Occupancy Modeling Workshop
OTS 2022
Diego J. Lizcano, Ph.D.
SCMAS, Awake-Travel
2022-06-26
1 / 35

2 / 35

Thanks toAdriana BravoPablo MuñozSofía Rodríguez-Brenes3 / 35

Get Started4 / 35

Diego J. Lizcano

5 / 35

Diego J. Lizcano

Biologist. Universidad de los Andes, Bogotá-Colombia.

5 / 35

Diego J. Lizcano

Biologist. Universidad de los Andes, Bogotá-Colombia.
Ph.D. University of Kent, Canterbury, UK.

5 / 35

Diego J. Lizcano

Biologist. Universidad de los Andes, Bogotá-Colombia.
Ph.D. University of Kent, Canterbury, UK.
Ecology and conservation of mammals (Tapirs).

5 / 35

Now You...6 / 35

In this workshop:

We are going to use

And strongly recommended to use

7 / 35

Ecology

Charles Krebs

8 / 35

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Where are they.

Abundance:

How many?.

9 / 35

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Where are they.

Abundance:

How many?.

Related to the problem of counting organisms!

9 / 35

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Where are they.

Abundance:

How many?.

Related to the problem of counting organisms!

9 / 35

Counting animals is not a trivial problem...

Animals move!

10 / 35

As ecologist: The map of our dreams

Mapa de densidad

at some point, we had to count the kangaroos

11 / 35

Conting Animals

Obtener densidad

Easy for animals that are conspicuous and that group together.

12 / 35

Conting Animals

Obtener densidad

Not so easy if they don't group. Capture - Mark - Recapture. Distance

13 / 35

Conting Animals

Obtener densidad

For some species it is cumbersome, impractical and very expensive.

14 / 35

Relative abundance

An indicator variable of the state of the population

I don't know how many there are, but I do know where there are more and where there are less.

15 / 35

However...

Animals move and hide (camouflage)

16 / 35

Sampling is not infallible

Biologist are not super heroes. We make mistakes!

Detectability and Imperfect detection concept

17 / 35

Detectability depends of18 / 35

Detectability depends of1. Sampling conditions (weather, time).18 / 35

Detectability depends of1. Sampling conditions (weather, time).2. The ability of the observer (sensor).18 / 35

Detectability depends of1. Sampling conditions (weather, time).2. The ability of the observer (sensor).3. The biology of the species being sampled.18 / 35

Detectability depends of1. Sampling conditions (weather, time).2. The ability of the observer (sensor).3. The biology of the species being sampled.This error should be considered carefully to avoid bias in abundance estimates.18 / 35

How the detection error occurs (Guillera‐Arroita 2016)

see ppt

It is an important error that must be considered in the sampling design!!!

19 / 35

Mackenzie et al 2002, 2003 to the rescue

unnoticed...

20 / 35

Book and presence program 2006

Mackenzie book

presence
software

Mackenzie popularizes occupancy $(\psi)$ as a proxy of abundance taking into account detectability $(p)$

21 / 35

Allows you to set goals and to monitor them over time.

	visit1	visit2	visit4
site1	1	0	1
site2	0	0	0
site3	1	1	0
sitex	0	0	0

Example calculating $\psi$ and $p$

Frequentist method (Maximum likelihood)

	v 1	v 2	v 4
s 1	1	0	1
s 2	0	0	0
s 3	1	1	0
s x	0	0	0

Detection History
$H_{1} \psi$ × p1(1-p2)(1-p3)p4
$H_{2} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4
$H_{3} \psi$ × p1p2(1-p3)(1-p4)
$H_{4} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4

Histories Combined in a Model:

$\begin{aligned} L(\psi, p \mid H_{1},...,H_{x}) = \prod_{i=1}^{x} Pr (H_{i}) \end{aligned}$

26 / 35

Example calculating $\psi$ and $p$

Frequentist method (Maximum likelihood)

	v 1	v 2	v 4
s 1	1	0	1
s 2	0	0	0
s 3	1	1	0
s x	0	0	0

Detection History
$H_{1} \psi$ × p1(1-p2)(1-p3)p4
$H_{2} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4
$H_{3} \psi$ × p1p2(1-p3)(1-p4)
$H_{4} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4

Histories Combined in a Model:

$\begin{aligned} L(\psi, p \mid H_{1},...,H_{x}) = \prod_{i=1}^{x} Pr (H_{i}) \end{aligned}$ The model admits incorporating covariates to explain $\psi$ and $p$

