Occupancy Modeling Workshop

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.title[
# Occupancy Modeling Workshop
]
.subtitle[
## OTS 2022
]
.author[
### Diego J. Lizcano, Ph.D.
]
.institute[
### SCMAS, Awake-Travel
]
.date[
### 2022-06-26
]

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# Thanks to

## Adriana Bravo
## Pablo Muñoz
## Sofía Rodríguez-Brenes

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# Get Started

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# Diego J. Lizcano

![:scale 40%](http://dlizcano.github.io/images/bio-photo5.jpg)

- Biologist. Universidad de los Andes, Bogotá-Colombia.

- Ph.D. University of Kent, Canterbury, UK.

- Ecology and conservation of mammals (Tapirs).

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# Now You...

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# In this workshop:

We are going to use 
![:scale 30%](https://www.r-project.org/logo/Rlogo.png)

And strongly recommended to use ![:scale 30%](https://www.rstudio.com/wp-content/uploads/2018/10/RStudio-Logo-Flat.png)

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# Ecology
### Charles Krebs
![](https://www.zoology.ubc.ca/~krebs/images/charley_cleth.jpg)

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# Ecology: Study of interactions that determine **Distribution and Abundance**

.left-column[
![](img/ecology.jpg)
]

.right-column[
### Distribution:

Where are they.

### Abundance:

How many?.

]

Related to the problem of counting organisms!

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# Counting animals is not a trivial problem...

![](https://media.giphy.com/media/11aqMcSy5tsgow/giphy.gif)

Animals move!

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### As ecologist: The map of our dreams

![Mapa de densidad](img/kanguro.png)

#### at some point, we had to count the kangaroos

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# Conting Animals

![Obtener densidad](img/pinguinos.jpg)

#### Easy for animals that are conspicuous and that group together.

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# Conting Animals

![Obtener densidad](img/432.jpg)
#### Not so easy if they don't group. Capture - Mark - Recapture. Distance

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# Conting Animals

![Obtener densidad](img/Moose-capture_011.jpg)

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

---

### Relative abundance

![:scale 80%](img/bird_abundance.jpg)

#### 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.

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# However...

![:scale 80%](http://i.giphy.com/nejXhE8hnCiQ0.gif)
#### Animals move and hide (camouflage)

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# Sampling is not infallible

![:scale 120%](https://i.giphy.com/media/piPn7Cv4KmlVbOSa5c/giphy.webp)

Biologist are not super heroes. We make mistakes!

#### Detectability and Imperfect detection concept

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# 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.

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# How the detection error occurs (Guillera‐Arroita 2016)

see ppt ![:scale 70%](img/detection.png)

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

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# Mackenzie et al 2002, 2003 to the rescue

![](img/mackenzie.png)
unnoticed...

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# Book and presence program 2006

.left-column[
![Mackenzie book](img/mackenziebook.jpg)
]

.right-column[
![presence
software](http://www.mbr-pwrc.usgs.gov/software/doc/presence/falsePos.jpg)
]

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

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

![meta](img/meta.png)

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## Occupancy 
# `$$\psi$$`

## Detection probability

# `$$p$$`

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

---

## 1.  `$(\psi)$` 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.

## `$(\psi)$` 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

|      | visit1| visit2| visit3| visit4|
|:-----|------:|------:|------:|------:|
|site1 |      1|      0|      0|      1|
|site2 |      0|      0|      0|      0|
|site3 |      1|      1|      0|      0|
|sitex |      0|      0|      0|      0|

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# Example calculating `$\psi$` and `$p$`

### Frequentist method (Maximum likelihood)

.pull-left[

|    | v 1| v 2| v 3| v 4|
|:---|---:|---:|---:|---:|
|s 1 |   1|   0|   0|   1|
|s 2 |   0|   0|   0|   0|
|s 3 |   1|   1|   0|   0|
|s x |   0|   0|   0|   0|
]

.pull-right[

| **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 `$p$`

---

# Same example calculating `$\psi$` and `$p$`

### Bayesian method

.pull-left[

|    | v 1| v 2| v 3| v 4|
|:---|---:|---:|---:|---:|
|s 1 |   1|   0|   0|   1|
|s 2 |   0|   0|   0|   0|
|s 3 |   1|   1|   0|   0|
|s x |   0|   0|   0|   0|
]

.pull-right[

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: `$\psi =Pr(z_{i}=1)$`

]

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### A hierarchical (Bayesian) model

![Full Occu Bayes](img/Occu_Bayes.png)

### Admits Covariates

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

.pull-left[ 
ML

- Package [unmarked](https://cran.r-project.org/web/packages/unmarked/index.html)
- 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

.pull-right[
- 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.

]

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# Going Deep

![libro
azul](https://secure-ecsd.elsevier.com/covers/80/Tango2/large/9780123740977.jpg)

### Andy Royle (2008)

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

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# Dragon-fly book (2015)

.pull-left[ 
![libro
libelula](https://images-na.ssl-images-amazon.com/images/I/513ulKHhAKL._SX404_BO1,204,203,200_.jpg)
]

.pull-right[ 
### More recent by [Marc Kery](http://store.elsevier.com/Marc-Kery/ELS_1059944/)

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.
]

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# Let's do it!

![Coding now](https://www.r-project.org/Rlogo.png) 
- R level? 
- Objects?, Vectors?
- DataFrame?
- Loops?
- Functions?

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# Schedule

.left-column[
![Coding fast](http://i.giphy.com/fQZX2aoRC1Tqw.gif)
]

.right-column[

| Day       | Topic                                                                                                                                |
|-----------------|------------------------------------------------------|
| Tuesday 28 pm |  Remembering R                                                                                                                |
|           | [R as model tool](https://dlizcano.github.io/IntroOccuPresent/R_toModel_E.html)                                    |
| Wednesday 29 am | [Occupancy concept](https://dlizcano.github.io/IntroOccuPresent/modelOccuData_E.html)                        |
|           | Intro Occu Static model - [unmarked101](https://dlizcano.github.io/IntroOccuPresent/unmarked_101_E.html)                            |
| Wednesday 29 pm | Static Model in deep I- [Sim Machalilla](https://dlizcano.github.io/occu_book/)                                             |
|           | Static Model in deep II- [Data in unmarked](https://dlizcano.github.io/occu_book/unmarked.html) |
| Thursday 30 am | Questions. Real World Data - [Deer](https://github.com/dlizcano/Mazama_rufina)          |
|           | [More models](https://dlizcano.github.io/IntroOccuPresent/Otros_modelos_jerarquicos.html)                        |

]

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# Thanks!

Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan).

Contact: Diego J. Lizcano

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