Helen Regan

Postdoctoral Research Fellow 
National Center for Ecological Analysis and Synthesis
University of California Santa Barbara
735 State St, Suite 300
Santa Barbara, CA 93101
Phone: +1 805 892 2522
Fax: +1 805 892 2510
Email: regan@nceas.ucsb.edu 

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Research Interests

I work predominantly on the characterisation and treatment of epistemic and linguistic uncertainty in ecology and conservation biology. I have applied Monte Carlo techniques, dependency bounds convolution, interval analysis and fuzzy set theory to a variety of problems. These include: calculation of global extinction rates; individual-based population models for Australian plants; the treatment of vagueness in the IUCN categories; the calculation of soil screening levels for contaminants; and contaminant exposure models for food webs. I am currently working on developing and testing methods for classifying conservation status and estimating risk.



Uncertainty can be categorised into two main types: epistemic and linguistic uncertainty. Epistemic uncertainty is the uncertainty associated with determinate facts - there is a fact of the matter about the state of a system but we are uncertain of what that fact is. Linguistic uncertainty, on the other hand, arises because much of our natural language, including our scientific vocabulary, is vague, ambiguous, context dependent and underspecific. Almost all of the scientific literature deals with epistemic uncertainty and yet linguistic uncertainty is prevalent in science, particularly in conservation biology and wildlife management where policy and decision-making play important roles. The most appropriate treatment of uncertainty depends on its source and the failure to deal with uncertainty appropriately can lead to misleading, or false, conclusions. I have investigated, compared and utilised a range of methods for the treatment of both types of uncertainty in a variety of problems in ecology and conservation biology. These treatments include: Relevant papers

Regan, H.M., B.E. Sample, and S. Ferson. Deterministic and Probabilistic Ecological Soil Screening Levels for Wildlife. Environmental Toxicology and Chemistry, 21(4):882-890, 2002.

Regan, H.M., M. Colyvan, and M.A. Burgman. A taxonomy and treatment of uncertainty for ecology and conservation biology. Ecological Applications, 12(2):618-628, 2002.

Elith, J., M.A. Burgman and H.M. Regan. Mapping epistemic uncertainty and vague concepts in predictions of species' distribution. Ecological Modelling, 157:313-329, 2002.

Regan, H.M., R. Lupia, A.N. Drinnan and M.A. Burgman. The currency and tempo of extinction. The American Naturalist, 157(1):1-10, January 2001.

Regan, H.M., M. Colyvan and M.A. Burgman. A Proposal for Fuzzy IUCN Categories and Criteria, Biological Conservation, 92(1):101-108, 2000.

Regan, H.M., and M. Colyvan. Fuzzy Sets and Threatened Species Classification, Conservation Biology, 14(4):1197-1199, August 2000.

Regan, H.M., B.K. Hope, and S. Ferson. Analysis and portrayal of uncertainty in a food web exposure model. Human and Ecological Risk Assessment, (in press).

Regan, H.M., H.R. Akçakaya, S. Ferson, K.V. Root, S. Carroll and L.R. Ginzburg. Treatments of uncertainty and variability in ecological risk assessment of single-species populations. Human and Ecological Risk Assessment, (in press).

Regan, H.M., S. Ferson, and D. Berleant. Equivalence of five methods for bounding uncertainty. International Journal of Approximate Reasoning, (in revision).


Decision Making

Uncertainty has considerable impact on our ability to make decisions. This is particularly relevant in conservation biology where it is often necessary to make decisions about the most beneficial course of action for species recovery plans and resource allocation. I am currently developing and testing methods for the treatment of uncertainty in threatened species classification protocols that are used at local, regional and global levels to make decisions about species conservation priorities. I am also using multi-criteria decision making processes to set conservation priorities at a state-wide level in California. These priorities will address key issues related to parkland requirements of California residents, public safety issues from increased natural threats arising from urban expansion, habitat preservation, agricultural land and ranchland preservation, maintenance of wetlands, and declining forestlands due to urban and suburban development. The results of this work will assist conservation managers and planners in making decisions in the face of uncertainty.

Relevant papers
Colyvan, M., H.M. Regan, and S. Ferson. Is it a crime to belong to a reference class?, The Journal of Political Philosophy, 9(2):168-181, 2001.
Also reprinted in H. Kyburg and M. Thalos (eds.) Probability is the Very Guide of Life, Open Court, Chicago (in press).

Regan, H.M., S.J. Andelman, M.A. Burgman, et al. A guide to setting bounds on parameters for threatened species classification. (in prep.)


