Fit the N-mixture model of Royle (2004)

pcount(formula, data, K, mixture=c("P", "NB", "ZIP"),
    starts, method="BFGS", se=TRUE, engine=c("C", "R", "TMB"), threads=1, ...)



Double right-hand side formula describing covariates of detection and abundance, in that order


an unmarkedFramePCount object supplying data to the model.


Integer upper index of integration for N-mixture. This should be set high enough so that it does not affect the parameter estimates. Note that computation time will increase with K.


character specifying mixture: "P", "NB", or "ZIP".


vector of starting values


Optimization method used by optim.


logical specifying whether or not to compute standard errors.


Either "C", "R", or "TMB" to use fast C++ code, native R code, or TMB (required for random effects) during the optimization.


Set the number of threads to use for optimization in C++, if OpenMP is available on your system. Increasing the number of threads may speed up optimization in some cases by running the likelihood calculation in parallel. If threads=1 (the default), OpenMP is disabled.


Additional arguments to optim, such as lower and upper bounds


This function fits N-mixture model of Royle (2004) to spatially replicated count data.

See unmarkedFramePCount for a description of how to format data for pcount.

This function fits the latent N-mixture model for point count data (Royle 2004, Kery et al 2005).

The latent abundance distribution, \(f(N | \mathbf{\theta})\) can be set as a Poisson, negative binomial, or zero-inflated Poisson random variable, depending on the setting of the mixture argument, mixture = "P", mixture = "NB", mixture = "ZIP" respectively. For the first two distributions, the mean of \(N_i\) is \(\lambda_i\). If \(N_i \sim NB\), then an additional parameter, \(\alpha\), describes dispersion (lower \(\alpha\) implies higher variance). For the ZIP distribution, the mean is \(\lambda_i(1-\psi)\), where psi is the zero-inflation parameter.

The detection process is modeled as binomial: \(y_{ij} \sim Binomial(N_i, p_{ij})\).

Covariates of \(\lambda_i\) use the log link and covariates of \(p_{ij}\) use the logit link.


unmarkedFit object describing the model fit.


Ian Fiske and Richard Chandler

See also


Royle, J. A. (2004) N-Mixture Models for Estimating Population Size from Spatially Replicated Counts. Biometrics 60, pp. 108--105.

Kery, M., Royle, J. A., and Schmid, H. (2005) Modeling Avaian Abundance from Replicated Counts Using Binomial Mixture Models. Ecological Applications 15(4), pp. 1450--1461.

Johnson, N.L, A.W. Kemp, and S. Kotz. (2005) Univariate Discrete Distributions, 3rd ed. Wiley.


if (FALSE) { # Simulate data set.seed(35) nSites <- 100 nVisits <- 3 x <- rnorm(nSites) # a covariate beta0 <- 0 beta1 <- 1 lambda <- exp(beta0 + beta1*x) # expected counts at each site N <- rpois(nSites, lambda) # latent abundance y <- matrix(NA, nSites, nVisits) p <- c(0.3, 0.6, 0.8) # detection prob for each visit for(j in 1:nVisits) { y[,j] <- rbinom(nSites, N, p[j]) } # Organize data visitMat <- matrix(as.character(1:nVisits), nSites, nVisits, byrow=TRUE) umf <- unmarkedFramePCount(y=y, siteCovs=data.frame(x=x), obsCovs=list(visit=visitMat)) summary(umf) # Fit a model fm1 <- pcount(~visit-1 ~ x, umf, K=50) fm1 plogis(coef(fm1, type="det")) # Should be close to p # Empirical Bayes estimation of random effects (fm1re <- ranef(fm1)) plot(fm1re, subset=site %in% 1:25, xlim=c(-1,40)) sum(bup(fm1re)) # Estimated population size sum(N) # Actual population size # Real data data(mallard) mallardUMF <- unmarkedFramePCount(mallard.y, siteCovs =, obsCovs = mallard.obs) (fm.mallard <- pcount(~ ivel+ date + I(date^2) ~ length + elev + forest, mallardUMF, K=30)) (fm.mallard.nb <- pcount(~ date + I(date^2) ~ length + elev, mixture = "NB", mallardUMF, K=30)) }