Bianca Bauch

1. Assessing the efficiency of simple Bayesian Belief Network models in predicting the effects of human activities on species at risk Bianca Bauch

2. Outline • Possible use of simple Bayesian Belief Network (BBN) models in wildlife management decision processes • What is a Bayesian Belief Network? • How can it be evaluated? • Results • Discussion

3. Use of BBN in wildlife management • Wildlife managers have to assess possible adverse impact of proposed human activities (logging, harvest, road construction, research,…) on the survival or recovery of Species at Risk • Problem: for most species there is not enough information on which to base sound decision • Possible solution: - use of simple BBN models to predict the probability of decline or increase in population size of species at risk in reponse to management activities - BBN models were built for different groups of species - Assumed that species with similar life history characteristics will react in a similar way tomanagement activities - offers advantage of having a tool that is based on consistent criteria and that can easily be applied • 9 BBN models for groups of species with similar life history characteristics

4. Whooping Crane BBN models for: • Long lived medium sized terrestrial herbivorous mammals • Long lived large terrestrial carnivorous mammals • Whales • Turtles • Snakes • Long lived birds • Short lived birds • Perennial shrubs • Perennial herbaceous monocarpic plants

5. Illustration of a Bayesian Belief Network (BBN) Bayesian Belief Networks were named after Reverend Thomas Bayes (1702-1761), a British theologian and mathematician, who established a basic rule of probability, the Bayes Rule: p(B|A) = p(A|B) x p(B) / p(A) where p(B|A) is the probability of B given that A has occurred p(A) is the probability of A, p(A|B) is the probability of A given that B has occurred http://www.norsys.com/tutorials/netica/secA/tut_A1.htm#WhatIsABayesNet Example: What is the probability that if it is cloudy, it also rains or snows in Ottawa (p(B|A))? Assumptions: - probability that it’s cloudy (p(A)) = 0.6 - probability of rain/snow (p(B)) = 0.2 - probability that it’s cloudy when it rains/snows (p(A|B) = 1 P(B|A) = 1 x 0.2 / 0.6 = 0.33 33 % of the times when there is cloud cover, it also rains or snows!

6. parent node input variable Bayesian Belief Network Conditional Probability Table (CPT) (cloudy: yes / no) Calculates probability for each outcome depending on state of parent node child node output variable (probability of rain)

7. Simple Bayesian Belief Network R program runs 1000s of possible combinations of changes in the vital rates and generates Δλ for different combinations these possible Δλ are fed into the CPT parent node Vital rates • Survival of yearlings, rise or decline juveniles or adults Conditional Probability Table (CPT) • fecundity Calculates probability for each outcome depending on state of parent node child node probability (p(B|A)) ofchange in λ

8. parent node juvenile survival Simple Bayesian Belief Network Example: p(B|A) = probability of Δλ between -1 and -10% given that survival of juveniles is low (-0.9% to -9%) p(A) = probability that survival of juveniles is low p(B) = probability of Δλ between -1 and -10% p(A|B) = probability that juvenile survival is low when Δλ lays between -1 and -10% What is the probability that when negative impact on juvenile survival is low (- 0.9% to - 9%), the percentage change in the population growth rate (Δλ) will be between -1% and -10%? - 0.9% to -9% Conditional Probability Table (CPT) Calculates probability for each outcome depending on state of parent node child node probability (p(B|A)) of-1 to -10% change in λ

9. simple Bayesian Belief Network in Netica Parks Canada • Uses conditional probability table (CPT) to calculate effect of changes in input variables (vital rates) on output variable (change in population growth rate λ) • Outputs the probability that change in growth rate will be within a certain range (here: -10 to -1 60.8 %) MeadowThistle Input variables output variable

10. Seaside Sparrow How can it be evaluated? • Used population viability analysis (PVA) case studies on single species (in RAMAS Metapop and R) • compared BBN model outputs with RAMAS Metapop or R models model output change in the population growth rate (Δλ) • BBN model: Test impact of changes in vital rates on population growth rate • RAMAS Metapop: Test impact of human activities (= harvest or introductions of yearlings, juveniles or adults) on population growth rate

12. RAMAS Metapop • Single species population viability analysis (PVA) program • Predicts possible future fate of populations based on vital rates and environmental factors • Limitations: depends on data availability and quality predictions have to be viewed as relative rather than absolute numbers! • Used here, because PVAs offer best possible estimates • Assumption: RAMAS best simulates reality

13. Black Rat Snake Simulating in RAMAS Metapop, R and BBN For each species and each BBN species group model: - simulation of 20 different impact scenarios - over 2, 5 and 8 years 60 different impact scenarios RAMAS/R = harvest or introductions of individuals of specific stage BBN models = decrease or increase in vital rates Example: BBN RAMAS/R (harvest) -0.9 to -9% = - 5% -49 to -90% = - 75%

14. Simulating in RAMAS Metapop Population management: 75% harvest of juveniles for 2 years

15. RAMAS Metapop results Output: trajectory summary Whooping Crane Massasauga Rattle Snake Start of population management, (harvest of 75% of adults over 2 years)

16. Calculating the percentage change in the population growth rate λ λ after impact N(t+x)/N(t) Geometric mean of λ before impact (λ1* λ2*…..* λn)/t change in λ : Δλ = (λafter – λbefore)/ λbefore

17. Direct comparison of BBN model vs RAMAS/R case study results n ∑ (Pj2) SPO =MOAC Pc j = 1 Massasauga Rattle Snake Spherical Pay-off (SPO) • gives a measure of the goodness of fit betw. predictions • of BBN and RAMAS/R models (SPO = 1 perfect overlap; • SPO = 0 no overlap • here: compares if Δλ of RAMAS/R overlaps with ranges of • Δλ given by simple BBN models Mean over all cases Probability of state j Probability of the correct state

18. 1 = perfect overlap; 0 = no overlap

19. 1.0 1.0 Green Sea Turtle 0.8 0.8 0.6 0.6 33 14 13 0.4 0.4 0.2 0.2 0.0 0.0 wrong BBN spatial aspatial right BBN Results Spherical pay-off Spherical pay-off • mean (spatial) = 0.71 • mean (aspatial) = 0.67. • Wilcoxon Signed Rank Test • for paired cases displayed a • significant difference (p = 0.001) • No obvious difference btw. right • and wrong BBN -RAMAS/R • combinations

20. Turkish Mouflon Discussion • Limitations of study: - too few PVA case studies (1 to 2 PVAs per BBN model) - time! • assumed PVAs are a better simulation of reality – is that the case? • Used upper and lower bound std of population trajectory to estimate Δλ – thus, rather extreme values were compared against BBN output

21. Future work • Find and test further PVA case studies against BBN models • Include more than two possible Δλ values of single species PVA results in comparison • Include possible management scenarios with medium impact on vital rates (here: only high and low impact was tested) Mountain Golden Heather

22. Acknowledgements Many thanks for supervision and support to Kathryn Lindsay, Environment Canada, GLEL Carleton University Patrick Nantel, Parks Canada and Lutz Tischendorf, ELUTIS Modelling and Consulting Inc. The study was supported with funding from Parks Canada

23. Black Rat Snake Direct comparison of BBN models vs RAMAS/R case studies Spherical pay-off • gives the goodness of fit betw. predictions of BBN and RAMAS/R models • Based on confusion table • Takes BBN probabilities of all possible outcomes into account