.white[Mark-Recapture and Index Counts]

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.title[
# .white[Mark-Recapture and Index Counts]
]
.subtitle[
## .white[EFB 390: Wildlife Ecology and Management]
]
.author[
### .white[Dr. Elie Gurarie]
]
.date[
### .white[September 24, 2024]
]

---

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.pull-left-40[

### Welcome **Special Guest Lecturer**:

.center[# Dr. Ophélie Couriot]

**SUNY-ESF** (but currently in Fairbanks, Alaska)

]

.pull-right-60[
    ![](ophelie.png)
]

.pull-left[

### Spatial / Movement / Wildlife Ecologist

- Migrations and Climate Change, mainly in Caribou
- Co-production of Knowledge
- Indigenous-led Resource Management

]

.pull-right[

### Ph.D. Université de Toulouse

Migration / Space-Use / Behavior of

- Roe Deer (*Capreolus capreolus*)
- Red Deer (*Cervus elaphus*)
]

---

## Mark-Recapture is Super Simple

1. mark random subset, 2. release, 3. recapture, 4. count marked

![](images/OphelieFish.png)

---

## Mark-Recapture
.pull-left-70[![](images/OphelieFish.png)

Basic idea, **ratios should be similar**:

`$${marked\,(M) \over total\,(N)} = {marked\,in\,recapture\,(R) \over recapture\,(C)}$$`

]

.pull-right-30[
Convert that to estimate: 
`$$\widehat{N} = {𝑀 \times 𝐶\over 𝑅}$$`
 
 **Lincoln-Petersen Index**
]

---

## Mark-Recapture
.pull-left-50[![](images/OphelieFish.png)
]

.pull-right-50[
Point Estimate:

`$$\widehat{N} = {𝑀 \times 𝐶\over 𝑅}$$`
 
And (approximate) precision:

`$$SE(\widehat{N}) = \sqrt{M^2(C+1)(C-R)\over{(C+1)^2(C+2)}}$$`

]

---

## I banded students!

.pull-left-50[
![](images/MISS-O.gif)
]

.pull-right-50.center[

... by going back in time and elaborately manipulating family histories so that exactly

.Large.red[**M<sub>t</sub> = 20**]

of you have the letter

.Large.red[**O**]

in your last name.

]

---

## How many O's? 
.pull-left.large[
You have **5 minutes** to ask as many students in the class as you can (but not more than 20).

Ask whether they have an .red[**"O"**] in their last name.

Count yourself!

Report your results here:

Remember, your sample should be **random**! (*do not seek out 'O's*).
]

.pull-right[
![](images/QR_HowManyTs.png)
https://forms.gle/JpVNNjxpsHcTRM3a9
]

---
class:center
## Pause to compute the results

![](images/MISS-O.gif)

---

## Important assumptions of the Lincoln-Petersen Index

.large[
1. No deaths | no births
3. No immigration | no emigration
5. Random and equal probability sampling of marked and unmarked
5. No marks get lost

**Do these assumptions hold for the Great Banded Student Count?**
]

---

## But when they don't hold

and if you go deep into statistical methods, you can learn a lot...

for example about Steller sea lions (*Eumetopias jubatus*).

![](images/SSL.png)
---
.pull-left[.content-box-blue[#### Mark-recapture study (since 2004)
- `$>$` 200,000 - daily resights
- `$>$` 4,765 animals - all photo controlled
- `$>$` 40,000 - photos of marked animals
]]

.pull-right[.content-box-green[#### Estimates of:
- Survival
- Reproduction rates
- Migration 
]
**AFAIK - the best age-specific vital rates of any large mammal**. 
]

![](images/survival4.png)

.center[[Altukhov, A. et al. (2015) PLoS One 10(5):e0127292](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0127292)]]

---
class:

## Non-invasive mark-recapture

---
background-image: url('images/noninvasive.png')
background-size: cover

## Non-invasive mark-recapture

- Visual identification of natural markings
  - Camera traps
  - Binoculars
- Fur snags  - (**genetic mark-recapture**)
- Fecal samples - (**genetic mark-recapture**)

---

### Example of estimates based on genetic mark-recapture

.pull-left-40[
![](images/LutraLutra.jpg)
Eurasian otter (*Lutra lutra*).  Elusive, aquatic, nocturnal.

Deposits:  ***spraint***
]

.pull-right-60[
![](images/spraint.png)
]

--- 
--

.pull-left-40[

**Methods:**

1. Collect spraint
2. Genotype microsattelites - those are the marks
3. Recapture (of spraint) proceeds as before

]

.pull-right-60[
.blockquote[.blue.small[*Using 2132 otter faeces of a wild otter population ...  collected over six years (2006–2012) ... We provide precise population size estimate with confidence intervals (for 2012: `$\widehat{N} = 20 ± 2.1$`, `$95\%\, \text{CI} = 16–25$`)*

.center[[(Lampa et al. 2015, PLOS)](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0125684)]]]
]

---

## Index counts

are indirect observations which can be *related* to total abundances OR which can be useful for detecting trends / comparisons where you don't care (or can't get) absolute abundances.

