Tail associations in ecological variables and their impact on extinction risk

Abstract

Extreme climatic events (ECEs) are becoming more frequent and more intense due to climate change. Furthermore, there is reason to believe ECEs may modify "tail associations" between distinct population vital rates, or between values of an environmental variable measured in different locations. "Tail associations" between two variables are associations that occur between values in the left or right tails of the distributions of the variables. Two positively associated variables can be principally "left-tail associated" (i.e., more correlated when they take low values than when they take high values) or "right-tail associated" (more correlated when they take high than low values), even with the same overall correlation coefficient in both cases. We tested, in the context of non-spatial stage-structured matrix models, whether tail associations between stage-specific vital rates may influence extinction risk. We also tested whether the nature of spatial tail associations of environmental variables can influence metapopulation extinction risk. For instance, if low values of an environmental variable reduce the growth rates of local populations, one may expect that left-tail associations increase metapopulation extinction risks because then environmental "catastrophes" are spatially synchronized, presumably reducing the potential for rescue effects. For the non-spatial, stage-structured models we considered, left-tail associations between vital rates did accentuate extinction risk compared to right-tail associations, but the effect was small. In contrast, we showed that density dependence interacts with tail associations to influence metapopulation extinction risk substantially: For population models showing undercompensatory density dependence, left-tail associations in environmental variables often strongly accentuated and right-tail associations mitigated extinction risk, whereas the reverse was usually true for models showing overcompensatory density dependence. Tail associations and their asymmetries are taken into account in assessing risks in finance and other fields, but to our knowledge, our study is one of the first to consider how tail associations influence population extinction risk. Our modeling results provide an initial demonstration of a new mechanism influencing extinction risks and, in our view, should help motivate more comprehensive study of the mechanism and its importance for real populations in future work.