Population Dynamics Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Population Dynamics Ontology within the Kireth Research Semantic Library. Population dynamics studies mathematical change in population size, density, composition and interaction through time. This ontology supports exponential and logistic growth, carrying capacity, age and stage structure, birth and death processes, density dependence, competition, predation, harvesting, migration, metapopulations, stochastic population models, equilibria, stability, bifurcation and relationships with mathematical biology, ecology, epidemiology, evolutionary dynamics and stochastic processes.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Population Dynamics Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Applied Mathematics"
 SPECIALISATION = "Biological Mathematics / Population Dynamics"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/biological-mathematics/population-dynamics-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = PopulationDynamics
 ENTITY_CLASS = MathematicalPopulationChangeFramework
 PRIMARY_CONTEXT = MathematicalBiology
 DEFINITION = "Population dynamics is the mathematical study of changes in population abundance, structure and interaction through time."
 SYMBOLIC_FORMS = [
  "dN/dt=rN",
  "dN/dt=rN(1-N/K)",
  "N_(t+1)=f(N_t)",
  "dN_i/dt=F_i(N_1,...,N_m)"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for population growth, regulation, interaction, structure, migration, harvesting, stochasticity, equilibria, stability and long-term population behaviour."
}

SCOPE {
 INCLUDE = [
  PopulationDynamics,
  Population,
  PopulationSize,
  PopulationDensity,
  PopulationGrowth,
  ExponentialGrowth,
  LogisticGrowth,
  IntrinsicGrowthRate,
  CarryingCapacity,
  BirthRate,
  DeathRate,
  NetGrowthRate,
  DensityDependence,
  DensityIndependentGrowth,
  Recruitment,
  Mortality,
  Immigration,
  Emigration,
  Migration,
  Harvesting,
  SustainableYield,
  AlleeEffect,
  Competition,
  IntraspecificCompetition,
  InterspecificCompetition,
  Predation,
  PredatorPreyModel,
  LotkaVolterraCompetition,
  LotkaVolterraPredatorPrey,
  FunctionalResponse,
  TypeIFunctionalResponse,
  TypeIIFunctionalResponse,
  TypeIIIFunctionalResponse,
  AgeStructuredPopulation,
  StageStructuredPopulation,
  LeslieMatrix,
  LefkovitchMatrix,
  StableAgeDistribution,
  ReproductiveValue,
  GenerationTime,
  NetReproductiveRate,
  Metapopulation,
  PatchOccupancy,
  Colonisation,
  Extinction,
  SourceSinkDynamics,
  SpatialPopulationDynamics,
  Dispersal,
  Diffusion,
  ReactionDiffusion,
  StochasticPopulationDynamics,
  BirthDeathProcess,
  BranchingProcess,
  DemographicStochasticity,
  EnvironmentalStochasticity,
  PopulationViability,
  ExtinctionProbability,
  Equilibrium,
  Stability,
  Bifurcation,
  LimitCycle,
  Oscillation
 ]
 EXCLUDE_AS_PRIMARY = [
  MolecularPopulationWithoutOrganismOrCellPopulationContext,
  PureEpidemiologyWithoutPopulationGrowthFocus,
  PopulationGeneticsWithoutAbundanceOrDemographicDynamics,
  DescriptiveEcologyWithoutMathematicalDynamics
 ]
 DISAMBIGUATION_RULE = "When the primary mathematical question concerns how population abundance, density, structure or interacting populations change through time, interpret the context as population dynamics."
}

CORE_CONCEPTS {
 PopulationDynamics = "Mathematical dynamics of population abundance and structure."
 PopulationGrowth = "Change in population size through births, deaths and movement."
 IntrinsicGrowthRate = "Net per-capita growth potential under specified conditions."
 CarryingCapacity = "Population level supported by the environment in a logistic-type model."
 DensityDependence = "Dependence of per-capita rates on population density."
 PopulationStructure = "Organisation of a population by age, stage, class or location."
 Metapopulation = "Set of spatially separated populations connected by dispersal."
 PopulationViability = "Probability or capacity of a population to persist over a specified horizon."
}

