tl;dr: pick a segregation measure from the seg package, probably the isp() function as an implementation of White (1983).
I'd recommend using an entropy segregation measure. Probably you need some sort of conditional entropy, telling you how much of the information in one spatial distribution is contained in the other.
Segregation is not easily expressed on a single dimension. E.g. Massey & Denton (1988) try to split it into evenness, exposure, concentration, centralization, and clustering. That's not a big problem, you just need to know what the measure you use does exactly and whether that's what matters in your case.
There's a lot of literature on the subject, here's a (far from comprehensive) overview. If you have a look at only the publications marked in italic you should get a rough idea of what's been going on in the field.
Mesuring segregation literature
- Jahn, J., Schmid, C. F. & Schrag, C. The mea- surement of ecological segregation. American Sociological Review 293–303 (1947).
- Williams, J. J. Another commentary on so-called segregation indices. American Sociological Re- view 298–303 (1948).
- Duncan, O. D. & Duncan, B. A methodological analysis of segregation indexes. American sociological review 210–217 (1955).
- Taeuber, K. E. & Taeuber, A. F. Negroes in cities: Residential segregation and neighborhood change (Atheneum, 1969).
- Henri Theil, A. J. F. A note on the measure- ment of racial integration of schools by means of informational concepts. The Journal of Mathematical Sociology 1:2, 187–193 (1971).
- White, M. J. The measurement of spatial segregation. American journal of sociology 1008–1018 (1983)
- Morgan, B. S. An alternate approach to the development of a distance-based measure of racial segregation. American Journal of Sociology 1237– 1249 (1983)
- _Massey, D. S. & Denton, N. A. The dimensions of residential segregation. Social forces 67, 281–315 (1988).
- Wong, D. W. Spatial dependency of segregation indices. The Canadian Geographer/Le Géographe canadien 41, 128–136 (1997)
- Leibovici, D. G. Defining spatial entropy from multivariate distributions of co-occurrences. In International Conference on Spatial Information Theory, 392–404 (Springer, 2009).
- Leibovici, D. G., Claramunt, C., Le Guyader, D. & Brosset, D. Local and global spatio-temporal entropy indices based on distance-ratios and co- occurrences distributions. International Journal of Geographical Information Science 28, 1061– 1084 (2014)
- Vranken, I., Baudry, J., Aubinet, M., Visser, M. & Bogaert, J. A review on the use of entropy in landscape ecology: heterogeneity, unpredictability, scale dependence and their links with thermodynamics. Landscape Ecology 30, 51– 65 (2015). URL http://dx.doi.org/10.1007/ s10980-014-0105-0. DOI 10.1007/s10980-014- 0105-0.
White 1983 may be directly applicable in your case. Duncan & Duncan 1955 is a beautiful paper that sums up the literature to that point perfectly. Massey & Denton 1988 give you really good insight into the different dimensions of segregation. Vranken et al. 2015 is an insane overview over entropy measures in landscape ecology.
Mesuring segregation in R
- have a look at the seg package. It's an implementation of a number of indicies mentioned above and a few other important ones. You should check the publications mentioned in the documentation.
- Also, Leibovici et al. published some code, it is for point data though I think. Maybe it's overly complicated for what you are trying to achieve, but I included them anyway because they deal specifically with co-occurances, which closely matches your question.
Please be aware that a lot of these measures are highly sensitive to the resolution / zones that you use!