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Reproduction and Mutation Tutorial

Source: vignettes/reproduction-mutation-tutorial.Rmd
reproduction-mutation-tutorial.Rmd

Purpose

This tutorial introduces simulate_reproduction() and simulate_mutation(). Reproduction and mutation are central to artificial life because they allow traits to persist and vary across generations.

The goal is to show how offspring inherit traits and how mutation introduces variation.

Create agents 

agents <- create_agents(
  n_agents = 30,
  energy_mean = 1.8,
  seed = 4
)

head(agents)
#>   agent           x         y   energy      speed efficiency
#> 1     1 0.585800305 0.5671122 1.823020 0.02862954  0.3722340
#> 2     2 0.008945796 0.2389489 1.957790 0.07128901  0.4201988
#> 3     3 0.293739612 0.8779959 1.686868 0.02374556  0.5159082
#> 4     4 0.277374958 0.6545220 1.577672 0.09127389  0.5614798
#> 5     5 0.813574215 0.4823709 1.929170 0.05262766  0.5687948
#> 6     6 0.260427771 0.9710298 1.739322 0.04536623  0.4952949
#>   reproduction_threshold age alive
#> 1               1.486676   0  TRUE
#> 2               1.400023   0  TRUE
#> 3               1.687376   0  TRUE
#> 4               1.466261   0  TRUE
#> 5               1.597327   0  TRUE
#> 6               1.598783   0  TRUE

Simulate reproduction 

offspring_pop <- simulate_reproduction(
  agents,
  mutation_rate = 0.10,
  mutation_sd = 0.03,
  seed = 4
)

nrow(agents)
#> [1] 30
nrow(offspring_pop)
#> [1] 58
head(offspring_pop)
#>   agent           x         y    energy      speed efficiency
#> 1     1 0.585800305 0.5671122 0.9115098 0.02862954  0.3722340
#> 2     2 0.008945796 0.2389489 0.9788949 0.07128901  0.4201988
#> 3     3 0.293739612 0.8779959 1.6868683 0.02374556  0.5159082
#> 4     4 0.277374958 0.6545220 0.7888358 0.09127389  0.5614798
#> 5     5 0.813574215 0.4823709 0.9645849 0.05262766  0.5687948
#> 6     6 0.260427771 0.9710298 0.8696610 0.04536623  0.4952949
#>   reproduction_threshold age alive
#> 1               1.486676   0  TRUE
#> 2               1.400023   0  TRUE
#> 3               1.687376   0  TRUE
#> 4               1.466261   0  TRUE
#> 5               1.597327   0  TRUE
#> 6               1.598783   0  TRUE

Interpretation

Agents with enough energy can produce offspring. Offspring inherit traits from parents, with optional mutation. This is a simplified representation of inheritance, not a full biological reproduction model.

Apply mutation to one trait 

mutated <- simulate_mutation(
  agents,
  trait = "efficiency",
  mutation_rate = 0.50,
  mutation_sd = 0.08,
  lower = 0.01,
  upper = 1,
  seed = 5
)

head(mutated)
#>   agent           x         y   energy      speed efficiency
#> 1     1 0.585800305 0.5671122 1.823020 0.02862954  0.3611151
#> 2     2 0.008945796 0.2389489 1.957790 0.07128901  0.4201988
#> 3     3 0.293739612 0.8779959 1.686868 0.02374556  0.5159082
#> 4     4 0.277374958 0.6545220 1.577672 0.09127389  0.5136947
#> 5     5 0.813574215 0.4823709 1.929170 0.05262766  0.3940775
#> 6     6 0.260427771 0.9710298 1.739322 0.04536623  0.4952949
#>   reproduction_threshold age alive
#> 1               1.486676   0  TRUE
#> 2               1.400023   0  TRUE
#> 3               1.687376   0  TRUE
#> 4               1.466261   0  TRUE
#> 5               1.597327   0  TRUE
#> 6               1.598783   0  TRUE

Compare trait summaries 

rbind(
  original = measure_life_like_complexity(agents, trait_col = "efficiency"),
  mutated = measure_life_like_complexity(mutated, trait_col = "efficiency")
)
#>           n unique_values  entropy      mean         sd temporal_variability
#> original 30            30 2.990759 0.5065472 0.09620988                   NA
#> mutated  30            30 3.057426 0.5154198 0.10882956                   NA
#>          mean_abs_change
#> original              NA
#> mutated               NA

Compare low and high mutation rates 

low_mutation <- simulate_mutation(
  agents,
  trait = "efficiency",
  mutation_rate = 0.05,
  mutation_sd = 0.08,
  lower = 0.01,
  upper = 1,
  seed = 5
)

high_mutation <- simulate_mutation(
  agents,
  trait = "efficiency",
  mutation_rate = 0.80,
  mutation_sd = 0.08,
  lower = 0.01,
  upper = 1,
  seed = 5
)

rbind(
  low_mutation = measure_life_like_complexity(low_mutation, trait_col = "efficiency"),
  high_mutation = measure_life_like_complexity(high_mutation, trait_col = "efficiency")
)
#>                n unique_values  entropy      mean         sd
#> low_mutation  30            30 2.990759 0.5065472 0.09620988
#> high_mutation 30            30 2.919369 0.5313225 0.11819427
#>               temporal_variability mean_abs_change
#> low_mutation                    NA              NA
#> high_mutation                   NA              NA

Interpretation of mutation

Mutation introduces trait variation. Without variation, selection has little material to act on. With too much mutation, inherited structure may become unstable.

A careful interpretation is:

Mutation changes trait distributions in the artificial population.

not:

Mutation alone creates biological evolution.

Suggested exercises

  • Change mutation_sd and observe trait variability.
  • Mutate speed instead of efficiency.
  • Increase initial energy and observe reproduction.
  • Ask how inheritance and variation work together.

Key takeaway

simulate_reproduction() and simulate_mutation() provide simplified tools for exploring inheritance and variation. Together, they help illustrate how artificial populations can change across generations.