26 / 35

Example calculating $\psi$ and $p$

Frequentist method (Maximum likelihood)

	v 1	v 2	v 4
s 1	1	0	1
s 2	0	0	0
s 3	1	1	0
s x	0	0	0

Detection History
$H_{1} \psi$ × p1(1-p2)(1-p3)p4
$H_{2} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4
$H_{3} \psi$ × p1p2(1-p3)(1-p4)
$H_{4} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4

Histories Combined in a Model:

$\begin{aligned} L(\psi, p \mid H_{1},...,H_{x}) = \prod_{i=1}^{x} Pr (H_{i}) \end{aligned}$ The model admits incorporating covariates to explain $\psi$ and $p$

26 / 35

Same example calculating $\psi$ and $p$

Bayesian method

	v 1	v 2	v 4
s 1	1	0	1
s 2	0	0	0
s 3	1	1	0
s x	0	0	0

It is important to understand that there are two processes that can be modeled hierarchically

The ecological process ($\psi$) follows a Bernoulli distribution.
The observation model ($p$) follows a Bernoulli distribution.

The probability of observing the species given that it is present:

$p = Pr(y_{i}=1 \mid z_{i}=1)$

The Occupancy probability: $\psi =Pr(z_{i}=1)$

27 / 35

A hierarchical (Bayesian) model

Full Occu Bayes

Admits Covariates

28 / 35

Which one should I use? The maximum likelihood or Bayesian?

Package unmarked
In R
Admits "automatic" model selection AIC
Problems with many NAs
Hesian problem. estimates ok.
Difficulty from 1 to 10: 3 if you already know R.

Bayesian

BUGS or Stan language, called from R
Model selection is not that easy, BIC is not suitable
You don't have as many problems with many NAs in the matrix
Estimates are more accurate.
Difficulty from 1 to 10: 7 if you already know R.

29 / 35

Going Deep

libro
azul

Andy Royle (2008)

Advanced level book with lots of details, formulas, examples and code in R and BUGS language.

30 / 35

Dragon-fly book (2015)

libro
libelula

More recent by Marc Kery

More than 700 pages clearly explaining where the theory comes from, in a tutorial style, starting with a basic level of R to advanced models and their implementation in R and the BUGS language.

31 / 35

Let's do it!

Coding now

R level?
Objects?, Vectors?
DataFrame?
Loops?
Functions?

32 / 35

Schedule

Day	Topic
Tuesday 28 pm	Remembering R
	R as model tool
Wednesday 29 am	Occupancy concept
	Intro Occu Static model - unmarked101
Wednesday 29 pm	Static Model in deep I- Sim Machalilla
	Static Model in deep II- Data in unmarked
Thursday 30 am	Questions. Real World Data - Deer
	More models

33 / 35

Thanks!

Slides created via the R package xaringan.

Contact: Diego J. Lizcano

34 / 35

35 / 35

Occupancy Modeling Workshop
OTS 2022
Diego J. Lizcano, Ph.D.
SCMAS, Awake-Travel
2022-06-26
1 / 35

2 / 35

Thanks toAdriana BravoPablo MuñozSofía Rodríguez-Brenes3 / 35

Get Started4 / 35

Diego J. Lizcano

5 / 35

Diego J. Lizcano

Biologist. Universidad de los Andes, Bogotá-Colombia.

5 / 35

Diego J. Lizcano

Biologist. Universidad de los Andes, Bogotá-Colombia.
Ph.D. University of Kent, Canterbury, UK.

5 / 35

Diego J. Lizcano

Biologist. Universidad de los Andes, Bogotá-Colombia.
Ph.D. University of Kent, Canterbury, UK.
Ecology and conservation of mammals (Tapirs).

5 / 35

Now You...6 / 35

In this workshop:

We are going to use

And strongly recommended to use

7 / 35

Ecology

Charles Krebs

8 / 35

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Where are they.

Abundance:

How many?.

9 / 35

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Where are they.

Abundance:

How many?.

Related to the problem of counting organisms!

9 / 35

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Where are they.

Abundance:

How many?.

Related to the problem of counting organisms!

9 / 35

Counting animals is not a trivial problem...

Animals move!

10 / 35

As ecologist: The map of our dreams

Mapa de densidad

at some point, we had to count the kangaroos

11 / 35

Conting Animals

Obtener densidad

Easy for animals that are conspicuous and that group together.

