[R-sig-Geo] Center of mass of a SpatialPointsDataFrame object - Which projection?

[PCB]

Dear All,

I have a dataset that represents measurements of fish density at a number of
sampling locations at sea, in several different occasions (the sampling
locations are not always the same), stored as a a list of
SpatialPointsDataFrame objects.

I want to calculate the center of mass of each distribution, to describe
whether there is a trend in the overall distribution of the fish.

I have three main questions:
a) Should I use the original points for calculating the centre of mass, or
should I interpolate them first to a grid? I assume doing it on the original
points will make the result dependent on the location of these points, that
is really not linked to the underlying fish distribution
b) Should I reproject the data before calculating the center of mass (they
are in lon-lat). If so, which projection should I use?
c) A rectangular grid will include many locations on land, where no fish
could have been recorded anyway. How do I get a grid I can use to
meaningfully calculate the center of mass?

Thanks for your time, and any pointers will be highly appreciated.

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