided into residents and tourists (migrants). While it can sometimes be assumed that a sampled habitat is closed to migrants, when sampling large scale systems over extended periods this cannot be the case. This method estimates the species richness of the resident species and the rate of arrival of migrants for a habitat open to migrants.
The species acquisition curve is fitted to a hyperbolic-linear model that takes the form:
where S(n) is the number of species recorded after n samples,
Smax is the total number of resident species,
k1 is a parameter that determines the rate of acquisition of resident species it is the sampling effort needed to collect half the total number of resident species and
k2 is a parameter that describes the rate of acquisition of migratory (non-resident) species.
The hyperbolic-linear model is fitted using non-linear regression. For some sets of data the initial values chosen by the program may be inappropriate, leading to a failure to find a solution. This is most likely to occur if you are using data which do not fit this model.
This equation is best fitted to a species acquisition curve smoothed by averaging the randomised order of the samples.
The output gives the predicted increase in species number with sampling effort which is also presented graphically.
At the top of the output grid (see below) the estimated model parameters are given:
Resident Species: this is the estimated number of resident species living permanently in the habitat. In the example below the community is estimated to hold about 61 residents.
No Sample for 1/2 Sp. Max.: this gives the number of samples required to produce a species list comprising half the total number of resident species.
Migrant Sp./sample: This gives the rate of acquisition of migrants in migrants per sample. In the example below 0.085 migrants arrive per sample, or expressed another way, it requires on average 100 samples to capture 8.5 migrant species.
Note that this model solves using a non-linear regression method that can fail to give a result if the initial parameter guesses are poor or if the data set is inappropriate.
The graph below shows the type of data that are appropriate and the predicted curve that was fitted by the program.