Lecture 16

class: center, middle, inverse, title-slide

# Lecture 16
## Source-sink dynamics
### <br/><br/><br/>WILD3810 (Spring 2020)

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## Readings

> ### Mills 188-194

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## Metapopulations

#### Focus of Levins metapopulation models and mainland-island model is on colonization and extinction

- Consider only presence and complete absence

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#### In reality, `$\large \lambda$` within patches is governed by:

- Births

- Immigration

- Deaths

- Emigration

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#### How does movement interact with local birth/death processes to determine `$\large \lambda$`?

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class: inverse, middle, center

# Source-sink dynamics

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## Source-sink dynamics

#### Variation in habitat quality and biotic interactions (competition, predation, etc.) lead to patch-specific demography

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#### Source populations:

- `$\large b > d$`

- produce a net surplus of individuals

--
#### Sink populations

- `$\large d > b$`

- produce a net deficit of individuals

---
## Source-sink dynamics

#### In high-quality source habitat, dominant individuals prevent young/inferior individuals from settling 
- *despotism*

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#### Dispersing individuals forced to move from sources to sinks

- dispersal can ‘rescue’ sinks from extinction

- sinks can have `$\large \lambda > 1$` but would decline without influx of immigrants

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#### Sources and sinks **cannot** be identified based on:

- abundance

- `$\large \lambda$`

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## Source-sink dynamics

#### "Contribution" metric `$(\large C)$`

`$$\Large C_i = R_i + E_i$$`

- `$\large R_i$`: Self-recruitment rate

- `$\large E_i$`: Emigration rate

---
## Source-sink dynamics

#### "Contribution" metric `$(\large C)$`

- Sources: 
    + `$\large C_i > 1$`
    + contribute more individuals to the metapopulation (births and emigration) than lose to mortality

- Sinks: 
    + `$\large C_i < 1$`
    + lose more individuals to mortality than contribute to metapopulation
  
    
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#### How can `$\large C_i$` be measured?

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## Source-sink dynamics

#### Self-recruitment rate `$\large R_i$`
.pull-left[
- `$\large \lambda_i - I_i$`

- `$\large I_i$` measured via:
    + telemetry
]

.pull-right[
<img src="https://upload.wikimedia.org/wikipedia/commons/2/2a/Handheld_telemetry.jpg" width="100%" style="display: block; margin: auto;" />
]

???
Image courtesy of Red Wolf Recovery Program, via Wikimedia Commons

---
## Source-sink dynamics

#### Self-recruitment rate `$\large R_i$`
.pull-left[
- `$\large \lambda_i - I_i$`

- `$\large I_i$` measured via:
    + telemetry    
    + genetics
]

.pull-right[
<img src="figs/snp_map.png" width="100%" style="display: block; margin: auto;" />
]

???

Image courtesy of [https://theconversation.com/heres-how-genetics-helped-crack-the-history-of-human-migration-52918](https://theconversation.com/heres-how-genetics-helped-crack-the-history-of-human-migration-52918)

---
## Source-sink dynamics

#### Self-recruitment rate `$\large R_i$`
.pull-left[
- `$\large \lambda_i - I_i$`

- `$\large I_i$` measured via:
    + telemetry    
    + genetics
    + mark-recapture
]

.pull-right[
<img src="figs/Sutherland_connectivity.png" width="120%" style="display: block; margin: auto;" />
]

???

Figure from: Royle, J.A., Fuller, A.K. and Sutherland, C., 2018. Unifying population and landscape ecology with spatial capture–recapture. *Ecography*, 41(3), pp.444-456.

---
## Source-sink dynamics

#### Self-recruitment rate `$\large R_i$`

.pull-left[
- `$\large \lambda_i - I_i$`

- `$\large I_i$` measured via:
    + telemetry    
    + genetics
    + mark-recapture    
    + stable isotopes
]

.pull-right[
<img src="figs/hma_NAmer copy.jpg" width="100%" style="display: block; margin: auto;" />
]

---
## Source-sink dynamics

#### Emigration rate `$\large E_i$`

- `$\large \epsilon_i \sum_{j \neq i} \phi^{ij}_i$`

- `$\large \epsilon_i$` (prob. emigration) and `$\phi^{ij}_i$` measured via:
    + telemetry
    + mark-recapture

---
## Source-sink dynamics

#### Cougars in Yellowstone National Park (Newby et al. 2012)
.pull-left[
- `$\large \lambda = 1.1$`

- `$\large I = 0.13$`

- `$\large \epsilon = 0.17$`

- `$\large \phi = 0.59$`
]

.pull-right[
<img src="https://upload.wikimedia.org/wikipedia/commons/e/e5/Mountain_Lion_in_Grand_Teton_National_Park.jpg" width="100%" style="display: block; margin: auto;" />
]

<br/>

--
`$$\Large C = (1.11 - 0.13) + (0.17 \times 0.59) = 1.08$$`

???