12 / 35

Conting Animals

Obtener densidad

Not so easy if they don't group. Capture - Mark - Recapture. Distance

13 / 35

Conting Animals

Obtener densidad

For some species it is cumbersome, impractical and very expensive.

14 / 35

Relative abundance

An indicator variable of the state of the population

I don't know how many there are, but I do know where there are more and where there are less.

15 / 35

However...

Animals move and hide (camouflage)

16 / 35

Sampling is not infallible

Biologist are not super heroes. We make mistakes!

Detectability and Imperfect detection concept

17 / 35

Detectability depends of18 / 35

Detectability depends of1. Sampling conditions (weather, time).18 / 35

Detectability depends of1. Sampling conditions (weather, time).2. The ability of the observer (sensor).18 / 35

Detectability depends of1. Sampling conditions (weather, time).2. The ability of the observer (sensor).3. The biology of the species being sampled.18 / 35

Detectability depends of1. Sampling conditions (weather, time).2. The ability of the observer (sensor).3. The biology of the species being sampled.This error should be considered carefully to avoid bias in abundance estimates.18 / 35

How the detection error occurs (Guillera‐Arroita 2016)

see ppt

It is an important error that must be considered in the sampling design!!!

19 / 35

Mackenzie et al 2002, 2003 to the rescue

unnoticed...

20 / 35

Book and presence program 2006

Mackenzie book

presence
software

Mackenzie popularizes occupancy $(\psi)$ as a proxy of abundance taking into account detectability $(p)$

21 / 35

Allows you to set goals and to monitor them over time.

	visit1	visit2	visit4
site1	1	0	1
site2	0	0	0
site3	1	1	0
sitex	0	0	0

Example calculating $\psi$ and $p$

Frequentist method (Maximum likelihood)

	v 1	v 2	v 4
s 1	1	0	1
s 2	0	0	0
s 3	1	1	0
s x	0	0	0

Detection History
$H_{1} \psi$ × p1(1-p2)(1-p3)p4
$H_{2} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4
$H_{3} \psi$ × p1p2(1-p3)(1-p4)
$H_{4} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4

Histories Combined in a Model:

$\begin{aligned} L(\psi, p \mid H_{1},...,H_{x}) = \prod_{i=1}^{x} Pr (H_{i}) \end{aligned}$

26 / 35

Example calculating $\psi$ and $p$

Frequentist method (Maximum likelihood)

	v 1	v 2	v 4
s 1	1	0	1
s 2	0	0	0
s 3	1	1	0
s x	0	0	0

Detection History
$H_{1} \psi$ × p1(1-p2)(1-p3)p4
$H_{2} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4
$H_{3} \psi$ × p1p2(1-p3)(1-p4)
$H_{4} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4

Histories Combined in a Model:

$\begin{aligned} L(\psi, p \mid H_{1},...,H_{x}) = \prod_{i=1}^{x} Pr (H_{i}) \end{aligned}$ The model admits incorporating covariates to explain $\psi$ and $p$

26 / 35

Example calculating $\psi$ and $p$

Frequentist method (Maximum likelihood)

	v 1	v 2	v 4
s 1	1	0	1
s 2	0	0	0
s 3	1	1	0
s x	0	0	0

Detection History
$H_{1} \psi$ × p1(1-p2)(1-p3)p4
$H_{2} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4
$H_{3} \psi$ × p1p2(1-p3)(1-p4)
$H_{4} \psi$ × (1-p2)(1-p2)(1-p3)(1-p4)p4

Histories Combined in a Model:

$\begin{aligned} L(\psi, p \mid H_{1},...,H_{x}) = \prod_{i=1}^{x} Pr (H_{i}) \end{aligned}$ The model admits incorporating covariates to explain $\psi$ and $p$

26 / 35

Same example calculating $\psi$ and $p$

Bayesian method

	v 1	v 2	v 4
s 1	1	0	1
s 2	0	0	0
s 3	1	1	0
s x	0	0	0

It is important to understand that there are two processes that can be modeled hierarchically

The ecological process ($\psi$) follows a Bernoulli distribution.
The observation model ($p$) follows a Bernoulli distribution.

The probability of observing the species given that it is present:

$p = Pr(y_{i}=1 \mid z_{i}=1)$

The Occupancy probability: $\psi =Pr(z_{i}=1)$

27 / 35

A hierarchical (Bayesian) model

Full Occu Bayes

Admits Covariates

28 / 35

Which one should I use? The maximum likelihood or Bayesian?