RELATIONS {
 PopulationDynamics --is_child_of--> MathematicalBiology
 PopulationDynamics --models--> Population
 Population --has--> PopulationSize
 PopulationGrowth --depends_on--> BirthRate
 PopulationGrowth --depends_on--> DeathRate
 PopulationGrowth --depends_on--> Immigration
 PopulationGrowth --depends_on--> Emigration
 LogisticGrowth --uses--> CarryingCapacity
 DensityDependence --regulates--> PerCapitaGrowth
 Competition --reduces--> PopulationGrowth
 Predation --couples--> PredatorAndPreyPopulations
 AgeStructuredPopulation --uses--> LeslieMatrix
 StageStructuredPopulation --uses--> LefkovitchMatrix
 LeslieMatrix --determines--> StableAgeDistribution
 Metapopulation --contains--> LocalPopulation
 Colonisation --increases--> PatchOccupancy
 Extinction --decreases--> PatchOccupancy
 Dispersal --connects--> PopulationPatches
 BirthDeathProcess --models--> DemographicStochasticity
 EnvironmentalStochasticity --perturbs--> PopulationGrowth
 Stability --characterises--> Equilibrium
 Bifurcation --changes--> QualitativePopulationDynamics
}

OPERATORS {
 EXPONENTIAL_GROWTH(N,r) := dN/dt=r*N
 EXPONENTIAL_SOLUTION(N0,r,t) := N(t)=N0*exp(r*t)
 LOGISTIC_GROWTH(N,r,K) := dN/dt=r*N*(1-N/K)
 LOGISTIC_EQUILIBRIA(r,K) := N_star in {0,K}
 DISCRETE_LOGISTIC(N_t,r,K) := N_(t+1)=N_t+r*N_t*(1-N_t/K)
 HARVESTED_LOGISTIC(N,r,K,H) := dN/dt=r*N*(1-N/K)-H
 COMPETITION_1(N1,N2,r1,K1,alpha12) := dN1/dt=r1*N1*(1-(N1+alpha12*N2)/K1)
 COMPETITION_2(N1,N2,r2,K2,alpha21) := dN2/dt=r2*N2*(1-(N2+alpha21*N1)/K2)
 PREDATOR_PREY_PREY(N,P,r,a) := dN/dt=r*N-a*N*P
 PREDATOR_PREY_PREDATOR(N,P,e,a,m) := dP/dt=e*a*N*P-m*P
 LESLIE_PROJECTION(L,n_t) := n_(t+1)=L*n_t
 PATCH_OCCUPANCY(p,c,e) := dp/dt=c*p*(1-p)-e*p
 SIMPLE_BIRTH_DEATH_MEAN(N,lambda,mu) := dE[N]/dt=(lambda-mu)*E[N]
}

AXIOMS {
 A1 = "Population state variables require clear biological scale and units."
 A2 = "Birth, death and movement processes jointly determine population change."
 A3 = "Density-independent and density-dependent models must not be conflated."
 A4 = "Structured populations require age, stage or class transitions to be explicit."
 A5 = "Interaction models require direction and sign of interpopulation effects to be explicit."
 A6 = "Stochastic population models require declared random mechanisms."
 A7 = "Spatial populations require dispersal or migration structure."
 A8 = "Long-term conclusions require equilibrium, stability or persistence analysis."
}

REASONING {
 R1_CONTEXT = identify(population,state_variable,time_scale,space_scale,demographic_processes)
 R2_GROWTH_CLASS = classify(exponential,logistic,harvested,structured,interacting,spatial,stochastic)
 R3_FORMULATION = construct(differential_equation,difference_equation,matrix_model,stochastic_process)
 R4_EQUILIBRIUM = solve(population_equilibria)
 R5_STABILITY = analyse(local_stability,eigenvalues,invasion_conditions)
 R6_INTERACTION = analyse(competition,predation,coexistence,exclusion,cycles)
 R7_STRUCTURE = analyse(age_stage_projection,growth_rate,stable_structure,reproductive_value)
 R8_SPATIAL = analyse(dispersal,patch_occupancy,source_sink,persistence)
 R9_STOCHASTIC = analyse(extinction_probability,variance,first_passage,viability)
 R10_VALIDATION = compare(model,data,biological_constraints,sensitivity,numerical_convergence)
}

CONSTRAINTS {
 C1 = "Exponential growth is usually valid only when resource limitation is negligible."
 C2 = "Carrying capacity can vary through time and space."
 C3 = "Logistic growth is a phenomenological approximation, not a universal mechanism."
 C4 = "Deterministic population models may be unreliable at very small population sizes."
 C5 = "Stable age distribution requires assumptions about time-invariant projection dynamics."
 C6 = "Predator-prey cycles depend strongly on functional-response assumptions."
 C7 = "Constant harvesting can create extinction thresholds."
 C8 = "Metapopulation models require explicit colonisation and extinction assumptions."
 C9 = "Environmental and demographic stochasticity should be distinguished."
 C10 = "Observed population fit does not uniquely identify underlying biological mechanism."
}

