Reproduction and Inheritance • artificialLifeR

library(artificialLifeR)

Purpose

This article explains reproduction and inheritance in artificial-life models. Reproduction allows a population to persist across time. Inheritance allows traits to be transmitted from parent to offspring (Darwin 1859; Nowak 2006).

The purpose of this chapter is to show how reproduction transforms individual-level traits into population-level continuity.

The guiding question is:

How does reproduction transform individual traits into population-level continuity?

Why reproduction matters

Reproduction is central to artificial life because it creates continuity across time. Without reproduction, a population may disappear as agents die, lose energy, or reach the end of their simulated lifespan.

Reproduction allows a system to move from a collection of individual agents to a population with generational structure. Once agents can reproduce, traits can persist, spread, disappear, or change across time.

This matters because artificial-life systems are often interested not only in what agents do now, but in how populations change across repeated cycles.

Reproduction as continuity

Reproduction creates continuity. It allows traits to appear in later generations.

In artificialLifeR, reproduction is simplified. Agents with enough energy can create offspring. Offspring inherit traits from the parent, with optional mutation.

This is not a full biological model. It does not represent sexual reproduction, meiosis, DNA, embryological development, or real heredity. Instead, it represents a general artificial-life principle:

A population can persist when agents produce offspring that carry forward some traits.

Inheritance as structured persistence

Inheritance matters because it preserves structure. If offspring were completely unrelated to parents, selection would have little cumulative effect. A useful trait could appear in one generation but vanish immediately in the next.

Inheritance allows traits to persist long enough for population-level change to occur.

This does not require a full genetic model. Even simple trait copying can illustrate the idea that offspring resemble parents. This resemblance is what makes cumulative change possible.

Process	Why it matters
Reproduction	Creates new agents
Inheritance	Preserves parent-offspring similarity
Mutation	Introduces variation
Selection	Changes which traits become more common
Population dynamics	Shows the system-level consequence

Reproduction and inheritance provide continuity. Mutation and selection provide change.

Relation to the package

The function simulate_reproduction() provides a simplified reproduction model.

Argument	Conceptual meaning
`agents`	Starting population
`mutation_rate`	Probability of trait change in offspring
`mutation_sd`	Size of mutation-like trait change
`seed`	Reproducibility

The exact reproduction rule is simplified. The goal is to make the logic of parent-offspring continuity visible and teachable.

Example: create a starting population

Start by creating a population with relatively high energy so that some agents can reproduce.

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
)

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

Compare population size before and after reproduction

data.frame(
  before = nrow(agents),
  after = nrow(offspring_pop)
)
#>   before after
#> 1     30    58

Interpretation

The population may increase because some agents had enough energy to reproduce. Offspring inherit traits from their parent, so the population after reproduction contains continuity with the previous population.

A careful interpretation is:

The simulation illustrates simplified reproduction and trait continuity in an artificial population.

An overstatement would be:

The simulation fully models biological reproduction.

The first statement is appropriate. The second is not.

Measuring inherited trait structure

We can compare trait summaries before and after reproduction.

rbind(
  before = measure_life_like_complexity(
    agents,
    trait_col = "efficiency"
  ),
  after = measure_life_like_complexity(
    offspring_pop,
    trait_col = "efficiency"
  )
)
#>         n unique_values  entropy      mean         sd temporal_variability
#> before 30            30 2.990759 0.5065472 0.09620988                   NA
#> after  58            32 2.964487 0.5100594 0.09335160                   NA
#>        mean_abs_change
#> before              NA
#> after               NA

Interpretation of trait summaries

The summary helps show whether trait variation changed after reproduction. If offspring inherit traits from parents, the population after reproduction should retain some connection to the previous population.

However, the metric does not prove biological inheritance. It summarizes a simulated trait distribution.

Reproduction with low mutation

Low mutation preserves stronger similarity between parent and offspring.

low_mutation_pop <- simulate_reproduction(
  agents,
  mutation_rate = 0.02,
  mutation_sd = 0.02,
  seed = 4
)

rbind(
  before = measure_life_like_complexity(
    agents,
    trait_col = "efficiency"
  ),
  low_mutation = measure_life_like_complexity(
    low_mutation_pop,
    trait_col = "efficiency"
  )
)
#>               n unique_values  entropy      mean         sd
#> before       30            30 2.990759 0.5065472 0.09620988
#> low_mutation 58            30 2.964487 0.5094780 0.09404328
#>              temporal_variability mean_abs_change
#> before                         NA              NA
#> low_mutation                   NA              NA

Reproduction with higher mutation

Higher mutation introduces more variation into offspring traits.

high_mutation_pop <- simulate_reproduction(
  agents,
  mutation_rate = 0.50,
  mutation_sd = 0.10,
  seed = 4
)

rbind(
  before = measure_life_like_complexity(
    agents,
    trait_col = "efficiency"
  ),
  high_mutation = measure_life_like_complexity(
    high_mutation_pop,
    trait_col = "efficiency"
  )
)
#>                n unique_values  entropy      mean         sd
#> before        30            30 2.990759 0.5065472 0.09620988
#> high_mutation 58            47 2.881063 0.5223238 0.10760506
#>               temporal_variability mean_abs_change
#> before                          NA              NA
#> high_mutation                   NA              NA

Interpretation of mutation during reproduction

Mutation changes how strongly offspring resemble parents.