Examples:

- Bird calls
- Nest counts
- Roost counts
- Animal tracks
- Fecal counts

![](images/Bull_title.png)

---

## Fecal counts

---

## Index-manipulation-index method

1. Obtain one index of population size: `$I_1$` 
2. Remove a bunch of animals `$C$`
3. Obtain another index of population size: `$I_2$`

Then ...
`$$\widehat{N_1} = {I_1 C \over I_1 − I_2}$$`

`$$SD(\widehat{N_1}) = \widehat{N_1} {q^* \over p^*} \sqrt{{1 \over I_1} + {1 \over I_2}}$$`

- `$p^*$` is proportion removed: `$I_1 - I_2 \over I_1$`
- `$q^*$` is proportion remaining: `$1 - p^*$`

.content-box[**Very important assumption:**  Closed population, i.e. no births / deaths / emigration]

---

## Feral horse - fecal index + cull + fecal index

.pull-left-40[

.red[
#### Data: 
`$I_1 = 301$`; `$I_2 = 76$`

`$C = 357$`; `$p* = 0.748$`
]

]

.pull-right-60[
![](images/BeatysButteHorses.jpg)
Feral horses - Beaty's Butte, Oregon
]

.blue[

#### Estimates:

`$\widehat{N_1} = (301 × 357)/(301 − 76) = 478$`

with standard error:

`$SE(\widehat{N_1}) ≈ 478\times(0.252/0.748)\times\sqrt{(1/301 + 1/76)} = 21$`
]

.center[(see: [Eberhardt 1982](https://www.jstor.org/stable/pdf/3808648.pdf))]

---
# North American Breeding Bird Survey

Based mainly on volunteer expert birder detection of male breeding songs.

![](images/BirdSurvey.png)

---
# North American Breeding Bird Survey

Good for identifying large-scale trends ... but hard to get abundance estimates:
.center[
<img src="images/shrike.jpg" width="70%" />
]

---
## Counting tracks

Used widely in Russia and Finland in standardized, repeated, long-term random transects.

**Method:** ski, and count (and ID) every track you cross

.pull-left-40[
![](images/snowtracks.jpg)
]

.pull-right-60[
Conversion to density estimate:

**Formozov–Malyshev–Pereleshin** (FMP)

`$\widehat{D} = {\pi \over 2} {x\over S \hat{M}}$`

where: 
- *x* - number of track crossings 
- *S* - transect length
- *M* - animal movement length

Very simple, surprisingly effective. 
]

---
.pull-left-30[

4 km / side x 3

Note intense coverage!

<img src="images/finland.jpeg" width="80%" />
]

.pull-right-70[
## Finland Wildlife Triangles

![](images/FinlandTrends.png)
]
Detecting trends, and inferring predator-prey interactions.

([Kauhala and Helle 2000](https://www.jstor.org/stable/23735998))

---

## Large-scale patterns

50,000 transects between 1950-2010

.pull-left[
![](images/RussianFauna.png)
]
.pull-right[
**Moose trends**

![](images/MooseTrends.png)
]

Reveal impact of socioeconomic upheaval on wildlife.

([Bragina et al. 2015](https://www.jstor.org/stable/23735998))

---

### Take-aways

.blockquote[
Thinking about **abundance estimation** helps us think about: (a) tools for oberving and monitoring wildlife, (b) creative ways to make inferences about wildlife, (c) some of the sources of randomness and variability that characterize *ALL* observations of wildlife. 
]
<br>
.pull-left-30[
.content-box-yellow[
**Total counts**
- expensive
- hard
- possible for few animals

**Sample counts**
- involve stats and good design
- possible for more animals
]
]

.pull-right-70[
.content-box-green[
**Mark-Recapture**
- can give you MORE than just a count!
- requires long-term, multiple sampling
- some strong assumptions (if just abundance)
- often (not always) invasive

**Index counts**
- Least invasive
- Least precise estimates
- Can be scaled up - see growth of Citizen Science
- Useful for relative differences and trends
]]

---

## References
.small[
1. Altukhov, A. V., R. D. Andrews, D. G. Calkins, T. S. Gelatt, E. D. Gurarie, T. R. Loughlin, E. G. Mamaev, V. S. Nikulin, P. A. Permyakov, S. D. Ryazanov, V. V. Vertyankin, and V. N. Burkanov. 2015. Age Specific Survival Rates of Steller Sea Lions at Rookeries with Divergent Population Trends in the Russian Far East. *PLOS ONE* 10:e0127292.
2. Bragina, E. V., A. R. Ives, A. M. Pidgeon, T. Kuemmerle, L. M. Baskin, Y. P. Gubar, M. Piquer-Rodríguez, N. S. Keuler, V. G. Petrosyan, and V. C. Radeloff. 2015. Rapid declines of large mammal populations after the collapse of the Soviet Union: Wildlife Decline after Collapse of Socialism. *Conservation Biology* 29:844–853.
3. Eberhardt, L. L., A. K. Majorowicz, and J. A. Wilcox. 1982. Apparent Rates of Increase for Two Feral Horse Herds. *The Journal of Wildlife Management* 46:367.
3. Kauhala, K., and P. Helle. 2000. The interactions of predator and hare populations in Finland — a study based on wildlife monitoring counts. *Annales Zoologici Fennici* 37:151–160.
3. Lampa, S., J.-B. Mihoub, B. Gruber, R. Klenke, and K. Henle. 2015. Non-Invasive Genetic Mark-Recapture as a Means to Study Population Sizes and Marking Behaviour of the Elusive Eurasian Otter (Lutra lutra). *PLOS ONE* 10:e0125684.
3. Morgan, B. J. T., P. M. North, C. J. Ralph, and J. M. Scott. 1983. Estimating Numbers of Terrestrial Birds. *Biometrics* 39:1123.
3. Petit, E., and N. Valiere. 2006. Contributed Papers: Estimating Population Size with Noninvasive Capture-Mark-Recapture Data: Noninvasive Capture-Mark-Recapture Data. *Conservation Biology* 20:1062–1073.
3. Stephens, P. A., O. Yu. Zaumyslova, D. G. Miquelle, A. I. Myslenkov, and G. D. Hayward. 2006. Estimating population density from indirect sign: track counts and the Formozov–Malyshev–Pereleshin formula. *Animal Conservation* 9:339–348.
]