# Population Ecology, Biodiversity, and Food Web Calculators Model population growth, carrying capacity, species interactions, field estimates, biodiversity, and trophic energy transfer in one ecology workflow. > Canonical page: https://elysiatools.com/en/hubs/population-ecology-biodiversity-food-web-calculators - **Category:** analyze-model - **Keywords:** population ecology calculator, biodiversity calculator, Shannon diversity index, Simpson diversity index, carrying capacity calculator, Lotka Volterra simulator, mark recapture estimator, logistic population growth, food web energy transfer, trophic level calculator ## Overview This hub brings together the calculations used to move from field observations to a clearer ecological picture. Model exponential and logistic population growth, estimate carrying capacity, compare competition and predator-prey dynamics, estimate abundance from mark-recapture data, and describe community diversity with richness, Shannon, and Simpson metrics. Food-web tools then connect those populations to biomass and trophic energy transfer. The calculators make their equations and assumptions visible for classroom, field-planning, and data-checking use. ## Tools - Biomass Pyramid & Energy Flow (10% Law): Trophic pyramid from producer energy and transfer efficiency: per-level energy, % of base, losses, and why energy pyramids stay upright. - Carrying Capacity Estimator (Fit K from Time-Series Data): Least-squares logistic fit of K, r, t₀ from `time, population` observations, with fitted curve, residuals, and plateau warnings. - Exponential Population Growth (N_t = N₀·e^(rt)): Compute N_t = N₀·e^(rt) with fold change, doublings, doubling time, or half-life. - Logistic Population Growth (N_t = K/(1+((K−N₀)/N₀)·e^(−rt))): Compute Verhulst logistic growth toward carrying capacity K, with instantaneous dN/dt and capacity percentage. - Lotka–Volterra Interspecific Competition Simulator: RK4 simulation of two competing species with phase plane, isoclines, equilibrium, and automatic outcome classification. - Lotka–Volterra Predator-Prey Dynamics Simulator: RK4 simulation of the classic predator–prey oscillator with phase plane, closed orbits, equilibrium, and period analysis. - Mark-Recapture Population Estimate (Lincoln–Petersen & Chapman): Closed-population size from n₁ marked, n₂ caught, m₂ recaptured: Lincoln–Petersen and Chapman estimates with SE and 95% CI. - Population/Resource Doubling Time (Rule of 70): Doubling/halving time from a periodic growth rate: rule-of-70/72/69.3 estimate vs exact discrete and continuous times, with a milestone table. - Shannon Diversity Index (H′ = −Σpᵢ·ln pᵢ): Compute Shannon H′ from species counts with H′max and Pielou evenness, in ln, log₂, or log₁₀ base. - Simpson Diversity Index (D = 1 − Σpᵢ²): Compute Gini–Simpson D, dominance λ, reciprocal 1/λ, and Simpson evenness from species counts. - Species Richness & Evenness (S, Margalef, Menhinick, J = H′/H′max): Richness S with Margalef/Menhinick indices, Shannon H′, Pielou evenness J, and Berger–Parker dominance from a named or plain species list. - Trophic Level Energy Transfer Efficiency (from Measured Levels): Per-step and mean trophic transfer efficiencies from measured level values, with band grading, weakest transfer, and next-level projection. ## Frequently asked questions ### What ecology workflows does this hub cover? It covers population growth and carrying capacity, competition and predator-prey dynamics, abundance estimation, community diversity metrics, biomass pyramids, and trophic transfer efficiency. ### When should I use exponential versus logistic growth? Use exponential growth as a short-term, unconstrained reference model. Use logistic growth when a population is expected to slow as it approaches a carrying capacity; neither model replaces evidence from the actual population time series. ### Can a diversity index alone describe ecosystem health? No. Shannon, Simpson, richness, and evenness summarize different aspects of a sampled community. 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