Species richness and occupancy estimation in communities subject to temporary emigration

Species richness is the most common biodiversity metric, although typically some species remain unobserved. Therefore, estimates of species richness and related quantities should account for imperfect detectability. Community dynamics can often be represented as superposition of species-specific phenologies (e. g., in taxa with well-defined flight [insects], activity [rodents], or vegetation periods [plants]). We develop a model for such predictably open communities wherein species richness is expressed as the sum over observed and unobserved species of estimated species-specific and site-specific occurrence indicators and where seasonal occurrence is modeled as a species-specific function of time. Our model is a multispecies extension of a multistate model with one unobservable state and represents a parsimonious way of dealing with a widespread form of 'temporary emigration.'' For illustration we use Swiss butterfly monitoring data collected under a robust design (RD); species were recorded on 13 transects during two secondary periods within