Basic ideas behind spatial CMR

As we have seen, we can use capture histories over multiple occasions to estimate abundance (N), dealing with various sources of heterogeneity in capture probabilities (p) by a series of models.   Although this approach can provide reliable estimation of N, these estimates can prove to be of limited use unless it is known what the spatial extent (area=A) of the capture influence is.  That is, suppose we estimate N=100 but do not know if this applies to 100 ha or to 200 ha.  The estimate of N will be of little biological meaning, and likewise we don't have a reliable way of estimating density (N/A).  In Week 7 we looked at some possible ways of estimating an 'effective trap area', as well as alternatives such as trapping webs based on distance sampling that directly provide estimates of D.

Here we consider a different approach, in which spatial information about "trap" locations is used along with capture-recapture information, to model how animals move in space, and therefore, provide inference about density. A common (but not required) design would involve a trapping grid such as the one below, in which the locations of each trap area recorded in an array (A1-- H8) in the example but are ultimately expressable in the Cartesian coordinate system (e.g., as UTM eastings and northings).    The data then are the captures of animals on multiple occasions at one or more trap location. Below are is an example of the spatio-temporal captures of 20 individuals (circles may represent > 1 individual) over 6 sampling occasions, with focus on 3 individuals (red circles; see Efford et al. 2009a for more details).

An important part of the estimation problem hinges on the scale parameter (sigma), which can be roughly interpreted as the average movement radius.  A basic model is then based on a half-normal distribution of distance of animals from each trap location (s). 

ps = g0 exp[d2/(2sigma2)]

where d is the Euclidian distance of a trap location from an animals home range center.   Animals home range centers are assumed to be distributed uniformly over a  landscape ("state-space") that contains the trap grid but may expand beyond it.  The parameter g0 then represents the capture probability for an animal at a trap placed exactly at its home range center.

An important point to note is that "traps" may-- and often will - be "passive" rather than "active".  That is, they may simply record animals that happen to be passing through the trap grid rather than those that are actively attracted to and /or captured in a physical trap. Obvious example include arrays of camera traps, particularly in cases where animals are "marked" by observation of some physical characteristic, such as antler configurations (male deer), stripes (tigers), or scars (marine mammals).  Alternatively, detection of marine vertebrates by acoustic arrays can be consider a form of passive detection. 

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