A low mutation rate supports continuity. A higher mutation rate introduces more novelty. Both are important in artificial-life systems.

Too little mutation may limit novelty. Too much mutation may weaken inherited structure. Interesting artificial-life dynamics often depend on a balance between continuity and change.

Reproduction is not enough

Reproduction alone does not fully explain evolution-like change. Evolution-like dynamics require more than producing offspring.

At minimum, they require:

Variation: agents must differ.
Inheritance: some traits must persist across generations.
Differential success: some traits must become more common because they affect survival or reproduction.

If every individual reproduces equally and offspring are identical, population composition may remain stable. Reproduction creates continuity, but selection-like processes are needed for directional change.

This distinction is important:

Reproduction allows persistence. Selection changes composition.

Reproduction and energy

In many artificial-life models, reproduction depends on energy. An agent must have enough energy to produce offspring.

This creates a connection between environment, resource use, and population growth. Agents that acquire enough energy can reproduce. Agents that do not may fail to reproduce or may die.

This makes reproduction a bridge between individual-level state and population-level dynamics.

Level	Example
Individual state	Energy level
Rule	Reproduce if energy is high enough
Population outcome	Population growth or continuity

Reproduction and open-ended dynamics

Artificial-life systems often use reproduction to study open-ended dynamics, adaptation, and population change (Ray 1991; Bedau 2003).

Reproduction allows a simulation to continue beyond the lifespan or state of any single agent. Once reproduction, inheritance, mutation, and selection-like processes are combined, the system can show more complex long-term behavior.

However, open-endedness in artificial life is difficult. A simple reproduction function does not guarantee open-ended evolution. It only provides one necessary ingredient.

Relation to other artificial-life processes

Reproduction is most meaningful when connected to other processes.

Process	Relationship to reproduction
Resource competition	Determines which agents gain enough energy
Mutation	Introduces variation into offspring
Selection	Changes which traits persist
Population dynamics	Shows the system-level consequences
Complexity metrics	Summarize trait and population changes

simulate_reproduction() should therefore be understood as one part of the artificial-life toolkit, not a complete model by itself.

What the model captures

The reproduction model captures several important ideas:

populations can persist through offspring;
offspring can inherit parent traits;
mutation can introduce variation;
reproduction links individual state to population growth;
continuity across generations makes selection-like change possible.

These ideas are central to artificial-life modelling.

What the model does not capture

The model is intentionally simplified. It does not include:

sexual reproduction;
real genetics;
DNA or RNA;
meiosis;
development;
parental investment;
complex life cycles;
biological inheritance systems;
real reproductive ecology.

It is a teaching model for conceptual exploration.

Responsible interpretation

The function does not model sexual reproduction, genetics, development, or real heredity. It illustrates the general idea that offspring can inherit traits from parents.

It is better to say:

The simulation illustrates simplified reproduction and inheritance-like continuity.

than:

The simulation models biological reproduction.

It is better to say:

Mutation during reproduction can introduce trait variation.

than:

The model represents real genetic mutation.

Careful interpretation keeps the model useful and academically credible.

Educational use

This chapter can support several classroom or self-study questions:

Why is reproduction important for artificial life?
How does inheritance create continuity?
Why is reproduction alone not enough for evolution?
How does mutation affect parent-offspring similarity?
Why does energy matter for reproduction?
What is the difference between persistence and adaptation?
What would need to be added to model biological reproduction more realistically?

These questions help learners understand reproduction as one ingredient in a broader artificial-life system.

Key takeaway

Reproduction and inheritance allow artificial populations to persist and change over time. Reproduction creates new agents. Inheritance preserves continuity between generations. Mutation introduces novelty.

Together, these processes make selection and adaptation-like dynamics possible. In artificialLifeR, they are represented in simplified form to make the logic of artificial-life systems visible and teachable.

References

Bedau, Mark A. 2003. “Artificial Life: Organization, Adaptation and Complexity from the Bottom Up.” Trends in Cognitive Sciences 7 (11): 505–12.

Darwin, Charles. 1859. On the Origin of Species. John Murray.

Nowak, Martin A. 2006. Evolutionary Dynamics: Exploring the Equations of Life. Harvard University Press.

Ray, Thomas S. 1991. “An Approach to the Synthesis of Life.” In Artificial Life II, 371–408. Addison-Wesley.