Population Viability Analysis Online

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Overview of Population Viability Analysis Online Model

Mathematical models play a central role in population management programs by enhancing conservation efforts through creating protected areas, improving security in those areas, and / or translocating individuals to bolster or reestablish populations in selected areas. At the core of the most comprehensive and successful of these models lies the Leslie matrix formulation, which incorporates population vital rates with sustainable management and population viability analysis (PVA).

This model is the online compliment of the NOVA Population Viability Analysis Desktop version. These extended PVA models use a Leslie matrix to account for management (harvesting and stocking) and movement between subpopulations along with standard population viability analysis. Demographic rates (births, survival, aging) are calculated at the PVA level, before harvesting, stocking, and movement. Movement can occur with or without relative fitness of the various populations in calculating a multinomial distribution.

Users can interact with the PVA Online model through changing sliders, switches, and entering various rates and values. The online model also allows results to be saved to a local file on your machine.

Sliders and Switches

  • Demographic Stochasticity: determines if the model uses demographic stochasticity or not. If this and Environmental Stochasticity are set to no the model will run in deterministic mode.
  • Environmental Stochasticity in Recruitment: determines if the model uses environmental stochasticity or not. Environmental stochasticity occurs as randomness applied to the survival rates of male and female offspring. The range of stochastic rates are determined by the Min and Max sliders below. If this and Demographic Stochasticity are set to no the model will run in deterministic mode.
  • Adult Male Pseudo-Extinction: this model contains a pseudo-extinction rule. Extinction will occur if / when the number of males per population gets as low (or lower) as the value set by this slider.
  • Adult Female Pseudo-Extinction: this model contains a pseudo-extinction rule. Extinction will occur if / when the number of females per population gets as low (or lower) as the value set by this slider.
  • Min/Max Environmental Stochasticity: if the Environmental Stochasticity switch is set to yes the range of stochastic values for offspring survival rates is chosen between the min and max values set by these sliders.
Users can adjust various sliders and switches
  • Transitions?: determines if there will be transitions between populations or not.
  • Save Data to File? user can export the data from each run to a file on their local machine.
  • Filename: user can set the name of the file to export.
  • Is DD1 / DD2 / DD3: this model can include density dependence of the first age class of males and females (DD1), last age class of males and females (DD2), and / or mature males (DD3).
  • Select Harvest of X: this model can incorporate selective harvesting at different age groups. Young is the first age class of males and females.
  • Female/Male Sex Ratio: this slider determines what percentage of individuals will be female. If set to 1.0, the model will be a single (female) sex model.
  • Include Relative Fitness: if transitions (movements) occurs it can be based on the relative fitness of each population or not.

Model Rates and Values

There are a set of matrices that users can change to determine model rates and values.

  • Connectance: this determines the connectance between populations in the model. It can be read as potential movement from the population at row index i to the population at column index j. Thus, the connectance between populations 2 and 3 is the value at row 2, column 3.
  • Random Harvest: this determines the number of randomly selected individuals that will be harvested (removed) from each population per model iteration.
  • Selective Harvesting Interval: this determines the rate (i.e. every X number of iterations) that selective harvesting will occur per population.
  • Stocking Interval: this determines the rate (i.e every X number of iterations) that stocking will occur per population.
Tableaus 1.png
  • Select Harvest by Class: if selective harvesting occurs, the user can specify which age classes in the populations will be harvested at a rate determined by Selective Harvesting Interval.
  • Propensity to Move by Class: if transitions occur, the user can specify the age-class-specific propensity to move. This is independent of the population-based connectance or relative fitness.
  • Relative Bio Weights by Class: when calculating biomass and relative fitness of each population, each age class has a respective scalar determining its weight in said calculations.
  • Stocking by Class: the user can specify which age classes are stocked (added to), and by what amount, in each population at a rate determined by Stocking Interval.
  • Density Scaling: these scaling values determine the weights of each density dependence calculations per population. These density dependence calculations (DD1, DD2, and DD3) are used in calculating relative fitness of each population.
  • Carrying Capacities: the user can set carrying capacity values for young (DD1: first age class of males and females), old (DD2: last age class of males and females), and mature males (DD3) per population. Note: if the respective Is DDX switches are set to No then these values will be ignored in the calculations.
Tableaus 2.png

The set of green matrices at the bottom of the HTML page represent the survival rates, birth rates, and initial number of individuals per population. Users can go through and change any of these rates and values to be population specific.

Init values rates.png

Multinomial Movement

Each population contains three measures of density dependence. These are calculated via carrying capacities of young (first age class of females and males), old (last age class of females and males), and mature males. In this model we measure the Attractivity (alpha) value of a subpopulation based on its young carrying capacity value (DD1). Each subpopulation also has a Connectivity (C) value, from the Connectance matrix. The relative fitness of each population can be used or not when calculating transitions.

The three values of importance in determining probabilities of transitioning to each location are age class propensity (q), Connectivity to each subpopulation (C), and Attractivity of each subpopulation (alpha). Age class propensity is taken from the Propensity to Move by Class matrix. These three variables (q, C, and alpha) are used to calculate the movement of individuals within each age class per subpopulation. In other words, the model calculates the probability of individuals within each age class to move into each of the six subpopulations, including their originating one.

Two ways to visualize the biomass of 6 different populations

Note: Individuals may end in their originating subpopulation. This could represent those individuals who either did not leave their originating subpopulation in the first place or went on some sort of walk-about and returned after sampling the attractivity of the other populations.