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 <= 7 primary sampling periods. We compare estimates with those under a variation of the model applied to standard data, where secondary samples are pooled. The latter model yielded unrealistically high estimates of total community size of 274 species. In contrast, estimates were similar under models applied to RD data with constant (122) or seasonally varying (126) detectability for each species, but the former was more parsimonious and therefore used for inference. Per transect, 6 44 (mean 21.1) species were detected. Species richness estimates averaged 29.3; therefore only 71% (range 32-92%) of all species present were ever detected. In any primary period, 0.4-5.6 species present were overlooked. Detectability varied by species and averaged 0.88 per primary sampling period. Our modeling framework is extremely flexible; extensions such as covariates for the occurrence or detectability of individual species are easy. It should be useful for communities with a predictable form of temporary emigration where rigorous estimation of community metrics has proved challenging so far.