Package unmarked
In R
Admits "automatic" model selection AIC
Problems with many NAs
Hesian problem. estimates ok.
Difficulty from 1 to 10: 3 if you already know R.

Bayesian

BUGS or Stan language, called from R
Model selection is not that easy, BIC is not suitable
You don't have as many problems with many NAs in the matrix
Estimates are more accurate.
Difficulty from 1 to 10: 7 if you already know R.

29 / 35

Going Deep

libro
azul

Andy Royle (2008)

Advanced level book with lots of details, formulas, examples and code in R and BUGS language.

30 / 35

Dragon-fly book (2015)

libro
libelula

More recent by Marc Kery

More than 700 pages clearly explaining where the theory comes from, in a tutorial style, starting with a basic level of R to advanced models and their implementation in R and the BUGS language.

31 / 35

Let's do it!

Coding now

R level?
Objects?, Vectors?
DataFrame?
Loops?
Functions?

32 / 35

Schedule

Day	Topic
Tuesday 28 pm	Remembering R
	R as model tool
Wednesday 29 am	Occupancy concept
	Intro Occu Static model - unmarked101
Wednesday 29 pm	Static Model in deep I- Sim Machalilla
	Static Model in deep II- Data in unmarked
Thursday 30 am	Questions. Real World Data - Deer
	More models

33 / 35

Thanks!

Slides created via the R package xaringan.

Contact: Diego J. Lizcano

34 / 35

35 / 35

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Occupancy Modeling Workshop

OTS 2022

Diego J. Lizcano, Ph.D.

SCMAS, Awake-Travel

2022-06-26

Thanks to

Adriana Bravo

Pablo Muñoz

Sofía Rodríguez-Brenes

Get Started

Diego J. Lizcano

Diego J. Lizcano

Diego J. Lizcano

Diego J. Lizcano

Now You...

In this workshop:

Ecology

Charles Krebs

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Abundance:

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Abundance:

Ecology: Study of interactions that determine Distribution and Abundance

Distribution:

Abundance:

Counting animals is not a trivial problem...

As ecologist: The map of our dreams

at some point, we had to count the kangaroos

Conting Animals

Easy for animals that are conspicuous and that group together.

Conting Animals

Not so easy if they don't group. Capture - Mark - Recapture. Distance

Conting Animals

For some species it is cumbersome, impractical and very expensive.

Relative abundance

An indicator variable of the state of the population

However...

Animals move and hide (camouflage)

Sampling is not infallible

Detectability and Imperfect detection concept

Detectability depends of

Detectability depends of

1. Sampling conditions (weather, time).

Detectability depends of

1. Sampling conditions (weather, time).

2. The ability of the observer (sensor).

Detectability depends of

1. Sampling conditions (weather, time).

2. The ability of the observer (sensor).

3. The biology of the species being sampled.

Detectability depends of

1. Sampling conditions (weather, time).

2. The ability of the observer (sensor).

3. The biology of the species being sampled.

This error should be considered carefully to avoid bias in abundance estimates.

How the detection error occurs (Guillera‐Arroita 2016)

It is an important error that must be considered in the sampling design!!!

Mackenzie et al 2002, 2003 to the rescue

Book and presence program 2006

Allows you to set goals and to monitor them over time.

Occupancy

ψ\psi

Detection probability

pp

Occupancy is a reflection of other important population parameters such as density.

1. (ψ)(\psi) is the proportion of the sampled area that is occupied by the species.

2. By visiting the site several times I can be more sure that I detect the species when it is found in that place.

3. Repeated sampling are key.

(ψ)(\psi) It is influenced by environmental variables (Covariables) such as vegetation cover, altitude, precipitation, etc.

This is what a data table with repeated sampling should look like

Example calculating ψ\psi and pp

Frequentist method (Maximum likelihood)

Histories Combined in a Model:

Example calculating ψ\psi and pp

Frequentist method (Maximum likelihood)

Histories Combined in a Model:

Example calculating ψ\psi and pp

Frequentist method (Maximum likelihood)

$\psi$

$p$

1. $(\psi)$ is the proportion of the sampled area that is occupied by the species.

$(\psi)$ It is influenced by environmental variables (Covariables) such as vegetation cover, altitude, precipitation, etc.

Example calculating $\psi$ and $p$

Example calculating $\psi$ and $p$

Example calculating $\psi$ and $p$

Same example calculating $\psi$ and $p$