Population Modeling

One way to deal with the uncertainty of potential outcomes of management actions for endangered species is to construct population models. By using all the available life history information about a species, and incorporating treatments for parameter uncertainty and environmental and demographic variation, it is possible to rank management alternatives according to which induces the lowest risk of decline or extinction. In collaboration with plant ecologists, I have constructed individual-based models for Australian plant species that incorporate density dependence through shading and clumping, predation of seeds by native rodents and birds, soil-stored seed banks and recruitment following fire events. I have also investigated the impact of a range of timber harvesting schedules on a rare carnivorous snail in north-west Tasmania using age-based matrix models.
Plant with flowering spear from the Australian grass tree family Xanthorrhoeaceae. Long grass-like leaves sprout from a trunk that can persist below or above ground level. Flowering generally occurs within four years after a fire. (Photo courtesy of the Australian National Botanic Gardens Seeds of Grevillea caleyi. Adult plants produce at most 15 seeds each, around 80% of which are eaten by native rodents before entering the soil-stored seed bank. (Photo courtesy of the Australian National Botanic Gardens
Relevant papers
Bearlin, A.R., M.A. Burgman, and H.M. Regan. A Stochastic Model for Seagrass (Zostera muelleri) in Port Phillip Bay, Victoria, Australia. Ecological Modelling, 118:131-148, 1999.

Regan, T.J., H.M. Regan, K. Bonham, R.J. Taylor, and M.A. Burgman. Modelling the impact of timber harvesting on a rare carnivorous land snail (Tasmaphena lamproides) in northwest Tasmania, Australia. Ecological Modelling, 139:253-264, 2001.

Regan H.M. Population Models: Individual-Based, in R.A. Pastorok, S.M. Bartell, S. Ferson, L.R. Ginzburg (eds.) Ecological Modeling in Risk Assessment: Chemical Effects on Populations, Ecosystems and Landscapes, Lewis Publishers, Boca Raton FL., pp. 65-82, 2002.

Akcakaya, H.R. and H.M. Regan. Population Models: Metapopulations, in R.A. Pastorok, S.M. Bartell, S. Ferson, L.R. Ginzburg (eds.) Ecological Modeling in Risk Assessment: Chemical Effects on Populations, Ecosystems and Landscapes, Lewis Publishers, Boca Raton FL., pp. 83-95, 2002.

Regan, H.M., T.D. Auld, D. Keith, and M.A. Burgman. The effects of fire and predation on the long-term persistence of an endangered shrub, Grevillea caleyi. Biological Conservation 109(1):73-83, 2003.

Taylor, R.J., T.J. Regan, H.M. Regan, M.A. Burgman and K.Bonham. Impacts of plantation development, harvesting schedules and rotation lengths on the rare snail Tasmaphena lamproides in northwest Tasmania: a population viability analysis. Forest Ecology and Management (in press).

Regan, H.M. and T.D. Auld. Using Population Viability Analysis for Management of an Endangered Australian Shrub, Grevillea caleyi. In H.R. Akçakaya, M.A. Burgman, O. Kindvall, P. Sjogren-Gulve, J. Hatfield, and M. McCarthy (eds.), Species Conservation and Management: Case Studies, Oxford University Press, (in press).

Pastorok, R.A., H.R. Akçakaya, H.M Regan, S. Ferson, and S.M. Bartell. Role of ecological modeling in risk assessment. Human and Ecological Risk Assessment, (in press).

Bartell, S.M., R.A. Pastorok, H.R. Akçakaya, H.M. Regan, S. Ferson and C. Mackay. Realism and relevance of ecological models used in chemical risk assessment. Human and Ecological Risk Assessment, (in press).

Tootell, N., H.M. Regan, D.A. Keith, and M. Tozer. Dynamics of disease and fire: an individual-based model of the grass tree Xanthorrhoea resinifera. (in prep.)


Numerical Solution to Partial Differential Equations

Uncertainty may also arise in models in which parameter values are known with certainty and stochastic processes are absent. Many equations that describe dynamic processes in the form of partial differential equations (PDEs) are prey to uncertainty when they are solved numerically. The extent of the introduced uncertainty depends on the algorithm adopted to solve them, the size of the time step and the spatial mesh imposed, and the stability criteria for the numerical method. For Hamiltonian wave equations, the impact of the numerical method on the solution can be monumental. Most of the standard algorithms used do not preserve the Hamiltonian dynamics and the resultant error propagation usually deems results unreliable. Symplectic methods, which discretise the Hamiltonian flow rather than the differential equations directly, are the best methods for preserving the Hamiltonian dynamics and reducing error propagation. Using von Neumann stability analysis, I have determined stability criteria for a variety of symplectic schemes applied to the sine-Gordon equation, the nonlinear Schrodinger equation, the linear wave equation and the KdV equation for both finite difference and pseudo-spectral spatial discretisation methods. I have also derived the conditions under which a variety of spatial discretisation approaches for these equations are equivalent.
Numerical solution of the nonlinear Schrodinger equation using a 2nd order symplectic integrator in combination with a pseudo-spectral spatial discretisation. 
Relevant papers
Stiles, P.J. and H.M. Regan. Transient Cellular Convection in Electrically Polarized Colloidal Suspensions, Journal of Colloid and Interface Science, 202(2):562-565, 1998.

Regan, H.M. Von Neumann stability analysis of symplectic integrators applied to Hamiltonian PDEs. Journal of Computational Mathematics, 20(6):pp, 2002.

Regan, H.M. Symplectic integration of Hamiltonian PDEs: equivalence of spatial discretisation techniques. (in prep.)