Image courtesy of the US National Park Service, via Wikicommons

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## Source-sink dynamics

#### Wood thrush (*Hylocichla mustelina*)

- In patches with `$\large R > 1$`, fecundity/juvenile survival drives population dynamics

- In patches with `$\large R < 1$`, adult survival drives dynamics

- Immigration rate is not related to `$\large R$`

???
Figure from Rushing et al. (2017)

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## Source-sink dynamics

#### Modeling source-sink dynamics using matrix models

--
`$$\LARGE \mathbf B = \begin{bmatrix}
    R_1 & 0 & 0\\
    E_{12} & R_2 & 0\\
    E_{13} & 0 & R_3
\end{bmatrix}$$`

---
## Source-sink dynamics

`$$\LARGE \begin{bmatrix}
    n_{1,t+1}\\
    n_{2,t+1}\\
    n_{3,t+1}\end{bmatrix}=
    \begin{bmatrix}
    R_1 & 0 & 0\\
    E_{12} & R_2 & 0\\
    E_{13} & 0 & R_3
\end{bmatrix} \times \begin{bmatrix}
    n_{1,t}\\
    n_{2,t}\\
    n_{3,t} \end{bmatrix}$$`

- In this example, what do the vectors of population abundance represent?

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## Source-sink dynamics

`$$\LARGE \begin{bmatrix}
    660\\
    330\\
    110\end{bmatrix}=
    \begin{bmatrix}
    1.1 & 0 & 0\\
    0.1 & 0.9 & 0\\
    0.05 & 0 & 0.8
\end{bmatrix} \times \begin{bmatrix}
    600\\
    300\\
    100 \end{bmatrix}$$`

- Metapopulation growth rate: `popbio::lambda(B) = ` 1.1

- Reproductive value: `popbio::reproductive.value(B) = ` 1, 0.5, 0.17

---
class: center, middle, inverse

# Ecological traps

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## Ecological traps

#### Animals attracted to a habitat because food resources or nesting cover appear to be high-quality

- Habitat cues that were reliable in the past become unreliable

- Often, anthropogenic changes to landscape impede successful completion of reproductive cycle

- Over-abundance of cowbirds (nest parasites), meso-predators (e.g., skunks, racoons), anthro-predators (e.g., housecats)

- Traps look like sources to the animal, but demographically they behave like sinks

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## Ecological traps

#### Polarized light

- For many insects, horizontal polarized light indicates the presence of rivers/steams for mating and egg laying

- Many windows and even asphalt also produce horizontal light, attracting insects which lay their eggs on artificial surfaces

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## Ecological traps

#### Grassland mowing

- Many grassland birds nest in tall, dense grass

- If these grasses are available early in the season but are then mowed after nesting has commenced, individuals may lose their entire clutch without enough time to renest

???
Image courtesy of CheepShot, via Wikicommons

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## Source-sink dynamics and management

#### Overall metapopulation dynamics in a source-sink system depend on:

- The net balance of `$B$`, `$D$`, `$I$`, and `$E$` amongst all source and sink populations in the region (habitat component)

- Environmental stochasticity (temporal environmental component)

- Demographic stochasticity (bad luck component)

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## Source-sink dynamics and management

#### Source habitats could mistakenly be ignored if managers preserve habitat with highest abundance abundant (B. van Horne 1983 J. Wildlife Management)

- Sink habitats may have high abundance if individuals forced into them (despotism)

- Ecological traps may result in misleading indicators of habitat quality

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#### If source habitats are not protected, the whole source-sink metapopulation could become threatened and collapse

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#### Must consider where species most productive (i.e., where `$\lambda \geq 1$`), on average, in a changing environment