Lecture 17

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class: center, middle, inverse, title-slide

# Lecture 17
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## Source-sink dynamics
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## Interspecific interactions
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### <br/><br/><br/>WILD3810 (Spring 2020)

---

## Interspecific interactions

#### Thus far, we have focus on the dynamics of populations composed of a single species

--
#### But species exist within a **community**

---
## Interspecific interactions

#### Interactions among different species can increase or decrease vital rates

- Fecundity

- Growth

- Survival

--
#### Interactions come in many different forms

---
## Interspecific interactions

#### Interactions come in many different forms
<br/>

<table class="table table-striped" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Species A </th>
   <th style="text-align:center;"> Species B </th>
   <th style="text-align:center;"> Interaction type </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> + </td>
   <td style="text-align:center;"> + </td>
   <td style="text-align:center;"> Mutualism </td>
  </tr>
  <tr>
   <td style="text-align:center;"> + </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> Commensalism </td>
  </tr>
  <tr>
   <td style="text-align:center;"> + </td>
   <td style="text-align:center;"> - </td>
   <td style="text-align:center;"> Contramensalism </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> - </td>
   <td style="text-align:center;"> Amensalism </td>
  </tr>
  <tr>
   <td style="text-align:center;"> - </td>
   <td style="text-align:center;"> - </td>
   <td style="text-align:center;"> Competition </td>
  </tr>
</tbody>
</table>

---
## Interspecific interactions

#### Interactions come in many different forms
<br/>

<table class="table table-striped" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;"> Species A </th>
   <th style="text-align:center;"> Species B </th>
   <th style="text-align:center;"> Interaction type </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;"> + </td>
   <td style="text-align:center;"> + </td>
   <td style="text-align:center;"> Mutualism </td>
  </tr>
  <tr>
   <td style="text-align:center;"> + </td>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> Commensalism </td>
  </tr>
  <tr>
   <td style="text-align:center;"> + </td>
   <td style="text-align:center;"> - </td>
   <td style="text-align:center;"> Contramensalism </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 0 </td>
   <td style="text-align:center;"> - </td>
   <td style="text-align:center;"> Amensalism </td>
  </tr>
  <tr>
   <td style="text-align:center;font-weight: bold;color: white;background-color: #446E9B;"> - </td>
   <td style="text-align:center;font-weight: bold;color: white;background-color: #446E9B;"> - </td>
   <td style="text-align:center;font-weight: bold;color: white;background-color: #446E9B;"> Competition </td>
  </tr>
</tbody>
</table>

---
class: middle, center, inverse

# Interspecific competition

---
## Interspecific competition

#### Direct

**Interference competition**

> individuals actively prevent others from attaining a resource in a given area or territory

---
## Interspecific competition

#### Direct

**Interference competition**

> individuals actively prevent others from attaining a resource in a given area or territory

*Allelopathy*: one plant releases toxic chemicals that poison the soil for others

---
## Interspecific competition

#### Indirect

**Exploitation competition**:

> consumption of limited resource by individuals makes it more difficult for others to attain the resource (scramble competition)

**Pre-emptive competition**:

> competition for space (e.g., nest sites)

---
class: inverse, center, middle

# The niche

---
## The niche

#### What is a niche?

--
- Niche = habitat where a species lives (Grinnell 1917)
    + e.g., the forest canopy

--
- Niche = trophic position; an organism’s role (Elton 1927)
    + e.g., birds of prey

--
- Niche = “n-dimensional hypervolume” (Hutchinson 1957)
    + the multi-dimensional resources (e.g., temperature, precipitation, light, etc.) required by a species to persist

--
#### Competition arises from niche overlap

---
## The Hutchinsonian niche

#### Niche dimensions are environmental factors (temperature, precipitation, light, etc.)

#### Niche dimensions can be visualized as “resource axes”

---
## Competition and the niche

#### **Fundamental niche**:

> Total range of environmental conditions that allow population persistence

--
#### Strength of competition between co-occurring species is related to the degree of overlap between their fundamental niches

- which set of species compete more strongly?
<br/>
<br/>

---
## Competition and the niche

#### Competition keeps species from occupying all of their fundamental niche

#### **Realized niche**:

> Portion of fundamental niche occupied after interactions w/ other species

---
## Competition and the niche

.pull-left[
#### Classic experiment:

- Joseph Connell (1961)

- Barnacles
    + *Balanus balanoides*
    + *Chthalamus stellatus*

- Fundamental niches overlap

- Competition w/ *Balanus* restricts *Chthamalus* to upper rocks (realized niche)
]

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

---
## Modeling competition

#### How can interspecific competition be modeled?

--
#### We aleady learned about modeling *intra*specific competition

`$$\large \frac{dN}{dt} = r_0N\bigg(1-\frac{N}{K}\bigg)$$`

--
<img src="figs/logistic_isocline.png" width="80%" style="display: block; margin: auto;" />

---
## Interspecific competition

#### If competing species are ecologically identical (use the same resources)
- Inter-specific competition is equivalent to intra-specific competition

- Each organism competes with all organisms of both species

- Population growth rate of each species is determined by the sum of numbers of both species combined:

`$$\large \frac{dN_1}{dt} = r_1N_1\bigg(1-\frac{N_1 + N_2}{K_1}\bigg)$$`

`$$\large \frac{dN_2}{dt} = r_2N_2\bigg(1-\frac{N_1 + N_2}{K_2}\bigg)$$`
---
## Interspecific competition

#### Isocline of single species logistic model

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

- `$\large \epsilon_i$` (prob. emigration) and `$\phi^{ij}_i$` measured via:
    + telemetry
    + mark-recapture
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<img src="figs/logistic_isocline.png" width="80%" style="display: block; margin: auto;" />

