Modeling extreme risks in ecology

Towards a statistically robust determination of minimum water potential and hydraulic risk in plants

Minimum water potential (Ψ_min ) is a key variable for characterizing dehydration tolerance and hydraulic safety margins (HSMs) in plants. Ψ_min is usually estimated as the absolute minimum tissue Ψ experienced by a species, but this is problematic because sample extremes are affected by sample size and the underlying probability distribution. We compare alternative approaches to estimate Ψ_min and assess the corresponding uncertainties and biases; propose statistically robust estimation methods based on extreme value theory (EVT); and assess the implications of our results for the characterization of hydraulic risk. Our results show that current estimates of Ψ_min and HSMs are biased, as they are strongly affected by sample size. Because sampling effort is generally higher for species living in dry environments, the differences in current Ψ_min estimates between these species and those living under milder conditions are partly artefactual. When this bias is corrected using EVT methods, resulting HSMs tend to increase substantially with resistance to embolism across species. Although data availability and representativeness remain the main challenges for proper determination of Ψ_min , a closer look at Ψ distributions and the use of statistically robust methods to estimate Ψ_min opens new ground for characterizing plant hydraulic risks.

Testing the adaptive advantage of a threatened species over an invasive species using a stochastic population model

Introduced species are a major threat to freshwater biodiversity. Often eradication is not feasible, and management must focus on reducing impacts on native wildlife. This requires an understanding of how native species are affected but also how environmental characteristics influence population dynamics of both invasive and native species. Such insights can inform how to manipulate systems in order to take advantage of life-history traits native species possesses that invaders do not. The highly invasive fish, Gambusia holbrooki, has been implicated in the decline of many freshwater fish and amphibians. In south-eastern Australia, one of these is the threatened native fish, Galaxiella pusilla. As G. pusilla can survive periods without surface water, this presents an opportunity for adaptive management, given G. holbrooki lack these adaptations. We develop a stochastic population model to explore the impact of G. holbrooki on G. pusilla and test the feasibility of both natural and management-induced drying to protect this species. Our results support recent empirical studies showing G. holbrooki are a serious threat to G. pusilla persistence, especially through impacts on larval survival. While persistence is more likely in water bodies that frequently dry out, even optimal natural drying regimes may be insufficient when impacts from G. holbrooki are high. However, management-induced drying may allow persistence of G. pusilla in sites inhabited by both species. Given our model outcomes, the biology of these species and the habitats they occupy, we recommend maintaining or restoring aquatic and riparian vegetation and natural drying regimes to protect G. pusilla from G. holbrooki, in addition to undertaking management-induced drying of invaded water bodies. Our results provide insights into how the effects of G. holbrooki may be mitigated for other native species, which is important given this species is perhaps the most pervasive invader of freshwater ecosystems. We conclude with a discussion of the potential for using disturbance processes in the management of invasive species more broadly in freshwater and terrestrial systems.

Development of economic consequence methodology for process risk analysis

A comprehensive methodology for economic consequence analysis with appropriate models for risk analysis of process systems is proposed. This methodology uses loss functions to relate process deviations in a given scenario to economic losses. It consists of four steps: definition of a scenario, identification of losses, quantification of losses, and integration of losses. In this methodology, the process deviations that contribute to a given accident scenario are identified and mapped to assess potential consequences. Losses are assessed with an appropriate loss function (revised Taguchi, modified inverted normal) for each type of loss. The total loss is quantified by integrating different loss functions. The proposed methodology has been examined on two industrial case studies. Implementation of this new economic consequence methodology in quantitative risk assessment will provide better understanding and quantification of risk. This will improve design, decision making, and risk management strategies.

Metamodels for transdisciplinary analysis of wildlife population dynamics

Wildlife population models have been criticized for their narrow disciplinary perspective when analyzing complexity in coupled biological – physical – human systems. We describe a “metamodel” approach to species risk assessment when diverse threats act at different spatiotemporal scales, interact in non-linear ways, and are addressed by distinct disciplines. A metamodel links discrete, individual models that depict components of a complex system, governing the flow of information among models and the sequence of simulated events. Each model simulates processes specific to its disciplinary realm while being informed of changes in other metamodel components by accessing common descriptors of the system, populations, and individuals. Interactions among models are revealed as emergent properties of the system. We introduce a new metamodel platform, both to further explain key elements of the metamodel approach and as an example that we hope will facilitate the development of other platforms for implementing metamodels in population biology, species risk assessments, and conservation planning. We present two examples – one exploring the interactions of dispersal in metapopulations and the spread of infectious disease, the other examining predator-prey dynamics – to illustrate how metamodels can reveal complex processes and unexpected patterns when population dynamics are linked to additional extrinsic factors. Metamodels provide a flexible, extensible method for expanding population viability analyses beyond models of isolated population demographics into more complete representations of the external and intrinsic threats that must be understood and managed for species conservation.