In jmaspons/LHR: Tools for Life History Modeling

The model description follows the ODD (Overview, Design concepts, Details) protocol for describing individual- and agent-based models (Grimm et al. 2006, 2010). A implementation of the model in R available at https://github.com/jmaspons/LHR.

1. Purpose

The model explore the effects of the life history and behavior in the establishment of introduced populations in new environments where the individuals don't have information on the available habitats.

2. Entities, state variables, and scales

Individuals are defined by the age class (sub-adult, adult), the habitat they are in (2 different habitats), and the reproductive state of the adults (non-breeder, succesful breeder or failed breeder). The two available habitats can modify the original demographic parameters by decreasing survival at a given age class or increasing the probability of a breeding failure. Every timestep represents a year and simulations run for 50 timesteps. At the end of the simulation we obtain the proportion of the replicated populations that survive.

3. Process overview and scheduling

At each timestep a proportion $Pb$ of the adults decide to breed. The others, $S$ skip the reproduction. The breeders try to reproduce $broods$ times. Every brood/litter can completely fail with a probability $PbF$. Failed breeders enter the state $Bf$ and succesful breeders, the state $B$. The number of offsprings surviving until the next timestep ($J$) depends on the juvenile survival ($j$) and the number of offspring per brood ($b$). Adults can decide to change habitat with a probability $c$ or $cF$ for failed breeders. The probability to go to the habitat 1 is $P_{1}$ and habitat 2 $1 - P_{1}$. Finally, we apply the mortality for the adults. Breeders survive with a probability $ab$ and the non-breedres with a probability of $a$.

The pseudocode below descrive a timestep transition for a strategy with no subadult stages (age at first reproduction = 1). For simplicity, only the populations of one of the two habitats are shown. For transitions involving habitat change, a numeric subindex refers to the population of a definite habitat ($N_{1}$ or $N_{2}$). $Bin(n, p)$ corresponds to a random samples from a binomial distribution with size parameter $n$ and probability $p$.
$N_{t+1} = f(N_t, Pb, broods, b, PbF, j, a, ab, c, cF, P1b, P1s)$

// Adult' state
$Adults = B_{t} + Bf_{t} + S_{t}$
$Breeders = Bin(Adults, Pb)$
$S = Adults - Breeders$
$J = 0$

// Breeding
$for~ i~ in~ 1:broods {$
$~~~ B = Bin(Breeders, 1 - PbF)$
$~~~ Bf = Breeders - B$
$~~~ J = J + Bin(B * b, j)$

// Movement of the breeders after each brood:
$~~~ Bf_{1} = Bf_{1} + Bin(Bf_{2}, cF * P_{1}b) - Bin(Bf_{1}, cF * (1 - P_{1}b))$
$~~~ B_{1} = B_{1} + Bin(B_{2}, c * P_{1}b) - Bin(B_{1}, c * (1 - P_{1}b))$
$}$

// Movements of the non-reproductive adults (once per timestep):
$S_{1} = S_{1} + Bin(S_{2}, c * P_{1}s) - Bin(S_{1}, c * (1 - P_{1}s))$

// Survival and age transitions:
$S_{t+1} = Bin(S, a)$
$Bf_{t+1} = Bin(Bf, ab)$
$B_{t+1} = Bin(B, ab) + J$

4. Design concepts

Demographyc stochasticity is at the core of the model and we explore how it affects the persistence of populations for different life history strategies and the effects of behavior.

TODO: references

We don't restrict nor link the life history and behavior. We want to understand and show mechanisms explaining the coevolution of life history and behavior by exploring the costs and benefits of behavior for different life history strategies even if no intrinsict cost are included for more complex behaviors like learning by past experience.

Individuals make decisions about changing the patch they are in or to skip a breeding attempt according to their current state.

Stochasticity is implemented at the demographic level by modeling survival from binomial distributions with different probabilities for each life history strategy and the state of individuals. For behavior, patch changes and skipping reproductive events also include stochasticity by means of random deviates from binomial distributions with different probabilities.

We collect the proportion of persisting populations for each simulation.

5. Initialization

The simulations start with a range of initial population sizes balanced between the two habitats (from 2 to 100). The initial population is composed by adults. The initial state of the adults doesn't affect the model because the state is determined at the begining of every timestep.

6. Submodels

The demographic parameters come from empirical data from birds. With the choosen parameters we estimated juvenile survival ($j$) for a given deterministic growth rate $\lambda$ corresponding to the Leslie matrix model by solving the Euler-Lotka equation:

$$j = \frac{sa^{1-AFR} \left(\lambda^{1+AFR} - a * \lambda^{AFR}\right)} {b * \lambda}$$ where $sa$ is the sub-adult survival, $a$ is the adult survival, $AFR$ is the age at first reproduction, and $b$ is the anual fecundity (broods * litter/clutch size).

jmaspons/LHR documentation built on May 13, 2019, 9:52 p.m.