Animal populations constantly rise and fall for many reasons. Scientists often use mathematical models to describe these patterns and to find out, for example, why a particular year was good or bad for a population, or why numbers were different in the past from the present. Answers can provide insight into population changes over time, including year-to-year variations and broader, long-term trends that may span decades. 

We at the U.S. Fish and Wildlife Service have built a population model that helps us predict population levels for both the eastern and western North American monarch populations. Our model is similar to previously published models in many ways. But unlike many other models, which focus only on reconstructing past population patterns, our model looks forward into future patterns. 

Monarch butterflies taking a break from migration by roosting in a tree in Illinois.

What is the goal of the monarch model? 

We developed our population model to predict the monarch’s future population size and help us determine whether monarchs are in danger of disappearing and in need of protection. Decision makers use our future-focused model to evaluate how policy or environmental changes may affect monarch population levels and risk of extinction. The monarch model can also provide information on the rate of population decline, indicating whether we have time to continue to collect data or if immediate action might be needed. The monarch model is one tool, among many others, to inform decision makers about the health of monarch populations. 

How does the monarch model work? 

We designed our monarch population model to predict two key factors: the future population size of the eastern or western populations, and the risk that the population might drop below a tipping point, when it becomes too small to avoid extinction. In our model, the population’s growth or decline is determined by: 

  • The latest estimate of the overwintering population 
  • The current rate that the population is growing or declining 
  • The tipping point, the threshold at which the population is too small to recover 
  • A random factor that accounts for environmental conditions that change every year (for example, total rainfall) 
  • The main factors (habitat, climate, pesticide use) that influence population levels 

We provide a set of starting values for each of these. For our main factors, we also include information about how they might change in the future. For example, we include information about projected climate change climate change
Climate change includes both global warming driven by human-induced emissions of greenhouse gases and the resulting large-scale shifts in weather patterns. Though there have been previous periods of climatic change, since the mid-20th century humans have had an unprecedented impact on Earth's climate system and caused change on a global scale.

Learn more about climate change
, rates of pesticide use and expected habitat loss or gain, and how each affects the monarch population. We run the model using a simulated population that grows and responds the way a real monarch population does. The results are predictions of monarch population size, year-by-year, extending as far into the future as we program the model to run (see figures 1 and 2). It allows us to answer the question “does the future monarch population ever reach the tipping point - a point at which extinction becomes inevitable?” 

We run the model separately for the eastern and western populations. In both cases, we test the model on a million experimental populations (1 million simulations each for east and west populations). Remember, there is a degree of randomness built into the model that reflects changing environmental conditions. This means each time we run the model, the simulation is a little different, providing one possible future scenario. After a million experimental runs, we see a wide variety of possible futures. Monarchs may go extinct in some of these futures, but not in others. 

How do you deal with the unknowns? 

Every model has areas of uncertainty, especially when attempting to predict the future. We do not know how the main factors – climate change, habitat loss, pesticide use -- will change in the future. And we don’t know how the population will respond to changes in these factors. Our model was built by having species experts provide predictions about the way a population is likely to respond to a threat or benefit of a given magnitude, but these predictions themselves rely to some extent on assumptions.  While we can get an idea of the where the “tipping point,” is, we can’t pinpoint it precisely. 

It’s not possible to create a model that tells us exactly what is going to happen to the monarch population. But we can address this uncertainty by running our model many times with slightly different assumptions and values each time. This gives us a portfolio of conditions, ranging from the likely best case to the likely worst case, and we can see how changing our assumptions can affect the monarch population. 

We don’t attempt to use models to predict the future with precision or rely on one single future scenario. Rather, we run many versions of our models many times each. This allows us to estimate the range of future conditions under various scenarios, how likely each is and even the potential impact of different human actions. Policy makers then have a wealth of information about possible and probable futures to work with. The results of modeling, together with other tools like expert elicitation or risk assessments give decision makers the scientific foundation they need to determine whether monarchs need protection, and if so, when and how to protect them.

Go to Monarch Initiative Page