Variance and extreme events in population ecology

Assessing, managing, and communicating variance and risk is fundamental to effective ecological decision making. One promising approach is to borrow concepts from financial portfolio management. Ecological populations behave like portfolios in many ways—we can treat the abundance of populations, such as salmon in streams, as financial stock value, and groups of populations, such as salmon within a river catchment, as portfolios. If a group of populations react differently to an environmental event then the probability of sudden decline may be lowered, similar to a diversified financial portfolio. This risk reduction has been referred to as the portfolio effect. In this thesis I consider three applications of portfolio concepts to ecology. I begin by evaluating ways of estimating portfolio effects and applying these metrics to moth, reef fish, and salmon metapopulations from around the world. I show an inherent bias to a commonly used method, develop a new method based on Taylor's power law of mean--variance scaling, and outline recommendations for estimating portfolio effects. Next, I use a portfolio approach to inform conservation priorities for salmon populations under a changing climate. I show that preserving a diversity of thermal tolerances minimizes risk and ensures persistence given long-term environmental change. However, this reduction in variability can come at the expense of long-term persistence if climate change increasingly restricts available habitat, forcing ecological managers to balance society's desire for short-term stability and long-term viability. Finally, I take the concept of black swans (extreme and unexpected events) from the financial literature and ask what the evidence is for these events across hundreds of bird, mammal, insect, and fish abundance time series. I find strong evidence for the infrequent (3–5\%) occurrence of ecological black swans. Black swans are predominantly (87%) downward events and tend to be associated with extreme climate, natural enemies (predators and parasites), or the combined effects of multiple factors, with little relationship to life history. My thesis demonstrates the importance of conserving ecological properties that may contribute to portfolio effects, such as thermal-tolerance diversity and habitat heterogeneity, and developing conservation strategies that are robust to unexpected extreme events.