# 8 Life history

WORK IN PROGRESS

See https://www.oxfordbibliographies.com/display/document/obo-9780199830060/obo-9780199830060-0016.xml and https://en.wikipedia.org/wiki/Life_history_theory for a definition. I think that all case studies below fall in the LH category. I might consider moving the disease ecology case study in the main Sites and states chapter. See however https://onlinelibrary.wiley.com/doi/epdf/10.1111/ele.13681 for a link between disease ecology and life history theory.

Transition matrix:

$\begin{matrix} & \\ \mathbf{\Gamma} = \left ( \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \\ 12 \\ 12 \end{matrix} } \right . \end{matrix} \hspace{-1.2em} \begin{matrix} z_t=J & z_t=1yNB & z_t=2yNB & z_t=B & z_t=D \\ \hdashline 0 & \phi_1 (1-\alpha_1) & 0 & \phi_1 \alpha_1 & 1 - \phi_1\\ 0 & 0 & \phi_2 (1-\alpha_2) & \phi_2 \alpha_2 & 1 - \phi_2\\ 0 & 0 & 0 & \phi_3 & 1 - \phi_3\\ 0 & 0 & 0 & \phi_B & 1 - \phi_B\\ 0 & 0 & 0 & 0 & 1 \end{matrix} \hspace{-0.2em} \begin{matrix} & \\ \left . \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \\ 12 \\ 12 \end{matrix} } \right ) \begin{matrix} z_{t-1} = J \\ z_{t-1} = 1yNB \\ z_{t-1} = 2yNB \\ z_{t-1} = B \\ z_{t-1} = D \end{matrix} \end{matrix}$

First-year and second-year individuals breed with probabilities $$\alpha_1$$ and $$\alpha_2$$. Then, everybody breeds from age 3.

Observation matrix:

$\begin{matrix} & \\ \mathbf{\Omega} = \left ( \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \\ 12 \\12 \end{matrix} } \right . \end{matrix} \hspace{-1.2em} \begin{matrix} y_t = 1 & y_t = 2 & y_t = 3 & y_t = 4\\ \hdashline 1 & 0 & 0 & 0\\ 1 - p_1 & p_1 & 0 & 0\\ 1 - p_2 & 0 & p_2 & 0\\ 1 - p_3 & 0 & 0 & p_3\\ 1 & 0 & 0 & 0 \end{matrix} \hspace{-0.2em} \begin{matrix} & \\ \left . \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \\ 12 \\12 \end{matrix} } \right ) \begin{matrix} z_t = J \\ z_t = 1yNB \\ z_t = 2yNB \\ z_t = B \\ z_t = D \end{matrix} \end{matrix}$

Juveniles are never detected.

Morano et al. (2013), Shefferson et al. (2003), and Cruz-Flores et al. (n.d.)

Case study with simulations as in Oikos paper, see Figure 1 and Table 2. Would be a nice example of the use of simulations. Another example could the statistical power analyses.

## 8.3 Breeding dynamics

Pradel, Choquet, and Béchet (2012), Desprez et al. (2011), Desprez et al. (2013), and Pacoureau et al. (2019)

## 8.4 Using data on dead recoveries

### 8.4.2 Combination of live captures and dead recoveries

Combine live recapture w/ dead recoveries by Lebreton, Almeras, and Pradel (1999).

Transition matrix

$\begin{matrix} & \\ \mathbf{\Gamma} = \left ( \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \end{matrix} } \right . \end{matrix} \hspace{-1.2em} \begin{matrix} z_t=A & z_t=JD & z_t=D \\ \hdashline s & 1-s & 0\\ 0 & 0 & 1\\ 0 & 0 & 1 \end{matrix} \hspace{-0.2em} \begin{matrix} & \\ \left . \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \end{matrix} } \right ) \begin{matrix} z_{t-1}=\text{alive} \\ z_{t-1}=\text{just dead} \\ z_{t-1}=\text{dead for good} \end{matrix} \end{matrix}$

Observation matrix

$\begin{matrix} & \\ \mathbf{\Omega} = \left ( \vphantom{ \begin{matrix} 12 \\ 12 \\ 12\end{matrix} } \right . \end{matrix} \hspace{-1.2em} \begin{matrix} y_t=1 & y_t=2 & y_t=3 \\ \hdashline 1 - p & 0 & p\\ 1 - r & r & 0\\ 1 & 0 & 0 \end{matrix} \hspace{-0.2em} \begin{matrix} & \\ \left . \vphantom{ \begin{matrix} 12 \\ 12 \\ 12 \end{matrix} } \right ) \begin{matrix} z_{t}=A \\ z_{t}=JD \\ z_{t}=D \end{matrix} \end{matrix}$

### 8.4.3 Cause-specific mortalities

Koons et al. (2014), Fernández-Chacón et al. (2016) and Ruette et al. (2015)

## 8.5 Stopover duration

Guérin et al. (2017) for a comparison of method, would be great to reproduce all analyses.

## 8.6 Actuarial senescence

Choquet et al. (2011), Péron et al. (2016) and Marzolin, Charmantier, and Gimenez (2011).

## 8.7 Uncertainty in age

E.g. Gervasi et al. (2017).

## 8.8 Uncertainty in age and size

E.g. Gowan et al. (2021).