What is the PoPS model?

The PoPS Model Equation

The flexible, customizable PoPS (Pest or Pathogen Spread) model simulates reproduction, dispersal, and establishment of pests (e.g., insects) and pathogens (i.e., viruses, bacteria, or other organisms that cause disease) through space and time. The PoPS model is the power-house behind the PoPS Forecasting Platform.

For every location in a landscape, at each time step, the PoPS model predicts the number of infested or infected hosts (Ψ). To better understand how the model works, let's take a detailed look at the equation governing the PoPS model.

The PoPS Equation

To break down how the model works, let’s consider pests dispersing from a single location (cell i) and arriving in another single location (cell j).

The PoPS Model Equation

At time t, the number of infested/infected hosts in cell j as a result of pests/pathogens in cell i is Ψijt, which can be described by the PoPS model equation:

The PoPS Model

The PoPS model equation can be conceptualized in terms of:

  1. Reproduction (How many pests leave cell i?)
  2. Dispersal (Where do the pests go?)
  3. Establishment (How many hosts in cell j become infected?)
We describe each component below:


Beta (β), the number of pests or pathogens that disperse from a single host under optimal environmental conditions, is the starting point of the PoPS model.

The PoPS Model

Conditions are rarely optimal and locations contain multiple hosts, so β is modified by the number of currently infested or infected hosts (I) and environmental conditions in a location (i) at a particular time (t) to determine reproduction.

The PoPS Model

The reproduction component of the PoPS equation gives the number of pests/pathogens dispersing from cell i to any cell at time t.

The PoPS Model


Now that we know how many pests/pathogens are dispersing from cell i, we need to determine where those pests/pathogens go.

This is where the dispersal component of the PoPS model comes in.

The PoPS Model

The dispersal kernel determines where the new dispersing propagules go; dispersal distance (d) is a function of gamma (γ), which indicates how much dispersal is due to natural processes (alpha-1, α1) or caused by human-mediated transport (alpha-2, α2). The distance of each propagule is determined by drawing from a distribution using either α1 or α2, and its direction is drawn from a distribution that accounts for predominant wind direction (ω) and wind strength (κ). If data are unavailable for these factors, then the distribution is a circle with equal probability in all directions.

The PoPS Model

The dispersal component of PoPS lets us know where the pests/pathogens from cell i go. From that, we determine how many pests/pathogens arrive at cell j.


Now that we know how many pests/pathogens arrive in cell j from cell i, we need to calculate how many hosts in cell j become infested/infected as a result.

Establishment depends on the environmental conditions in cell j and the availability of suitable hosts, calculated as the number of susceptible hosts (S) divided by the total number of potential hosts (N).

The PoPS Model

The establishment component of the PoPS equation predicts the number of infested or infected hosts in cell j at time t.

The PoPS Model

Putting it all together

Combining the reproduction, dispersal, and establishment components of PoPS, we can calculate Ψijt (the number of infested/infected hosts in cell j at time t as a result of pests/pathogens from cell i).

The PoPS Model

The PoPS Model

What we’ve described so far is a prediction of the number of infected hosts in a single cell as a result of pests/pathogens from another single cell. What we want to know is the total number of infected hosts across all cells in the entire landscape.

A spatially explicit, discrete-time model

The PoPS model performs these calculations for each cell in the landscape, for every time step in the simulation. The value of Ψ is predicted for each cell, forecasting the spread of a pest or pathogen from infested or infected hosts to susceptible hosts, among all cells, across the landscape.

Watch the video to see reproduction, dispersal and establishment across a landscape.

With considerable optimization and parallelization, PoPS runs quickly, even for landscapes with millions of cells.

The PoPS Model
Example PoPS simulation of a pest spreading across the United States

More model details

PoPS is a modular, spatially explicit, discrete-time model: various components (e.g., weather effects or long-range dispersal) can be included or excluded from the model as necessary (through intuitive on-off switches on the interface) depending on the drivers that influence the species of interest; the model accounts for spatial relationships and movements between grid cells in a landscape; and it forecasts across sequential time steps (which can be specified as either daily, weekly, monthly, or yearly).

Learn more about how PoPS handles:

How can I use PoPS?

PoPS is open source and freely available for anyone to use. There are two ways you can use PoPS:

Option 1: Download PoPS to run on your computer

Users may download the PoPS model code for:

  • R
  • Python (coming soon)

The PoPS Model

Option 2: Use the web-based PoPS Dashboard

(Available for public use soon.)

No coding experience? We developed an easy-to-use interface to run the PoPS model in the cloud. The dashboard is currently being used internally and will be made available for public use soon.

Get notified when the PoPS Dashboard is available:
The PoPS Model