Presynaptic population model. *A*: each of *n*_{e} = 150 presynaptic spike trains drives *M* = 5 synaptic contacts to produce the first neuron's total excitatory synaptic conductance, *g*_{E,1}(*t*). The sum of these presynaptic spike trains is denoted *E*_{1}(*t*) and similarly for *E*_{2}(*t*), *I*_{1}(*t*), and *I*_{2}(*t*). Every pair of presynaptic spike trains is correlated with coefficient, ρ_{in}(*t*). Correlation between the excitatory population spike trains is denoted ρ_{EE}(*t*) and similarly for ρ_{II} (*t*) and ρ_{EI}(*t*). *B*: population conductances, *g*_{E,2}(*t*), *g*_{I,1}(*t*), and *g*_{I,2}(*t*) are constructed analogously to *g*_{E,1}(*t*) in *A* and their pairwise correlations are denoted ρ_{gEgE}(*t*), ρ_{gIgI}(*t*), and ρ_{gEgI} (*t*). Population conductances drive two postsynaptic neurons to produce two output spike trains, *s*_{1}(*t*) and *s*_{2}(*t*), with correlation given by ρ_{out}(*t*). We are interested in how ρ_{in}(*t*) is transferred to ρ_{out}(*t*).