By Jillian Kunze
As climate change progresses, it will cause long-term global trends like rising sea levels, higher average annual temperatures, and desertification. Natural disasters such as hurricanes, fires, droughts, and floods will also increase in frequency and intensity. This is already becoming apparent, with recent examples including the 2020 wildfires in Australia and the western U.S. These extreme events lead to temporary evacuations, and the prevalence of these events along with long-term changes in temperature, weather, and agricultural suitability could lead groups of people to permanently migrate to new locations.
During a minisymposium presentation at the 2021 SIAM Conference on Applications of Dynamical Systems, which is taking place virtually this week, Skylar Grey of the University of Wisconsin-Madison presented preliminary results from a model of human migration. They particularly examined the impact that the demographic features of populations have on migration, and raised questions on how intersectionality—the combined influence of multiple demographic features, such as race and income—might play a part in migration dynamics.
There are particular climate niches that are particularly suited for humans to live and grow food. But climate change will gradually shift the locations of these niches and prompt humans to migrate along with them. For example, climate models predict that the most suitable place to live in Australia will shift further south, and the southern U.S. will become an overall less suitable place to live due to changes in temperature and the sustainability of farming. The question then becomes how different demographic features will impact who is able to migrate.
Figure 1. Two modeled patches with their own population demographics. Migration occurs between the patches.
A classic example of demographic effects during a natural disaster from sociological history concerns the impact of Hurricane Katrina on New Orleans. Back in the 1930s during the Great Depression, the Home Owners Loan Corporation decided what areas of the city in which they would to invest mortgage relief. Maps from the time show that the neighborhoods that were not provided with mortgage relief were largely the sections populated by racial minorities. The effects of this were still being felt decades later during Hurricane Katrina in 2005, during which lower-income Black communities were impacted especially heavily because their neighborhoods tended to have deeper floods. Maps depicting the floodwater depth in New Orleans during Hurricane Katrina are strikingly similar to the mortgage loan maps from the 1930s — the neighborhoods that did not receive mortgage relief during the Great Depression were also the areas that tended to flood more deeply during the hurricane.
To create a model that reflects the impact of demographics on human migration, Grey drew inspiration from several existing frameworks. “There exist many mathematical models of animal migration, and some statistical models of human migration,” they said. One useful example is the Lotka-Volterra competition model, which depicts animal dynamics and migration caused by resource competition. Other existing work investigates the ecological niche shifts that will occur due to climate change and asks whether species will be able to keep up when the location of their ecological niche moves. And a third model that Grey noted was the gravity model of migration, which uses Newton’s law of gravity to predict how much people will migrate between two locations and has been validated quite a bit in the sociological literature.
The insights from these previous works were helpful as Grey began building a new model of human migration. To consider both local demographics processes and migration dynamics, their new model incorporated two distinct patches—separate locations with their own local population dynamics—and allowed members of the population to migrate between them (see Figure 1). This validity of this patchy approach can be seen in looking at a U.S. census map, which depicts how different the demographics of disparate areas can be. Similar to how the Lotka-Volterra model depicts competition between species, Grey’s model depicts competition between patches, with each patch trying to attract more people.
Figure 2. Equilibrium points (red and blue dots) in the phase plane for the population migration model, along with trajectories (black lines) showing how the system will behave. \(x\) is the population of one of the patches, and \(y\) is the population of the other. In this particular scenario, both patches have a carrying capacity of 100,000 people, and the model tends to head to an equilibrium where both patches have a population of 100,000.
Grey next performed an equilibrium analysis to investigate when the system would be at a state of equilibrium—where the population sizes of patches do not change—for different possible values of model parameters, such as the patch carrying capacities. They then looked at the stability of equilibria and investigated how the system would behave when it began in different places. “If we start somewhere, where are we going to head?” they said. “It's not clear from just looking at the equilibria.” To depict this, Grey showed a graph of possible equilibria states along with the trajectories that the system might take (see Figure 2). The location of equilibria depended on the patch dynamics, but the stability of those equilibria depended on the migration parameters. Changing one of those parameters altered the output of the model, often very dramatically.
In the future, Grey hopes to inform the model using data from sources such as the U.S. 10-year census and the American Community Survey, which is smaller in scale but gathers information more frequently. Data such as the population size, number of births, and number of deaths in a county could be useful for teasing out the differences between local dynamics due to birth and death rates and migration dynamics.
Grey also plans to incorporate intersectionality into the model by changing the values of model inputs to be matrixes rather than single values. “For example, perhaps the rows of each matrix correspond to race classifications and the columns correspond to socioeconomic status classifications,” they said. Previous natural disaster events indicate that intersectionality will play a large role in future migration caused by climate change, and mathematical models of intersectional populations may reveal some interesting dynamics. “Sociologists have studied many aspects of intersectionality and how it impacts peoples’ lives in terms of the health care they receive, income they earn, and many other outcomes,” Grey elaborated. “It’s about time mathematicians joined in.”
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Jillian Kunze is the associate editor of SIAM News. |