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Predictive invasion ecology and management decisions under uncertainty Corey Chivers McGill University

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Ecological methodology for decision support Linking theory with data to make Inference, Prediction, & Decisions.

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Prediction is very hard, Prediction is very hard, especially about the future especially about the future -Niels Bohr, Danish physicist (1885-1962) -Niels Bohr, Danish physicist (1885-1962)

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Outcome A Outcome B Outcome C Outcome E Outcome F Do A Do B Do C Do D Do Nothing t = 0 t = 1 Time In a changing world, not making a decision has consequences, intended or otherwise.

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How do we make the best use of the data and theory that we have to make predictions which take into account (potentially large) inherent uncertainties?

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What information do I have? What can I go out and observe? Data The Process

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Data The Process

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All models are wrong, All models are wrong, But some are useful. But some are useful. -George E.P. Box -George E.P. Box

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Data The Process

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes Data The Process

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes Data The Process

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Data The Process pseudo-data

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Sampling periods

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Data The Process pseudo-data

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Data The Process pseudo-data

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Data The Process pseudo-data

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Does it fit the real data? Data The Process pseudo-data

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Does it fit the real data? Data The Process pseudo-data

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Does it fit the real data? Test Hypotheses Make forecasts (Forward Simulation) Data The Process pseudo-data

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Does it fit the real data? Test Hypotheses Make forecasts (Forward Simulation) Optimize Decisions Scenario Analysis Data The Process pseudo-data

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Invasive forest insects 1. International trade has many externalities 2. Total damages of existing pests 3. Estimate the probability of new high impact pest A. Guilds: which pathways? B. Economic sectors: who pays the costs?

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• Base line information lacking – Compile all known non-indigenous forest pests – Identify short list of intermediate damaging pests – • National economic estimates lacking – In depth analysis of the most damaging pests – 3 guilds (borers, sap suckers, foliage feeders) – 3 economic cost sectors (government, households, market) Emerald Ash Borer Hemlock Woolly Adelgid Gypsy Moth

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( ) ( ) ) ( ) | ( ) ( | | Pr 1 ϑ ϑ ϑ ϑ ϑ P c f P P M = m m       ∝ ∝ ∏ c c If we knew the cost of each pest, we can fit our models using the simple likelihood function. 0 1 2 3 4 5 6 7 8 0 2 4 6 8 Cost ($) Frequency of pests

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0 1 2 3 4 5 6 7 8 0 2 4 6 8 Cost ($) Frequency of pests 78 13 1 Pr (ϑ∣d)∝ [∏ i=1 I P(low∣ϑ) x∏ j=1 J P(intermediate∣ϑ) x∏ k=1 K P(high∣ϑ) ]P(ϑ) What we have are frequencies of species in different impact ranges.

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The Framework: A) Species Frequencies in 3 categories. B) Which Model? C) Model estimation D) Probability distribution of derived variable of interest (total cost, probability of new high impact pest) Aukema JE, Leung B, Kovacs K, Chivers C, Britton KO, et al. (2011) Economic Impacts of Non-Native Forest Insects in the Continental United States. PLoS ONE 6(9): e24587

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Does it fit the real data? Test Hypotheses Make forecasts (Forward Simulation) Optimize Decisions Scenario Analysis Data The Process pseudo-data

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Simulation Validation 1 Can we identify the Correct model?

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Simulation Validation 2 Given a model, can we recapture the parameters, and derived quantities of interest?

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Results Highest impact are the Borer guild. Costs are born primarily by local governments. ~1.7 Billion USD per annum Single most damaging pests in each guild accounts for 25-50% of the total impacts. At current establishment rates ~32% chance of another high impact pest in the next ten years. Aukema JE, Leung B, Kovacs K, Chivers C, Britton KO, et al. (2011) Economic Impacts of Non-Native Forest Insects in the Continental United States. PLoS ONE 6(9): e24587

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More imports, this time of the fishy sort. ● Given a proxy measure of propagule pressure, how well can we estimate the risk of establishment? Bradie, J., Chivers, C. & Leung, B. (2013) Importing risk: quantifying the propagule-pressure establishment relationship at the pathway level. in press Diversity and Distributions.