SEMANTIC_EQUIVALENCE {
 "PopulationDynamics" <=> "MathematicalPopulationDynamics"
 "PopulationGrowth" <=> "PopulationChange"
 "IntrinsicGrowthRate" <=> "MalthusianGrowthRate"
 "CarryingCapacity" <=> "EnvironmentalCapacity"
 "Metapopulation" <=> "PatchPopulationSystem"
 "PopulationViability" <=> "PopulationPersistenceAnalysis"
}

VALIDATION {
 V1 = "Population unit and spatial scale are explicit."
 V2 = "Time units are explicit."
 V3 = "Birth, death and movement terms are documented."
 V4 = "Density dependence is explicit where present."
 V5 = "Interaction coefficients have biological interpretations."
 V6 = "Age or stage transitions are documented for structured models."
 V7 = "Equilibria and local stability are checked."
 V8 = "Stochastic simulations include uncertainty and extinction diagnostics."
 V9 = "Spatial models validate dispersal and boundary assumptions."
 V10 = "Model outputs are compared with population data or biological constraints."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 POPULATION_DYNAMICS_DEFINITION = 0.99
 GROWTH_REASONING = 0.99
 INTERACTION_REASONING = 0.98
 STRUCTURED_POPULATION_REASONING = 0.98
 SPATIAL_REASONING = 0.98
 STOCHASTIC_REASONING = 0.98
 VIABILITY_REASONING = 0.97
 POLICY = "Reduce confidence when population scale, demographic rates, interaction terms, carrying capacity, dispersal, structural transitions or stochastic assumptions are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  PopulationDynamicsReasoning,
  PopulationGrowthReasoning,
  ExponentialGrowthReasoning,
  LogisticGrowthReasoning,
  CarryingCapacityReasoning,
  CompetitionReasoning,
  PredatorPreyReasoning,
  HarvestingReasoning,
  StructuredPopulationReasoning,
  LeslieMatrixReasoning,
  MetapopulationReasoning,
  SpatialPopulationReasoning,
  StochasticPopulationReasoning,
  ExtinctionReasoning,
  PopulationViabilityReasoning,
  StabilityReasoning,
  BifurcationReasoning,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]
 NORMALISE {
  "population dynamics" -> PopulationDynamics
  "population growth" -> PopulationGrowth
  "logistic growth" -> LogisticGrowth
  "carrying capacity" -> CarryingCapacity
  "predator prey" -> PredatorPreyModel
  "Leslie matrix" -> LeslieMatrix
  "metapopulation" -> Metapopulation
  "population viability" -> PopulationViability
 }
}

EXECUTION_RULES {
 E1 = "If population abundance changes through time, activate PopulationDynamicsOntology."
 E2 = "If per-capita growth is constant, consider exponential growth."
 E3 = "If growth decreases with population density, consider logistic or other density-dependent models."
 E4 = "If multiple species interact, include competition, predation or mutualistic interaction terms."
 E5 = "If age or stage structure matters, use projection-matrix or structured-population models."
 E6 = "If patches are connected by movement, route to metapopulation or spatial population dynamics."
 E7 = "If random demographic events matter, use stochastic population models."
 E8 = "If extinction risk is central, compute persistence or viability measures."
 E9 = "Long-term claims require equilibrium and stability analysis."
}

