It looks like most of the selection-based research is on temporal lobes (specifically the hippocampus) even in lower vertibrates. Admittedly, I've only read titles and abstracts here and my molecular and evolutionary background is lacking, but it seems in line with my thinking.
Spatial reasoning is selected for
"Natural selection, sexual selection and artificial selection have resulted in an increase in the size of the hippocampus in a remarkably diverse group of animals that rely on spatial abilities to solve ecologically important problems."
http://www.sciencedirect.com/science/article/pii/016622369290080R
"Hippocampal size is known to correlate positively with [...] selective pressure for spatial memory among passerine bird species."
http://www.pnas.org/content/87/16/6349
"We analyze here recent data indicating a close functional similarity between spatial cognition mechanisms in different groups of vertebrates, mammals, birds, reptiles, and teleost fish, and we show in addition that they rely on homologous neural mechanisms."
http://europepmc.org/abstract/MED/12937346/reload=0;jsessionid=wkOr9UZf7m88bA5u5O3H.4
" The hypothesis that gathering-specific spatial adaptations exist in the human mind is further supported by our finding that spatial memory is preferentially engaged for resources with higher nutritional quality (e.g. caloric density). "
http://www.ncbi.nlm.nih.gov/pubmed/17711835
" in the avian telencephalon, there is a separation of visual motion and spatial-pattern perception as there is in the mammalian telencephalon. However, this separation of function is in the targets of the tectofugal pathway in pigeons rather than in the thalamofugal pathway as described in mammals."
http://www.ncbi.nlm.nih.gov/pubmed/15163688spatial reasoning underlies abstract reasoning
This, I think, is why we so commonly use concept of space in the sciences, we even take non-spatial variables and plot them against each other and call it phase space in order to get better idea of what a system is doing. Every time we plot a variable, we're translating that variable to space. We assume all the properties of space for most classical variables (continuity, smoothness, deterministic trajectories in Euclidian space). Here's more research about using spatial reasoning for thinking about other things:
musical pitch:
http://www.sciencedirect.com/science/article/pii/S0010027705000260
numbers:
http://www.tandfonline.com/doi/abs/10.1080/135467996387552#.UrJAGPRDuMM
time:
http://onlinelibrary.wiley.com/doi/10.1111/j.1551-6709.2010.01094.x/abstract;jsessionid=7867474264EC5E729B9863EF5DE600E8.f02t04
Conflict with QM
Spatial reasoning relies on continuity, smoothness, and locality. The unintuitive concepts in QM are exactly the ones that conflict with these: nonlocality, discretization, uncertainty. Particles can't have a precisely defined position and momentum, a particles can exist in a superposition of states.
Ode to learning
Obviously, without learning, none of this would be possible... learning is necessary, but (imo) insufficient to explain our readily available grasp of spatial reasoning. It's interesting that how we learn is influenced by spatial concepts, so in some sense, the adaptation of learning itself may be closely tied to spatial reasoning.