Build detailed life cycle matrices for organisms. Compute lambda, reproductive values, sensitivities, and stage abundances. Turn biological assumptions into practical population insights today.
Enter a 3 × 3 stage transition matrix, starting abundances, and projection periods. The matrix may represent a Lefkovitch style life cycle.
| Stage | Starting abundance | Stasis | Progression | Fertility contribution |
|---|---|---|---|---|
| Juvenile | 120 | 0.00 | 0.55 to Subadult | 0.00 |
| Subadult | 60 | 0.25 | 0.60 to Adult | 0.00 |
| Adult | 35 | 0.85 | 0.00 | 1.80 juveniles per adult |
A stage structured model projects population change with a transition matrix. Each period uses the matrix equation n(t + 1) = A × n(t), where A is the stage matrix and n(t) is the population vector at time t.
The dominant eigenvalue λ estimates asymptotic growth. If λ is greater than 1, the population grows. If λ equals 1, the population is stable. If λ is less than 1, it declines.
The right eigenvector gives the stable stage distribution. The left eigenvector gives reproductive values. Sensitivity shows how λ changes when a matrix entry changes slightly. Elasticity scales that response proportionally, revealing the most influential life cycle transitions.
It is a population model that groups organisms by life stage instead of exact age. The matrix tracks survival, progression, stasis, and reproduction between stages over repeated time periods.
The dominant eigenvalue, λ, describes long run population growth per period. Values above 1 indicate growth, 1 indicates stability, and below 1 indicates decline under unchanged assumptions.
Many organisms are easier to monitor by stage because size, maturity, or reproductive status matters more than exact age. Stage models capture realistic biological transitions with fewer field data demands.
It is the long run proportion of individuals expected in each stage if the transition matrix remains constant. It helps compare current structure with eventual model behavior.
Reproductive values measure the relative long term contribution of each stage to future population growth. Higher values identify stages with stronger strategic importance for persistence.
Sensitivity shows the absolute effect of a small matrix change on λ. Elasticity shows the proportional effect, making it easier to compare entries that have different scales.
Yes. When λ is below 1, the model indicates decline. The halving time estimate helps show how quickly abundance shrinks under the current transition assumptions.
Accuracy depends on matrix quality and whether biological conditions remain similar across periods. Use the calculator for structured analysis, then validate assumptions with field observations or experiments.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.