Each history term is modulated by one θ parameter. Equation 1 represents the full model encompassing the influence of space, time, and distance on spiking activity (“S+T+D” model). We similarly defined six nested models (Figure S4A): Selleckchem AZD6738 equation(Equation 7) λS+T(t)=λtime(t)·λspace(t)·λspeed(t)·λhistory(t)λS+T(t)=λtime(t)·λspace(t)·λspeed(t)·λhistory(t) equation(Equation 8)

λT+D(t)=λtime(t)·λdistance(t)·λspeed(t)·λhistory(t)λT+D(t)=λtime(t)·λdistance(t)·λspeed(t)·λhistory(t) equation(Equation 9) λS+D(t)=λdistance(t)·λspace(t)·λspeed(t)·λhistory(t)λS+D(t)=λdistance(t)·λspace(t)·λspeed(t)·λhistory(t) equation(Equation 10) λD(t)=λdistance(t)·λspeed(t)·λhistory(t)λD(t)=λdistance(t)·λspeed(t)·λhistory(t) equation(Equation 11) λS(t)=λspace(t)·λspeed(t)·λhistory(t)λS(t)=λspace(t)·λspeed(t)·λhistory(t) equation(Equation 12) λT(t)=λtime(t)·λspeed(t)·λhistory(t)λT(t)=λtime(t)·λspeed(t)·λhistory(t) Equation 7 defines the space and time (“S+T”) model, Equation 8 defines Selleck BMS-387032 the time and distance (“T+D”) model, Equation 9 defines the space and distance (“S+D”) model, Equation 10 defines the distance (“D”) model, Equation 11 defines the space (“S”) model, and Equation 12 defines the time (“T”) model. The parameters for each model were estimated using

an iterative Newton-Raphson method to maximize the likelihood function, as described in Lepage et al. (2012). The resulting maximum likelihoods (Γi)(Γi) for each model (λiλi) were then used in likelihood ratio tests to compare each nested model to the full model to determine whether the additional covariates provided significant information about spiking. equation(Equation 13) Sodium butyrate D(S+T+D)−S=2(ln(ΓS+T+D)−ln(ΓT+D))D(S+T+D)−S=2(ln(ΓS+T+D)−ln(ΓT+D)) equation(Equation 14) D(S+T+D)−(T+D)=2(ln(ΓS+T+D)−ln(SΓ))D(S+T+D)−(T+D)=2(ln(ΓS+T+D)−ln(ΓS))

equation(Equation 15) D(S+T+D)−T=2(ln(ΓS+T+D)−ln(ΓS+D))D(S+T+D)−T=2(ln(ΓS+T+D)−ln(ΓS+D)) equation(Equation 16) D(S+T+D)−D=2(ln(ΓS+T+D)−ln(ΓS+T))D(S+T+D)−D=2(ln(ΓS+T+D)−ln(ΓS+T)) Equations 13 and 14 calculate the deviance of the “T+D” model and “S” model respectively from the full model due to the removal of the covariates missing from the nested model. The results are shown in Figures S4B and S4C. Note that D(S+T+D)−SD(S+T+D)−S is calculated using ΓT+DΓT+D (the likelihood of the model with time and distance, but without space), such that the larger the value of D(S+T+D)−SD(S+T+D)−S, the larger the influence of space on spiking activity. Under the null hypothesis, that the addition of space to the nested model containing time and distance does not provide more information about spiking activity, the test statistic D(S+T+D)−SD(S+T+D)−S has a χ2-distribution with 5 degrees of freedom.