Lecture 9

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# Lecture 9
## Reproduction
### <br/><br/><br/>WILD3810 (Spring 2021)

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## Readings

> Mills 70-71

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## Life tables

#### Last lecture, we learned *why* and *how* to estimate age-specific patterns of survival and mortality

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<img src="https://upload.wikimedia.org/wikipedia/commons/f/f6/Phlox_drummondii_-_Archer_FL_02.jpg" width="100%" style="display: block; margin: auto;" />
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<img src="figs/phlox_lt.png" width="80%" style="display: block; margin: auto;" />
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## Life tables

#### Survival is not the only demographic process that varies with age

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#### Reproductive output also varies with age

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# Reproduction

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## Reproduction

### Terminology

#### Breeding Probability

> chance an adult will breed

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#### Natality:

> average number of offspring born per individual that reproduces

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- Clutch Size: birds, monotremes, oviparous herps, fish & insects

- Litter Size: mammals, viviparous herps & fish

- Progeny number: all others

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## Reproduction

### Terminology

#### Fecundity `$\Large (m_x)$`

> average number of offspring born per mature adult of age `$x$`

- typically measured as the number of *female* offspring produced per adult female (limiting sex)
<br/>

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`$$\LARGE m_x = \frac{Breeding\;\; Probability_x \times Natality_x}{2}$$`

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## Reproduction

#### Estimation

**Breeding Probability estimation**

- Advanced multi-state CMR methods

- Hormone analysis (blood, hair/feather, or fecal samples)

- Flowering rates in mature plants

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**Natality estimation**

- Direct observations in a sample of clutches, litters, or seed sets

- Number of corpora lutea scars in ovaries of hunted mammals

- Field ultrasounds on live captured individuals

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## Reproduction

#### Estimation using life tables

- `$\Large F_x$`: Total offspring produced by each age class

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## Reproduction

- `$\Large m_x$`: Number of offspring produced per living individual in age class `$\Large x$` (fecundity)

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## Reproduction

- `$\Large l_xm_x$`: Number of offspring produced per **original** individual

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`$\large R_0$`: Basic reproductive rate 
`$\large = \sum l_xm_x = \frac{\sum F_x}{N_0} = 2.41$`

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## Reproduction

#### `$\large R_0$`: Basic reproductive rate

- includes the influence of both survival `$(\large l_x)$` and reproduction of survivors `$(\large m_x)$`

+ 15.5% of individuals survive to age 8
    + those survivors produce, on average, 3.13 offspring
    + the average number of offspring produced by 8yo individuals **per original individual** = 0.48

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- defines the overall extent to which population changes

+ `$\large R_0 = 1$` means the population exactly replaces itself per *generation*

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- `$\Large r \approx \frac{ln(R_0)}{T}$`
    + `$\large T$` = **average cohort lifespan** (average time from the birth of an individual to the birth of its offspring)
    + annual species: `$T = 1$`, `$r = ln(R_0)$`

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# Fecundity schedules

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## Fecundity schedules

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## Fecundity schedules

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#### Breeding probability vs. age

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

Image courtesy of Martin Kraft, via WikiCommons

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## Fecundity schedules

#### Change in Canadian fecundity schedules over time

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#### Births/1000 women

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