--
#### Becomes two-dimensional
- on the isocline, `$\frac{dN}{dt} = 0$`

<img src="figs/isoclines.png" width="45%" style="display: block; margin: auto;" />
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---
## Interspecific competition

#### When species utilize the same niche:

- Species with higher carrying capacity will competitively exclude the other

- Higher `$K$` means that a species can endure more crowding than the other, given the environment (e.g., more effective at getting the resources)

.pull-left[
<img src="figs/isoclines2.png" width="60%" style="display: block; margin: auto;" />
]

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

---
## Interspecific competition

Competitive Exclusion Principle was first eluded to by Grinnell (1904):

> "Two species of approximately the same food habits are not likely to remain long evenly balanced in numbers in the same region. One will crowd out the other; the one longest exposed to local conditions, and hence best fitted, though ever so slightly, will survive, to the exclusion of any less favored would-be invader"

---
## Interspecific competition

#### What if two competitors do not occupy the same niche? 
- Effect of numbers of another species will not be equivalent to numbers of conspecifics

- The force of interspecific competition will be < intraspecific competition because the other species occupies a (somewhat) different niche whereas conspecifics occupy the same niche

---
## Interspecific competition

#### Two individuals independently developed the same model during the 1920s and 1930s to accommodate the realities of competitive species occupying different niches

- Alfred J. Lotka and Vito Volterra

- Lotka-Volterra competition model

`$$\large \frac{dN_1}{dt} = r_1N_1\bigg(\frac{K_1 - [N_1 + \alpha N_2]}{K_1}\bigg)$$`

`$$\large \frac{dN_2}{dt} = r_2N_2\bigg( \frac{K_2 - [N_2 + \beta N_1]}{K_2}\bigg)$$`

- Competition coefficients
    + `$\alpha$` is the effect of species 2 on 1
    + `$\beta$` is the effect of species 1 on 2

---
## Lotka-Volterra competition model

`$$\large \frac{dN_1}{dt} = r_1N_1\bigg(\frac{K_1 - [N_1 + \alpha N_2]}{K_1}\bigg)$$`

`$$\large \frac{dN_2}{dt} = r_2N_2\bigg( \frac{K_2 - [N_2 + \beta N_1]}{K_2}\bigg)$$`

- `$\large \alpha < 0$` = Mutualism

- `$\large 0 < \alpha < 1$` = interspecific comp < intraspecific comp
 
- `$\large \alpha > 1$` = interspecific comp > intraspecific comp (rare)

- same relationships can be written for `$\large \beta$`

---
## Lotka-Volterra competition model

#### Can set Lotka-Volterra differential equations to 0 and solve for long-term equilibrium solutions of competition

`$$\large 0 = r_1N_1\bigg(\frac{K_1 - [N_1 + \alpha N_2]}{K_1}\bigg)$$`

`$$\large 0 = r_2N_2\bigg( \frac{K_2 - [N_2 + \beta N_1]}{K_2}\bigg)$$`

--
`$$\large \hat{N}_1 = K_1 - \alpha N_2$$`

`$$\large \hat{N}_2 = K_2 - \beta N_1$$`

--
- Equilibrium solutions depend on:
    + carrying capacities

+ competition coefficients

+ abundance of other species

---
## Lotka-Volterra competition model

#### Scenario 1: Isoclines do not cross, and that for species 1 is higher than that for 2

.pull-left[
<img src="figs/spp1_wins.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="figs/spp1_wins2.png" width="100%" style="display: block; margin: auto;" />
]

- Species 1 wins and competitively excludes 2

---
## Lotka-Volterra competition model

#### Scenario 2: Isoclines do not cross, and that for species 2 is higher than that for 1

.pull-left[
<img src="figs/spp2_wins.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="figs/spp2_wins2.png" width="100%" style="display: block; margin: auto;" />
]

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- Over-abundance of cowbirds (nest parasites), meso-predators (e.g., skunks, racoons), anthro-predators (e.g., housecats)
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- Species 2 wins and competitively excludes 1 
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---
## Lotka-Volterra competition model

#### Scenario 3: Isoclines cross, intraspecific comp stronger than interspecific comp

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- Many windows and even asphalt also produce horizontal light, attracting insects which lay their eggs on artificial surfaces
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.pull-left[
<img src="figs/coexist.png" width="80%" style="display: block; margin: auto;" />
]
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.pull-right[
<img src="figs/coexist2.png" width="100%" style="display: block; margin: auto;" />
]

- Stable equilibrium with coexistence

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## Coexistence

#### How to avoid competitive exclusion?

--
#### Reduce niche overlap (niche differentiation)
- **Spatially**

.pull-left[
Forage in the open
<img src="figs/mouse1.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[
Forage under shrubs
<img src="figs/mouse2.png" width="80%" style="display: block; margin: auto;" />
]

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## Coexistence

#### How to avoid competitive exclusion?

#### Reduce niche overlap (niche differentiation)
- **Temporally**

.pull-left[
Forage during the day
<img src="figs/TREE.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[
Forage at night
<img src="figs/CONH.png" width="80%" style="display: block; margin: auto;" />
]

---
## Coexistence

#### How to avoid competitive exclusion?

#### Reduce niche overlap (niche differentiation)
- **Temporally**

.pull-left[
Warm season 
<img src="figs/warm.png" width="80%" style="display: block; margin: auto;" />
]

.pull-right[
Cool season
<img src="figs/cool.png" width="80%" style="display: block; margin: auto;" />
]

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## Coexistence

.pull-left[
#### Many factors can result in niche differentiation

#### Over evolutionary time, species have partitioned the available niches on Earth

#### Species with sufficiently different ‘realized’ niches can coexist
]

.pull-right[
<img src="figs/finches.png" width="80%" style="display: block; margin: auto;" />
]