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

ceed

Centre of Excellence for Environmental Decisions

ARC

Gilbert et al. (2008) Proc. Natl.

• Acad. Sci. USA 105, 4769-4774

Optimal surveillance

Optimal surveillance

Orchi, Wikimedia Maelgwn, Wikimedia

4219 x 4-ha grid cells

Pr(hawkweed) 0.000 – 0.003 0.003 – 0.007 0.007 – 0.014 0.014 – 0.026 0.026 – 0.050

vegetation low grassy shrubby

Williams, Hahs & Morgan (2008) Ecological Applications

Orange hawkweed

Orchi, Wikimedia

• a simplification of decision problems

– straight-forward solutions – ability to deal with uncertainty

• examples
• an empirical evaluation

This talk

0.0 0.2 0.4 0.6 0.8 1.0 5 10 15

Effort (hr/ha) Prob non-detection

0.0 0.1 0.2 0.3 0.4 0.5 0.6 10 20 30 40 50

Pr(Extinction) Money spent on species ($'000)

Money spent on surveys Pr(Not detected)

) exp( ) (

i i i i i

x b a x p

0.0 0.1 0.2 0.3 0.4 0.5 0.6 10 20 30 40 50

Money spent on species ($'000) Pr(Extinction)

Money spent on surveys Pr(Not detected)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 10 20 30 40 50

Money spent on species ($'000) Pr(Extinction)

Money spent on surveys Pr(Not detected)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 10 20 30 40 50

Money spent on species ($'000) Pr(Extinction)

Pr(Not detected) Money spent on surveys

n i i i x

p L

1

) (

reward function summed over n options

Management outcome

n i i i x

p L

1

) ( B x

n i i 1

subject to

for ) (

* * i i i

x x p

the solution

Management outcome

Pr(presence)

Rate of detection

4219 x 4-ha grid cells

Pr(hawkweed) 0.000 – 0.003 0.003 – 0.007 0.007 – 0.014 0.014 – 0.026 0.026 – 0.050 Visit length (min) 0 – 7 7 – 24 24 – 54 54 – 92 92 – 175

vegetation low grassy shrubby

Williams, Hahs & Morgan (2008) Ecological Applications Hauser & McCarthy (2009) Ecology Letters

Orange hawkweed

Orchi, Wikimedia

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

0.0 0.2 0.4 0.6 0.8 1.0 5 10 15

Effort (hr/ha) Prob non-detection

Uncertain outcome

n i i i n i i i

x b x p L

1 1

) ( B x

n i i 1

subject to

Harry Markowitz

Uncertain outcome

Markowitz (1952) J Finance 7, 77-91

Max Pr(gain) Min Pr(loss)

Financial investment

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

Einadia Atriplex Lomandra Themeda Dianella

• abundance (+ve)
• experience (+ve)
• species
• height of vegetation (–ve)
• extra variation among

– searchers – quadrats

Factors driving detection rate

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 20 40 60

Proportion detected Budget (minutes)

Expected - optimal Observed - optimal Expected - uniform Observed - uniform

Expected benefit Observed benefit

1 2 3 4 5 6 7 8 9 10 20 30 40 50 60

Benefit (detections) Budget (minutes)

Expected benefit Observed benefit

Finding at least 2 occurrences

0.0 0.2 0.4 0.6 0.8 1.0 10 20 30

Probability of success Budget (minutes)

Predicted - optimal Predicted - uniform

Incorporates: assumptions of the stats binomial nature of data variation among quadrats uncertain detection rates correlations in this uncertainty

Relative predictions

0.00 0.05 0.10 0.15 0.20 0.25 0.30 10 20 30

Increased probability Budget (minutes)

Predicted Observed

n i i i x

p L

1

) ( B x

n i i 1

subject to

A useful model

Surveillance Hotspot investment Biodiversity surveys Reserve design Conservation triage Species management Vegetation management Greenhouse gas mitigation …. and it works experimentally

Thank you

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