Building and using detection models for ecological surveys Cindy - - PowerPoint PPT Presentation

Building and using detection models for ecological surveys

Cindy Hauser

cindyehauser.wordpress.com Kate Giljohann Joslin Moore Mick McCarthy Georgia Garrard Dave Kendal Nick Williams Roger Cousens

Ecological surveys

• Is my species present or absent here?
• How many individuals of my species are here?

(abundance)

• Where is my species located in the landscape?

(distribution)

• Walking (or swimming!) transects, standing at

a point, looking or listening, using cameras, sound recorders, satellites or aircraft, traps, ...

Imperfect detection

• What if my species is there but I don’t observe

it?

the study area was too big to survey all of it the frog was there but not calling the bird lives here but was foraging elsewhere the plant was hidden beneath a different, bigger plant I misidentified it as another species my species was there but I just failed to notice it

• Survey designs need to take this into account

Hawkweeds in alpine Victoria

• range hawkweed

Hieracium aurantiacum discovered 1999

http://en.wikipedia.org/wiki/Hawkweed

http://flora.nhm-wien.ac.at/Seiten-Arten/Hieracium-praealtum-prae.htm

King Devil hawkweed Hieracium praealtum discovered 2003

http://www.ct-botanical-society.org/galleries/hieraciumpilo.html

mouse-ear hawkweed Hieracium pilosella discovered 2011

site survey survey

weed absent weed present

no control action

no detection

no control action

no detection

control action

detection

• survey
• survey
• weed spread
• survey
• control
• (no spread)

Weed survey

Weed survey

We aim to minimise expected impacts of a weed

L(x) = p (1 - d(x)) R

probability of weed presence probability of failing to detect the weed using survey effort

x

consequences of detection failure

Hauser C.E. & McCarthy M.A. 2009. Streamlining ‘search and destroy’: cost effective surveillance for invasive species management. Ecology Letters 12: 683—692.

Detection function d(x)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

detection probability search effort, x

d(x) = 1 – exp(-λx)

Survey/impact trade-off

Minimise expected total cost of survey and impact

T(x) = x + p (1 – d(x)) R

Optimal survey effort is

( )

*

1 0, ln 1 pR x pR pR λ λ λ λ  ≤   =   >  

Optimal surveillance

( )

*

1 0, ln 1 pR x pR pR λ λ λ λ  ≤   =   >  

pR is the expected impact of a detection failure 1/λ is the average survey effort required to detect the weed if

it’s present

Optimal surveillance

( )

ln 1 * , pR x pR λ λ λ = >

probability of weed presence p

• ptimal

survey effort

x*

Optimal surveillance

( )

ln 1 * , pR x pR λ λ λ = >

impact of an undetected weed R

• ptimal

survey effort

x*

Optimal surveillance

( )

ln 1 * , pR x pR λ λ λ = >

search efficiency λ

• ptimal

survey effort

x*

Spatial variation

• We usually have a

heterogeneous landscape

• Varying…

– probability of weed presence – ability to detect the weed – ability to control the weed – value of weed absence

• Limited budget
• How should we prioritise

survey resources across such a space?

Survey budget

Minimise expected impacts of the weed across all sites subject to a budget on search effort

( )

1 2 1

( , ,..., ) 1 ( )

n n i i i i i

L x x x p d x R

=

= −

∑

1 n i i

x B

=

=

∑

( )

*

ln ( ) ( ) , 1,..., 0, 1,...,

i i i i i i

p R k B x k i k x k i k n λ λ λ λ    + − =    =     = +  where

Optimal surveillance with a budget

( )

1 1 1

ln 1 ( ) ( )

k i i i i i k i i

p R x k k k k λ λ λ λ

= − =

= =

∑ ∑

mean survey effort for each site, without a budget mean survey efficiency across sites

( )

