title: Viability of cyclic populations.
abstract: Theory on viability of small populations is well developed and has led to the standard methodology of population viability analysis (PVA) to assess vulnerability of single species. However, more complex situations involving community dynamics or environmental change violate theoretical assumptions. Synthesizing concepts from population, community, and conservation ecology, we develop a generic theory on the viability of cyclic populations. The interplay of periodic population decline and demography causes varying risk patterns that aggregate during cycles and modify the temporal structure of viability. This variability is visualized and quantitatively assessed. For two standard viability metrics that summarize immediate extinction risk and the general long-term conditions of populations, we mathematically describe the impact of population cycles. Finally, we suggest and demonstrate PVA for cyclic populations that respond to, e.g., seasonality, interannual variation, or trophic interactions. Our theoretical and methodological advancement opens a route to viability analysis in food webs and trophic meta-communities and equips biodiversity conservation with a long-missing tool.
authors.affiliation: Department of Ecological Modelling, Helmholtz-Centre for Environmental Research-UFZ, Permoserstrasse 15, D-04318, Leipzig, Germany.|German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5e, D-04103, Leipzig, Germany.
authors.forename: Alexander
authors.initials: A
authors.lastname: Singer
authors.affiliation: Department of Ecological Modelling, Helmholtz-Centre for Environmental Research-UFZ, Permoserstrasse 15, D-04318, Leipzig, Germany.|German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5e, D-04103, Leipzig, Germany.|Institute for Environmental Systems Research, University of Osnabrück, Barbarastrasse 12, D-49076, Osnabrück, Germany.
authors.forename: Karin
authors.initials: K
authors.lastname: Frank
mesh_terms: D000818:Animals; D053476:Extinction, Biological; D008954:Models, Biological; D010507:Periodicity; D011157:Population Dynamics; D012621:Seasons
keywords: community; interannual variation; periodicity; persistence; seasonality; stochastic