What is the Population Ecology Lab multi-solver?

Population Ecology Lab is a guided workflow that chains 4 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.

Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.

Biology & Aerospace Pack · Multi-Solver

Population Ecology Lab

Predator-prey to drift. This multi-solver chains 4 solvers into a single guided workflow — run each step in order and carry the result forward.

Workflow steps

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Lotka Volterra

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Lotka-Volterra Predator-PreyLive

coupled population cycles

Controls

Presets

Prey growth a

Predation rate b

Predator death c

Predator growth d

Two coupled equations produce the classic boom-and-bust cycle: prey multiply, predators feast and multiply, prey crash, predators starve, and the cycle repeats. The phase portrait shows the closed orbit — populations forever chasing each other, never settling.

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Data Inspector

Prey equilibrium20.0

Predator equilibrium10.0

Dynamicslimit cycle

Governing equation

\frac{d x}{d t} = 1 x - 0.1 x y, \frac{d y}{d t} = 0.075 x y - 1.5 y

Reading this result: These parameters trace a closed orbit: prey and predator populations cycle forever without settling, staying about a quarter-period out of phase — the predator peak lags the prey peak. The orbit encircles the fixed point at (prey 20.0, predator 10.0) = (c/d, a/b). Raising predation b (now 0.1) or predator death c (now 1.5) shifts and reshapes that orbit — a higher death rate c pushes the prey equilibrium up and tends to lengthen the boom-and-bust period, while stronger coupling widens the amplitude of each swing.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Logistic Growth

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Logistic Population GrowthLive

growth with a ceiling

Controls

Presets

Growth rate r

Carrying capacity K

Initial population N₀

Exponential growth assumes unlimited resources and explodes without bound. Logistic growth adds a carrying capacity K: as the population nears K, growth slows and levels off in a characteristic S-curve. It is the foundation of ecology, epidemiology, and resource management.

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Data Inspector

Carrying capacity1000

Max growth atN = 500

Growth rate r0.50

Governing equation

\frac{d P}{d t} = 0.50 P (1 - \frac{P}{1000})

Reading this result: Classic S-curve: from N₀=20 the population grows fastest as it crosses the inflection point N=K/2=500, then decelerates and levels off at the carrying capacity K=1000.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Genetic Drift

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Genetic Drift (Wright-Fisher)Live

chance changes allele frequencies

Controls

Presets

Population size N

Initial frequency p₀

Replicate populations

Even with no selection, allele frequencies wander purely by chance as each generation is randomly sampled from the last. In small populations this genetic drift is fast and alleles quickly fix or vanish; in large populations it is slow. Each colored line is an independent population starting from the same frequency.

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Data Inspector

Fixed (reached 1)0

Lost (reached 0)0

Population size50

Governing equation

Var (p) = \frac{p _{0} ( 1 - p _{0} )}{2 N} = \frac{0.5 ( 1 - 0.5 )}{2 \cdot 50} = 0.0025

Reading this result: Over many replicates the fraction that fix an allele converges on its starting frequency p₀=0.5 — drift is directionless, but the odds of fixation equal where you began.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Hardy Weinberg

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Hardy-Weinberg & SelectionLive

population genetics

Controls

Presets

Initial freq of A (p₀)

Fitness AA

Fitness Aa

Fitness aa

Without selection, allele frequencies stay put and genotypes settle at p², 2pq, q² — Hardy-Weinberg equilibrium. Give the genotypes different fitness and selection shifts the allele frequency each generation. Heterozygote advantage (high Aa fitness) can hold both alleles in a stable balance.

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Data Inspector

Final freq A0.500

Outcomepolymorphic

Mean fitness0.95

Governing equation

p^{2} + 2 pq + q^{2} = 0.25 + 0.50 + 0.25 = 1 (p = 0.5, q = 0.50)

Reading this result: Allele A is favored at every genotype, so directional selection drives p toward 1 and eventually fixes A.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Frequently asked questions

What is the Population Ecology Lab multi-solver?: Population Ecology Lab is a guided workflow that chains 4 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.
Is it free to use?: Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.