Contests over mates can be very costly.

Alternative reproductive strategies (ART's) can develop as a way to minimise these costs. This package implements an individual based model (sometimes called an agent based model), that explores how and why these ART's emerge in a theoretical species, which has non overlapping generations.

The males mature before the females. All females mature at the same time.

Starting at time `0`

, we pull the time of an immature males maturation from
the exponential distribution with scale parameter `maturation_rate`

, which is the average time at which a male will mature.

The longer males take to mature the more mass they have, this is influenced by
the parameters `growth_a`

and `growth_b`

.
Their mass increases according to the differential equation:

```
dm/dt = growth_a * m ^ growth_b
```

This is solved with the initial condtion `m(0) = initial_mass`

When males mature they have an `energy`

budget. The ammount of energy a male has
when it matures is given by `energy = mass * mass_to_energy`

.

Males have a metabolic cost of `metabolism`

per time unit.

Mature males then explore a patch and encounter nests.
For each male, we pull the time of the next nest
encounter from the exponential distribution
with the scale parameter `encounter_delta`

. Which is the average time between encounters.

A nest is then selected. If it is guarded/occupied by a male then a contest over ownership of the nest will take place, if it is not occupied the searching male will then guard/occupy the nest.

Males that are occupying nests when the females mature get to mate, and pass on their traits to the next generation of males.

Each occupied nest produces `males_per_nest`

immature males in the next generation.
The new males inherit their fathers genes with a chance `mutation_rate`

to add some gaussian noise with mean 0 and standard deviation `mutation_sd`

.

Males make a judgement on their opponent based on mass difference.
Each male calculates a commitment value, according to a commitment function.
Their traits
`alpha`

and `beta`

deterimine how sensitive a male are to percieved difference in mass.
For example male A's commitment against male B is

```
commitment = exp(beta)*((A.mass/B.mass)*z)^alpha
```

Where `z`

is a random number drawn from an f distribution with degrees of freedom `contest_noise`

, `contest_noise`

. To represent the two judgements that a male has to make, that about its own size and that of its opponents.
If `contest_noise`

equals 0 then z = 1.

The male that has chosen to commit more to the fight will win.

The cost of the fight to each male is the commitment, this is deducted from a males energy.

For each surviving male from a generation the following is logged
* What generation it is from
* The males alpha trait
* The males beta trait
* The males mass
* the number of contests (fights) that the male has been involved in

These results are returned as a dataframe.

- implement learning with contest experience

Parameter | Meaning
------------------|-------------------------------------------------------
max_gens | Maximum number of generations to run the simulation for.
males_per_winner | Number of male offspring per occupied nest.
num_nests | The number of nests that males can fight over. Also the initial number of males.
encounter_delta | Mean time between nest enounters for a male.
metabolism | How fast males use energy just by searching or occupying.
female_mat_time | The time at which females mature.
maturation_rate | Location parameter for the maturation of males.
mutation_rate | How frequently mutations to traits occur.
mutation_sd | mutations are mean zero with this much noise.
mass_to_energy | Mass to energy scaling factor.
growth_a | Growth parameter a.
growth_b | Growth parameter b.
initial_mass | The inital mass of a male.
alpha_mean | The mean used to initialiseation of the `alpha`

contest trait.
alpha_sd | The mean used to initialiseation of the `alpha`

contest trait.
beta_sd | The sd used to initialiseation of the `beta`

contest trait.
beta_max | The maximum value of the `beta`

contest trait.
beta_mean | The mean used to initialiseation of the `beta`

contest trait.
contest_noise | The degrees of freedom used to generate the contest error.
log_every | Log traits of winners ever this number of generations.
verbose | Whether or not to print detailed mesages to the console.
quiet | Whether or not to print generation messages.

You can install this package with devtools.

```
if(!require(devtools)) install.packages("devtools")
devtools::install_github("johnwilshire/contest")
```

You can then run the model like so:

```
library(ggplot2)
library(dplyr)
winners <- contest::run_simulation(
max_gens = 1000,
males_per_winner = 20,
num_nests = 500,
encounter_delta = 1,
metabolism = 1,
female_mat_time = 10,
maturation_rate = 1,
mutation_rate = 0.1,
mutation_sd = 0.1,
mass_to_energy = 10,
growth_a = 0.5,
growth_b = 0.1,
initial_mass = 5,
alpha_mean = 0,
alpha_sd = 3,
beta_sd = 3,
beta_mean = 0,
beta_max = 20,
contest_noise = 100,
verbose = F,
quiet = F)
winners %>% filter((generation %% 50) - 1 == 0) -> reduced_winners
# plots of traits through generations
ggplot(reduced_winners, aes(generation, alpha)) + geom_point()
ggplot(reduced_winners, aes(generation, beta)) + geom_point()
```

This package was created using Rcpp.

- Tests (Which? How? Where?)
- Males
- immature mortality ?
`Why is this needed in the model again?`

- immature mortality ?
- logging
- log deaths and energy expenditure

- update licence, (is GPL ok?)

johnWilshire/contest documentation built on May 18, 2017, 3:42 a.m.

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