cjabradshaw / lesliematrixshiny

This app projects a user-defined Leslie (age-classified) matrix to examine population changes through time.

LeslieMatrixShiny

Prof Corey J. A. Bradshaw
Global Ecology, Flinders University, Adelaide, Australia
December 2020
e-mail

Preamble

This app projects a user-defined Leslie (age-classified) matrix to examine population changes through time. This fully customisable app includes a density-feedback function on survival relative to desired initial population size and carrying capacity, stochastic projections with user-defined variance for survival, a generationally scaled catastrophe function, a single 'pulse' disturbance function, and a 'press' disturbance function with a user-defined time application.

A detailed instructions tab (tab H) is included for guidance, but a brief sequence description is included below. User- defined settings in each tab are carried over to subsequent tabs.

1. SET-UP: set matrix dimensions (longevity), age x-specific survival (s_x) and fertility (f_x) probabilities, offspring sex ratio, % variance around survival/fertility probabilties, and whether lifespan is abrupt or diffuse.
2. MATRIX PROPERTIES: shows Leslie matrix according to settings in tab A, as well as the dominant eigen value λ instaneous rate of population change r generation length G, and reproduction number R₀ (number of female offspring/adult female).
3. DENSITY FEEDBACK: set initial population size and carrying capacity K, as well as the three coefficients (a, b, c) from a logistic power function to define the relationship between a survival modifier S_mod and population size.
4. PROJECT: deterministic projection of the population, setting the number of years (or generations) to project the population, initial population size, and whether to invoke the density-feedback function set in the previous tab.
5. STOCHASTIC: stochastic projection of the population based on previous settings (including the % variances set in the first tab); the user can set the number of iterations to repeat the stochastic resampling, the quasi-extinction threshold (population size below which it is considered functionally extinct), and whether to invoke a generationally scaled catatastrophic mortality probability (the magnitude and variance of which can be set by the user).
6. SINGLE PULSE: a single 'pulse' disturbance, where the user can set the disturbance to be either a proportion of the total population that is removed, or a fixed number of individuals removed, at the time (year) the user wishes to invoke the pulse.
7. PRESS: a press disturbance, where the user can set the disturbance to be either a proportion of the total population that is removed, or a fixed number of individuals removed, during the interval over which the user wishes to invoke the press.
8. MVP: calculate the minimum viable population size according to the parameters set in previous tabs.

This Github repository provides all the 'under-the-bonnet' R code for the app.