*

ln ( ) ( ) , 1,..., 0, 1,...,

i i i i i i

p R k B x k i k x k i k n λ λ λ λ    + − =    =     = + 

Optimal surveillance with a budget

ideal survey effort if we didn’t have a budget

( )

*

ln ( ) ( ) , 1,..., 0, 1,...,

i i i i i i

p R k B x k i k x k i k n λ λ λ λ    + − =    =     = + 

Optimal surveillance with a budget

difference between ideal survey duration and what we have available per site

( )

*

ln ( ) ( ) , 1,..., 0, 1,...,

i i i i i i

p R k B x k i k x k i k n λ λ λ λ    + − =    =     = + 

Optimal surveillance with a budget

adapt to take surveillance efficiency at this site into account

Occurrence modeling for p

• Dominant wind

directions from source

• Vegetation community
• Wetness
• Disturbance

Williams, Hahs & Morgan. 2008. A dispersal-constrained habitat suitability model for predicting invasion of alpine vegetation. Ecological Applications 18: 347-359.

• range

hawkweed

Orange hawkweed detection

0.0 0.2 0.4 0.6 0.8 1.0 50 100

Search duration x (minutes/ha) Probability of detection d(x)

Low grassy Shrubby

Orange hawkweed in the Victorian alps

Williams N.S.G., Hahs A.K. & Morgan J.W. 2008. A dispersal-constrained habitat suitability model for predicting invasion of alpine vegetation. Ecological Applications 18:347—359.

low grassy (easy to search) shrubby (difficult to search)

0 – 1 1 – 2.5 2.5 – 5 5 – 10 10 – 20 0.000 – 0.003 0.003 – 0.007 0.007 – 0.014 0.014 – 0.026 0.026 – 0.050 10km Map 2. Vegetation categories Map 1. Predicted probability of

• range hawkweed occurrence

Map 3. Optimal search time (minutes per 4ha site)

Hawkweed detection

Hauser, Giljohann, Moore, McCarthy, Garrard & Kendal. In prep.

• 1. Set up 20m x 20m plots
• 2. Hide hawkweeds

in plots

• 3. Send searchers
• ut find hawkweeds

(and time them)

• 4. Interview

searchers about their experience

Detection models

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

detection probability, p search effort, x

p = 1 – exp(-λx)

ln(λijk) = a + b1y1 + b2 y2 +…

Hawkweed detection

Detection is influenced by...

• hawkweed appearance
• hawkweed cluster size
• hawkweed placement
• dominant background

vegetation

• distracting yellow flowers
• searcher experience
• time since starting

0.2 0.4 0.6 0.8 1 2 4 6 8 10

detection probability survey effort (min/plot)

prior, grass prior, heath experiment, grass experiment, heath Experimental result assumes the searcher is at peak experience and time of day.

Detection extremes

Experienced person searches for flowering orange hawkweed in a grassy plot without competing yellow flowers, 3 hours in Inexperienced person searches for flowering yellow hawkweed in a mixed grass/heath plot with high yellow flower coverage, early

0.2 0.4 0.6 0.8 1 10 20 30 40 50 60

detection probability survey effort (min/plot)

Ongoing research

• We’ve found detection differences amongst rosettes, orange-

flowering plants and yellow-flowering plants. How do we take these into account for survey design?

• Detection varies in ways we can’t predict or control. How

should we adapt surveys when our input parameters are uncertain?

• How should we design a survey for multiple species?
• How can we incorporate travel time into the optimisation?

Conclusions

• Optimisation, decision theory and statistics

have much to offer environmental management

• Posing the problem and defining objectives

can be challenging

• Mathematics bridges the gap between

ecologists’ observations and the true state of nature

Acknowledgements

• ARC Linkage grant to Cousens,

Williams & Duncan

• Research team: Sacha Jellinek,

Eric Ireland, Tracy Rout, Ellie Soh, Fran Alexander, Clare Brownridge

• Karen Herbert & Iris Curran
• Volunteer searchers
• 2013 Winter School & IMB