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● Not all species are equally likely to establish ● In the absence of species specific lifehistory information, how well can we estimate overal pathway risk?

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Bradie, J., Chivers, C. & Leung, B. (2013) Importing risk: quantifying the propagule-pressure establishment relationship at the pathway level. in press Diversity and Distributions. Effects of unaccounted variability

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Results At an import level of 100,000 individuals, establishment risk of 19% Importing 1 million individuals leads to just under a 1 in 2 chance of establishment. Bradie, J., Chivers, C. & Leung, B. (2013) Importing risk: quantifying the propagule-pressure establishment relationship at the pathway level. in press Diversity and Distributions.

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Alternative models of human behaviour ● Gravity Model – 'Pull' of attractive lakes ● Random Utility Model – Rational utility maximizers (Schneider et al. 1998, Leung et al. 2004, 2006) (Moore et al. 2005, Timar and Phaneuf 2009)

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Alternative models of human behaviour ● Gravity Model – 'Pull' of attractive lakes ● Random Utility Model – Rational utility maximizers PGM T nj =A n W j e D nj −d , n=1,... ,n , j=1,..., J. A n =1/∑ k =1 L W k e D nk −d . U nj =V nj +ϵ nj , n=1,... , N , j=1,... J V nj =   X nj PRUM T nj = expV nj  ∑ k=1 J expV nk  , n=1,... , N , j=1,... , J (Schneider et al. 1998, Leung et al. 2004, 2006) (Moore et al. 2005, Timar and Phaneuf 2009)

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Observing boater choice ● Online survey ● Which lakes did you visit? ● How many times?

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Chivers & Leung (2012)

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Figure A1: Simulated trip outcomes in a landscape of lakes with induced spatial auto-correlation. Size of circle is proportional to the size of the simulated lake.

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Figure A3: Generating vs maximum likelihood estimates for the four parameters (panels) of the random utility model. The 1:1 line is also plotted for comparison. Figure A2: Generating vs maximum likelihood estimates for the four parameters (panels) of the gravity model. The 1:1 line is also plotted for comparison. Re-capture the parameter values?

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Chivers & Leung (2012)

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∑ i=1 I w i =13 Low Entropy High Entropy Predicted Dispersal Networks ∑ i=1 I w i =13

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Chivers & Leung (2012)

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Managment of spreading aquatic invasives

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Behavioural Model The effect of costly cleaning impossed at a lake on boater choice. -Redistribute visits? -Reduce visits? -Both?

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1b =  P 1b  P 1b ∏ b=1 B N 1b N 1b '  1b N 1b ' 1− 1b N 1b −N 1b '  .N 2b ' N 2b  2b N 2b 1− 2b N 2b ' −N 2b  2b = P 2b P 2b  L ,|D= Where: , Policy Lake Non-Policy Lake Behavioural observation model

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Counterfactual stated preference

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Can I recapture model parameters from the amount and type of data I have?

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Scenario analysis

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What information do I have? What can I go out and observe? What are the hypothesized processes which generated the data? Theory/models Simulate Hypothesized Biological Processes How well can we recapture patterns and processes? (parameter estimation, model discrimination, & derived variables) Does it fit the real data? Test Hypotheses Make forecasts (Forward Simulation) Optimize Decisions Scenario Analysis Data Methodology for decision support pseudo-data

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Thank you Supervisors: Dr. Brian Leung Dr. Elena Bennett Dr. Claire De Mazancourt Dr. Gregor Fussman Lab Mates: Johanna Bradie Paul Edwards Kristina Marie Enciso Andrew Sellers Lidia Della Venezia Erin Gertzen