Lecture 1

class: center, middle, inverse, title-slide

# Lecture 1
## Introduction to population ecology
### WILD3810 (Spring 2021)

---

## Readings

> Mills 3-12

> Powell & Gale 6-10

---
class: inverse, center, middle
# What is population ecology?

---
class: center, middle
Population ecology is the study of the distribution of individuals in a population over time and space

---

---

---

### Population ecology forms the basis for modern natural resource management

- Conservation

???

Image: Pacific Southwest Region U.S. Fish and Wildlife Service from Sacramento, US [CC BY 2.0 (https://creativecommons.org/licenses/by/2.0) or Public domain], via Wikimedia Commons

---

### Population ecology forms the basis for modern natural resource management

- Conservation
- Management

???

Image: Yathin S Krishnappa [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], from Wikimedia Commons

---

### Population ecology forms the basis for modern natural resource management

- Conservation
- Management
- Population control

???

Image: Le.Loup.Gris [GFDL 1.3 (www.gnu.org/licenses/fdl-1.3.html) or CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], from Wikimedia Commons

---
class: inverse, center, middle
# Definitions

---
class: inverse
## Population

> A group of organisms of the same species occupying a particular space at a particular time

---
## Interactions

A common concept in all definitions of a population is some potential for *interactions* among individuals

- interactions can be direct (fighting for territories, reproducing) or indirect (food depletion)

- some definitions refer to reproduction - what about non-reproductive periods of the life cycle?

---
class: inverse

## Abundance (population size)

> the number of individual organisms in a population at a particular time

---
## Abundance (population size)

> the number of individual organisms in a population at a particular time `$^1$`

![](Screenshot_2018-12-11 Utah Moose Statewide Management Plan - moose_plan pdf.png)

???

Image: [https://wildlife.utah.gov/hunting/biggame/pdf/moose_plan.pdf](https://wildlife.utah.gov/hunting/biggame/pdf/moose_plan.pdf)

`$^1$` How is the "population" defined in this example? Does that make sense biologically? From a management perspective?

---
class: inverse

## Density

> the number of individuals relative to a critical resources (i.e., space)

---
## Density

> the number of individuals relative to a critical resources (i.e., space)

![](abun_v_density.png)

---
## Density

> the number of individuals relative to a critical resources (i.e., space) `$^2$`

???

`$^2$` Density doesn't always have to be relative to space. It could relative any limiting resource (e.g., nesting sites)

Image: Kevin Cole from Pacific Coast, USA (en:User:Kevinlcole) [CC BY 2.0 (https://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons

---
class: inverse, center, middle

## Why are you interested in population ecology?

---
## Questions that population ecologists ask:

--
+ *Why is this species found here and not there?*

--
+ *Are there more of this species than there used to be? Why?*

--
+ *How many individuals of this species can be harvested each year?*

--
+ *Will climate change cause this species to increase or decrease?*  
    
---
## Models of populations

Answering these questions **requires** models 
 
 
--
Models link **observations** to **processes**

--
Models are tools that allow us to learn about the real world

--
- By necessity, models are simplifications of reality  
     
---
class: inverse, center, middle

## By the end of the course, you will be a modeler!

---
class: inverse, center, middle
## The modeling process `$^3$`

???

`$^3$` For more information, refer to Powell & Gale pgs 7-9

---
## The modeling process  
1) Define the problem

--
- How many individuals will be in our population next year?

---
## The modeling process  
1) Define the problem

2) Identify the important variables

--
- population size this year `$(N_t)^4$`

???

`$^4$` `$t$` subscript refers to `time` and can be integer values `$(1,2,3...)$` that correspond to days, weeks, years, etc.

--
- number of births `$(B_t)$`

--
- number of deaths `$(D_t)$`

--
- number of immigrants `$(I_t)$`

--
- number of emigrants `$(E_t)$`

---
## The modeling process
1) Define the problem

2) Identify the important variables

3) Create the model
    `$$N_{t+1} = N_t + B_t + I_t - D_t - E_t$$`

---
## The modeling process
1) Define the problem

2) Identify the important variables

3) Create the model

4) Solve the model

--
- Count the individuals!

--
- Estimate birth/death rate

--
- Measure movement
    
---
## The modeling process
1) Define the problem

2) Identify the important variables

3) Create the model

4) Solve the model

5) Interpret the results

--
- Do the results make sense? `$^5$`

???

`$^5$` Checking whether the results make sense is a complex process that involves not just checking whether the results are consistent with your knowledge of the system but also more formal approaches like goodness-of-fit testing, sensitivity analysis, and model selection. We will discuss these more in lab as we work through some more specific models and questions

---
class: inverse, middle, center

# Abundance

---
## Abundance

Each definition of a population refers to it being a collection of individuals 
 
--
We denote the total number of individuals in a population as `$N$` 
 
--
`$N$` is the **State Variable** of a population