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Some Statistical Methods that I am working on

Spatial Capture-Recapture (SCR) methods are relatively new, and are rapidly replacing non-spatial capture-recapture methods for wildlife population abundance estimation. Here is a fairly recent review of these methods.

 

My introduction to the topic arose from a collaboration with Murray Efford that resulted in this paper estabilishing maximum likelihood SCR methods, and thence Murray's software package ``secr''. My work with PhD students and collaborators has focussed on flexible density surface estimation from SCR surveys (see here), acoustic SCR surveys (see here), continuous-time SCR methods (see here and here), theory unifying Distance Sampling and SCR methods (see here), and most recently methods for dealing with unknown recapture identities (work in progress).

Continuous-time survey models

Most wildlife survey models and abundance estimators treat time as discrete (separate "occasions" for each survey or survey component), but usually surveys happen over some continuous interval, not at discrete points. You loose information when you discard times of events. We can use this information by borrowing ideas from survival analysis and recurrent event analysis.

* Here's a preprint showing how continuous-time models improve conventional Distance Sampling inference.

* Here's a paper developing continuous-time models for Spatial Capture-Recapture

* Here's a paper developing continuous-time models for Distance Sampling with stochastic animal availability.

Surveying with digital detectors

Digital cameras, video recorders and acoustic detectors are increasingly replacing humans as detectors on wildlife surveys. Digital survey data bring new opportunities and new challenges for statisticians. I and colleagues are working on acoustic methods for surveying speicies like frogs, gibbons, birds and cetaceans, and together with HiDef Aerial Survey Ltd, on methods for surveying birds and marine mammals at sea using high-definition video cameras.

Spatial Modelling with Wildlife Survey Data

Knowledge of spatial distribution is important for management and conservation of wildlife populations. By combining models for how animal density depends on habitat and other spatial variables, with models for how we detect animals on surveys, we can use survey data to draw inferences about the things driving animal distribution, as well as about animal abundance. My work in this area is driven by the EPSRC-funded  ESSMod project, which in collaboration with Finn Lindgren at the Unversit of Bath, and Janine Illian and Steve Buckland at St Andrews, is bringing Integrated Nested Laplace Approximation (INLA) methods to bear on Distance Sampling and Spatial Capture-Recapture survey problems.

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Current Research
Some Species that I am working on

Snow Leopards

I am working with Dr Koustubh Sharma of (The Snow Leopard Trust), Dr Ian Durbach (University of St Andrews) and others to support the aims of the Global Snow Leopard & Ecosystem Protection Program. This research uses spatial capture-recapture methods, primarily from camera trap surveys.

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(Credit for Photo: Snow Leopard Trust)

Gibbons

I am working with Dr Camille Coudrat of Project Anoulak, Dr Susan Cheyne, and other scientists on the IUCN Section on Small Apes' working group on best practice guidelines for gibbon surveys, developing acoustic spatial capture-recapture methods for gibbon surveys - with colleagues and students Erica Ye, Ben Stevenson, Filippo Franchini and Yuheng Wang. The research uses acoustic spatial capture-recapture methods.

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(Photo from here: https://gibbons.asia/wp-content/uploads/2018/07/gibbons_branch_cropped1.jpg)

Jaguars

I and colleague Richard Glennie are working with Drs Rebecca Foster and Bart Harmsen of Panthera using camera trap data to estimate the distribution, abundance and population trajectories of jaguars in Belize, using spatial capture-recapture methods. 

Belugas and Narwhals

I am working with Drs Mads Peter Heide-Jørgensen and Rikke Guldborg-Hansen to estimate the abundance, distribution and trends of beluga and narwhal populations for aerial surveys. Hidden Markov model line transect survey methods are used to account for the fact that whales are missed due to their diving.

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(image Â© Jade V. Garcia / Norwegian Polar Institute)

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Species
Examples
Examples of Recent Research

Dealing with stochastic animal availability on distance sampling surveys. By combining double-observer distance samplng data with a Markov modulated Poisson process model for animal availability for detection, we have developed a way to estimate abundance without separate information on availability.

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We develop and test by simulation a spatial capture-recapture (SCR) method for analysis of high definition video survey data of diving marine animals, using two cameras on a single aircraft, in which recaptures are unknown.

Cambodian gibbon acoustic survey

Capture-recapture with a semi-complete data likelihood: Bayesian inference using data augmentation and a "complete data likelihood" is a popular way of drawing inferences from capture-recapture data with unobserved individual heterogeneity. We develop a much faster Bayesian inference method by exploiting the fact that it is often possible to efficiently marginalise the likelihood component for unobserved individuals.

Distance Sampling: 2D or not 2D?: Adapting ideas from survival analysis, we have developed methods that use time until detection as well as distance to detections, to allow unbiased density estimation when animals avoid, or are attracted to, the observer before they are detected.

Thing explainer

Some things I work on, explained in simple English

(inspired by https://xkcd.com/thing-explainer/ and written with the help of http://splasho.com/upgoer6/)

Distance Sampling

This method lets you work out how many things you missed by measuring how far from you the things you saw were.

 

The closer things are the easier they are to see, so the further away things are, the less of them you will see. If you see all things very close to you, then you can work out how many you missed further away by looking at how much smaller are the numbers of things you see further away than the numbers of things you see very close to you. This lets you work out how many things were present in total.

Mark-Recapture Distance Sampling

What it says on the can: This method mixes mark-recapture and distance sampling methods, using both distances to things you saw and the fraction of "marked" things you saw. It lets you use distance sampling methods when you don't see all things very close to you. Usually you don't actually mark anything, you rely on being able to recognise individuals when you see them again.

Hidden State Models

Something is going on that you can't see, but every now and then you do see something that is caused by what you can't see. Hidden state models let you work out what is going on that you can't see, from the little that you do see.

 

A surprising number of problems, including many distance sampling and capture-recapture problems, are of this sort - but often this is not clear at first sight.
 

Mark-Recapture (or Capture-recapture)

This method lets you work out how many things you missed by first marking some and then seeing what fraction of these you see later.

 

If marked and unmarked things have the same chance of being seen, then the fraction of a known number of marked things that you missed is on average the same as the fraction of all things that you missed. This lets you work out the number of unmarked things that you missed, and from that the total number of things there (which is just the number of marked plus the number of unmarked things).

Spatial Capture-Recapture

This method lets you work out both how many things you did not detect and where these things were. It uses distance sampling and capture-recapture ideas but is more complicated than either of these because in most cases you don't even know where the things you did detect were. For example you might only hear animals without ever seeing them, or you might only see their scat, or hair.

 

Usually you don't actually mark anything, you rely on being able to recognise individuals when you detect them again (or recognise their DNA in hair or scat; or recognise their sounds).

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