ceed Centre of Excellence for Environmental Decisions Optimal - PowerPoint PPT Presentation

Searching for needles in haystacks Michael McCarthy Quantitative and Applied Ecology Group qaeco.com ARC ceed Centre of Excellence for Environmental Decisions

Optimal surveillance Gilbert et al . (2008) Proc. Natl. Acad. Sci. USA 105, 4769-4774

Optimal surveillance Orchi, Wikimedia Maelgwn, Wikimedia

Orange hawkweed 4219 x 4-ha grid cells Orchi, Wikimedia Pr(hawkweed) vegetation 0.000 – 0.003 0.003 – 0.007 low grassy 0.007 – 0.014 shrubby 0.014 – 0.026 0.026 – 0.050 Williams, Hahs & Morgan (2008) Ecological Applications

This talk • a simplification of decision problems – straight-forward solutions – ability to deal with uncertainty • examples • an empirical evaluation

Prob non-detection 1.0 0.8 0.6 0.4 0.2 0.0 0 5 10 15 Effort (hr/ha)

p ( x ) a exp( b x ) Pr(Not detected) 0.6 i i i i i Pr(Extinction) 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 Money spent on surveys Money spent on species ($'000)

Pr(Not detected) 0.6 Pr(Extinction) 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 Money spent on surveys Money spent on species ($'000)

Pr(Not detected) 0.6 Pr(Extinction) 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 Money spent on surveys Money spent on species ($'000)

Pr(Not detected) 0.6 Pr(Extinction) 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 50 Money spent on surveys Money spent on species ($'000)

Management outcome n L p i x ( ) i i 1 reward function summed over n options

Management outcome n L p i x ( ) i i 1 n subject to x B i i 1 * * p ( x ) for x 0 the solution i i i

Pr(presence)

Rate of detection

Orange hawkweed 4219 x 4-ha grid cells Orchi, Wikimedia Pr(hawkweed) Visit length (min) vegetation 0.000 – 0.003 0 – 7 0.003 – 0.007 low grassy 7 – 24 0.007 – 0.014 24 – 54 shrubby 0.014 – 0.026 54 – 92 0.026 – 0.050 92 – 175 Williams, Hahs & Morgan (2008) Hauser & McCarthy (2009) Ecological Applications Ecology Letters

Gilbert et al . (2008) Proc. Natl. Acad. Sci. USA 105, 4769-4774

McCarthy et al. (2010) Ecology Letters 13: 1280-1289

Optimal number of flocks Min. expected no. undetected outbreaks Risk of H5N1 outbreak McCarthy et al. (2010) Ecology Letters 13: 1280-1289

Uncertain outcome Prob non-detection 1.0 0.8 0.6 0.4 0.2 0.0 0 5 10 15 Effort (hr/ha)

Uncertain outcome n n L p ( x ) b x i i i i i 1 i 1 n subject to x B i i 1 Harry Markowitz

Financial investment Max Pr(gain) Min Pr(loss) Markowitz (1952) J Finance 7, 77-91

Optimal number of flocks Min. expected no. undetected outbreaks Max. prob. detecting >5% of outbreaks Risk of H5N1 outbreak McCarthy et al. (2010) Ecology Letters 13: 1280-1289

Lomandra Dianella Themeda Einadia Atriplex

Factors driving detection rate • abundance (+ve) • experience (+ve) • species • height of vegetation ( – ve) • extra variation among – searchers – quadrats

Expected benefit 0.8 Proportion detected 0.7 0.6 Observed benefit 0.5 0.4 Expected - optimal 0.3 Observed - optimal 0.2 Expected - uniform 0.1 Observed - uniform 0.0 0 20 40 60 Budget (minutes)

9 8 Benefit (detections) 7 Observed benefit 6 5 Expected benefit 4 3 2 1 0 0 10 20 30 40 50 60 Budget (minutes)

Finding at least 2 occurrences 1.0 Probability of success 0.8 Incorporates: assumptions of the stats binomial nature of data 0.6 variation among quadrats uncertain detection rates correlations in this uncertainty 0.4 Predicted - optimal 0.2 Predicted - uniform 0.0 0 10 20 30 Budget (minutes)

Relative predictions 0.30 Increased probability Predicted 0.25 Observed 0.20 0.15 0.10 0.05 0.00 0 10 20 30 Budget (minutes)

A useful model n L p i x ( ) Surveillance i i 1 Hotspot investment Biodiversity surveys n subject to x B Reserve design i Conservation triage i 1 Species management Vegetation management Greenhouse gas mitigation …. and it works experimentally

Thank you mamcca@unimelb.edu.au mickresearch.wordpress.com qaeco.com