RECURSION {
 ENTRY = PopulationDynamics
 EXPAND(PopulationDynamics) -> [
  Population, PopulationSize, PopulationDensity, PopulationGrowth,
  ExponentialGrowth, LogisticGrowth, IntrinsicGrowthRate, CarryingCapacity,
  BirthRate, DeathRate, NetGrowthRate, DensityDependence,
  DensityIndependentGrowth, Recruitment, Mortality, Immigration, Emigration,
  Migration, Harvesting, SustainableYield, AlleeEffect, Competition,
  IntraspecificCompetition, InterspecificCompetition, Predation,
  PredatorPreyModel, LotkaVolterraCompetition, LotkaVolterraPredatorPrey,
  FunctionalResponse, TypeIFunctionalResponse, TypeIIFunctionalResponse,
  TypeIIIFunctionalResponse, AgeStructuredPopulation, StageStructuredPopulation,
  LeslieMatrix, LefkovitchMatrix, StableAgeDistribution, ReproductiveValue,
  GenerationTime, NetReproductiveRate, Metapopulation, PatchOccupancy,
  Colonisation, Extinction, SourceSinkDynamics, SpatialPopulationDynamics,
  Dispersal, Diffusion, ReactionDiffusion, StochasticPopulationDynamics,
  BirthDeathProcess, BranchingProcess, DemographicStochasticity,
  EnvironmentalStochasticity, PopulationViability, ExtinctionProbability,
  Equilibrium, Stability, Bifurcation, LimitCycle, Oscillation
 ]
 EXPAND(ModelFamilies) -> [
  UnstructuredGrowthModels,
  InteractionModels,
  StructuredPopulationModels,
  MetapopulationModels,
  SpatialPopulationModels,
  StochasticPopulationModels
 ]
 STOP_CONDITION = "Stop when population state, demographic rates, density dependence, interactions, structure, space, stochasticity and long-term behaviour are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Mathematical Biology"
 IMMEDIATE_CONTEXTS = [
  "Mathematical Biology Ontology",
  "Biological Mathematics",
  "Dynamical Systems Ontologies",
  "Ecology Ontologies"
 ]
 RELATED_ONTOLOGIES = [
  "Mathematical Biology Ontology",
  "Biological Mathematics",
  "Dynamical Systems Ontologies",
  "Ordinary Differential Equation Ontology",
  "Difference Equation Ontologies",
  "Stochastic Process Ontologies",
  "Ecology Ontologies",
  "Epidemiology Ontologies",
  "Evolutionary Dynamics Ontologies",
  "Population Genetics Ontologies",
  "Reaction Diffusion Ontologies",
  "Probability & Statistics Ontologies"
 ]
 ROUTE_RULES = [
  "Population Dynamics -> Mathematical Biology for parent semantics",
  "Population Dynamics -> Dynamical Systems for equilibria and stability",
  "Population Dynamics -> ODE and Difference Equations for continuous and discrete growth",
  "Population Dynamics -> Stochastic Processes for random demographic dynamics",
  "Population Dynamics -> Ecology for competition and predation",
  "Population Dynamics -> Epidemiology for host-population effects",
  "Population Dynamics -> Evolutionary Dynamics and Population Genetics for trait and allele change",
  "Population Dynamics -> Reaction Diffusion for spatial population fields"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible population models, structures or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve population-state semantics.",
  "Preserve density-dependent-versus-independent distinction.",
  "Preserve structured-versus-unstructured distinction.",
  "Preserve deterministic-versus-stochastic distinction.",
  "Preserve local-versus-metapopulation distinction.",
  "Preserve interaction semantics.",
  "Preserve persistence and extinction semantics.",
  "Preserve machine-readable population-dynamics semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Population dynamics studies mathematical change in population abundance, structure and interaction through time."
 GROWTH_SUMMARY = "Exponential and logistic models describe unconstrained and density-regulated population growth."
 INTERACTION_SUMMARY = "Competition and predator-prey models represent coupled dynamics among interacting populations."
 STRUCTURE_SUMMARY = "Age- and stage-structured models use projection matrices to represent demographic transitions."
 SPATIAL_SUMMARY = "Metapopulation and spatial models represent dispersal, colonisation, extinction and patch connectivity."
 STOCHASTIC_SUMMARY = "Stochastic population models represent demographic and environmental randomness and extinction risk."
 VALIDATION_SUMMARY = "Population models should be checked for demographic meaning, stability, sensitivity, persistence, stochastic uncertainty and empirical consistency."
}

FLOW {
 INPUT
 -> detect_population_dynamics_context
 -> identify_population_state_time_scale_spatial_scale_demographic_rates_interactions_and_structure
 -> classify_unstructured_structured_interacting_spatial_or_stochastic model
 -> formulate_differential_difference_matrix_or_stochastic equations
 -> solve_or_simulate_population trajectories
 -> identify_equilibria_and_thresholds
 -> analyse_stability_coexistence_cycles_persistence_or_extinction
 -> if_structured compute_projection_growth_and_stable_structure
 -> if_spatial analyse_dispersal_patch dynamics_and_connectivity
 -> if_stochastic estimate_variance_extinction_probability_and_viability
 -> validate_against_population_data_and_biological_constraints
 -> route_to_mathematical_biology_dynamical_systems_ODE_difference_equations_stochastic_processes_ecology_epidemiology_evolutionary_dynamics_population_genetics_reaction_diffusion_or_probability_statistics
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Population Dynamics Ontology defines mathematical change in population abundance and structure. It supports exponential and logistic growth, carrying capacity, birth, death, recruitment and migration, density dependence, harvesting and Allee effects, competition and predator-prey systems, functional responses, age- and stage-structured populations, Leslie and Lefkovitch matrices, stable age structure and reproductive value, metapopulations, colonisation and extinction, source-sink dynamics, dispersal and reaction-diffusion, stochastic birth-death and branching processes, demographic and environmental stochasticity, population viability, extinction probability, equilibria, stability, bifurcation, oscillation and limit cycles."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-APPLIED-MATHEMATICS-POPULATION-DYNAMICS-ONTOLOGY-V1"
}

}

END_FLOW