Lecture 7

class: center, middle, inverse, title-slide

# Lecture 7
## Life tables
### <br/><br/><br/>WILD3810 (Spring 2021)

---

## Assumptions of the density-independent models

#### Remember from the lecture 3 that our simple models of population growth were based on the following assumptions:

--
1) Population closed to immigration and emigration  
<br/>

--
2) Model pertains to only the limiting sex, usually females  
<br/>

--
3) Birth and death rates are independent of an individual’s age or biological stage  
<br/>

--
4) Birth and death rates are constant

---
## Assumptions of the density-independent models

#### In lectures 4 and 5, we learned about ways to model dynamics that do not meet assumption 4:

1) Population closed to immigration and emigration  
<br/>

2) Model pertains to only the limiting sex, usually females  
<br/>

3) Birth and death rates are independent of an individual’s age or biological stage  
<br/>

**4) Birth and death rates are constant**

???

In lecture 4, we learned about why birth and death rates might change as a function of abundance

In lecture 5, we learned about ways that birth and death rates might vary stochastically

---
## Assumptions of the density-independent models

#### Over the coming weeks, we will learn about why and how to relax assumption 3:

1) Population closed to immigration and emigration  
<br/>

2) Model pertains to only the limiting sex, usually females  
<br/>

**3) Birth and death rates are independent of an individual’s age or biological stage**  
<br/>

4) Birth and death rates are constant

---
class: inverse, center, middle

# Structured populations

---
## Age-structured populations

#### Survival and birth rates often vary with age

.left-column[
<img src="https://upload.wikimedia.org/wikipedia/commons/d/d2/Anser_caerulescens_CT4.jpg" width="100%" style="display: block; margin: auto;" />
]

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

???

Image courtesy of Cephas, from Wikimedia Commons

Figure from Rockwell et al. (1985) *Evolution*

---
## Stage-structured populations

#### In some cases, age is not a relevant predictor of survival and birth rates

--
#### Instead, survival and birth rates vary with **stage**

--
- life cycle stage

.pull-left[
<img src="figs/lifecycle_diagram.jpg" width="75%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="figs/lifecycle.gif" width="75%" style="display: block; margin: auto;" />
]

---
## Stage-structured populations

#### In some cases, age is not a relevant predictor of survival and birth rates

#### Instead, survival and birth rates vary with **stage**

- life cycle stage

- size

.left-column[
<img src="https://upload.wikimedia.org/wikipedia/commons/a/af/Gasterosteus_aculeatus_t%C3%BCsk%C3%A9s_pik%C3%B3.jpg" width="100%" style="display: block; margin: auto;" />
]

.right-column[
<img src="figs/stickleback_fecundity.png" width="60%" style="display: block; margin: auto;" />
]

???

Image courtesy of Kókay Szabolcs, via Wikimedia Commons
Figure from Moser et al. (2012)

---
class: inverse, center, middle

# Age-structured populations

---
## Age-structured populations

#### **Life tables**

- earliest accounting tool for calculating age-specific survival and mortality

--
#### Applications to:

-  Human demography

- Insurance industry (actuarial sciences)

- Health professions

--
[Pearl and Parker (1921)](https://www.journals.uchicago.edu/doi/pdfplus/10.1086/279836) were the first to calculate a non-human life table  
- *Drosophila melanogaster* (a fruit fly)

- Since used in ecology, evolution, and natural resource management

---
## Life tables

#### Cohort life table

- follow group of individuals born within short period (a **cohort**) until each individual's death

--
- develop life table for groups of individuals with similar traits (e.g., one for males, one for females)

--
- **longitudinal** study design

---
## Life tables

- `\(\Large x\)`: age of individuals

- `\(\Large N_x\)`: number of individuals observed alive at age `\(\Large x\)` (sometimes called `\(\Large S_x\)`)
<br/>

???

`\(S_x\)` stands for number of *survivors* at age `\(x\)`

---
## Life tables