By Jillian Kunze
Climate change is having a major impact on where many animal species are able to live. “Around the globe, species are shifting their geographical ranges — on average, they’re moving deeper into the oceans, to higher elevations, and towards the poles,” Alexa Fredston of Rutgers University said. “This is a global reorganization of biodiversity.” Though a few species may benefit from warming temperatures, most will be and are being harmed as their traditional habitat becomes too warm. Humans also feel the consequences as species move their ranges, such as the outbreak of Zika virus in North America that was enabled by an increased range of the mosquito species that carries the disease.
During a minisymposium presentation at the SIAM Annual Meeting, which took place virtually last week, Fredston presented a model of short-term changes in the range of marine species. The range is the geographical extent of a species, which—depending on the available data and how widespread the animal is—may be known with anywhere from a very high to fairly low resolution. “Keep this complexity at the back of your mind,” Fredston said. “The concept of range is hard to pin down precisely.” Scientists have detected shifts in the ranges of many species all over the world, and Fredston was interested in learning why and how they happen.
Figure 1. The spatial model included a series of patches going up the U.S. east coast, each one degree in latitude.
This research specifically focused on marine species because the dynamics of range shifts are much easier to study in the ocean. There are fewer barriers to migration, as well as more contiguous habitat — for example, there is less change on the sandy bottom of the ocean than in most terrestrial habitats. Many ocean creatures are also very sensitive to changes in temperature.
In addition, all regions of the global ocean are expected to warm due to climate change, and some are expected to warm a lot. “This is not just an academic question,” Fredston said. “The shifts that have already occurred have caused huge problems for communities of people who live near the oceans and rely on marine resources for their livelihood and culture.” Predicting when and how these range shifts will occur is essential for preparing for future changes and enacting policies that will help communities.
Changes in range for most species do not occur solely based on temperature. There are a number of fundamental drivers of species range, including nonlinear climate thresholds, temperature extremes, non-equilibrium dynamics, habitat availability, species interactions, non-temperature abiotic factors, and limitations on dispersal. Many marine species thus have a complex relationship with the climate, and these many factors cause them to undergo huge population booms and busts that are not well understood.
Fredston described the development of a process-based model to predict short-term changes in species range, with work done in collaboration with Andrew Allyn, Daniel Ovando, and Malin Pinsky. Process-based dynamic range models can estimate demographic properties that are not immediately evident in a data set and simulate how the number of individuals in a species will change in the future.
She developed this model in partnership with the Mid-Atlantic Fisheries Management Council, who were particularly interested in four marine species: the summer flounder, gray triggerfish, shortfin squid, and spiny dogfish. The spatial model incorporated a series of patches along the U.S. east coast, each with a height of one degree in latitude (see Figure 1). This was a relatively reasonable assumption for the marine species of interest, because most of these fish live primarily on the continental shelf.
The age structure of a population—i.e., how many individual fish there are in each age group—can reveal a lot of information about a fish population, as the quantity of fish at different ages reveals what conditions were like when they were born. Fredston implemented a Bayesian hierarchical model with a focus of estimating the true number of individuals of each age in a patch for a given year.
However, this is not easy to do based on the available data from the surveys of fish population that the National Oceanic and Atmospheric Administration have been conducting every year since the 1960s. “The observation process is hard to model, since small fish don’t get caught — they slip through the net,” Fredston said. The model needed to estimate how many fish there really were based on how many were caught, considering the population’s age structure. And the most common data point from the survey is zero fish, which Fredston accounted for with a two-stage model: it first estimates the probability of encountering the species at all, and from there attempts to determine how many fish there are of different ages.
The model incorporated a temperature dependence into recruitment, a parameter that represents the production of very small fish through both reproduction and early survivorship — i.e., how many tiny fish enter the population. It estimated the optimal temperature for that process and how much the recruitment drops off when the fish’s habitat diverges from that temperature. Fredston passed the model the true temperature, as well as the true estimated mortality rate since there were already many other parameters that it needed to estimate.
Figure 2. Preliminary model results for the summer flounder in a single patch. Each panel represents a different age group of the fish. The black dots are survey records, and red lines are model predictions with blue as the credible interval.
In Figure 2, Fredston presented some preliminary results using the new model on data for the summer flounder in one patch. While the eventual goal is to see how fish move between patches from year to year in response to temperature changes and other dynamics, the actual nuts and bolts of the model occur at the patch level. These results show what the model predicted would be caught in the survey, compared to actual data of what was caught. The model was able to capture a recruitment pulse throughout the age groups — one year with particularly good conditions creates a peak in the abundance of fish recruited that year, which then propagates through the age groups over time as those fish grow older.
While the model was able to capture recent trends in the abundance of summer flounder, the real test is to see how the model performs when it is not drawing from samples. Fredston tried training the model on 35 years of data, then forecasting future years without giving the model the relevant data for those years. The model again was able to capture how a peak would propagate throughout different age groups over the years, though it did not perform very well at predicting the abundance of fish at older ages.
In the future, Fredston plans to fit the model to other species, compare to more traditional modeling frameworks, and explore how different model choices affect the fit to the data. “I feel fairly encouraged by the preliminary results,” Fredston said. “The model qualitatively recreated recent trends in summer flounder abundance.” She is optimistic that the model will eventually be able to provide useful short-term forecasts that will help researchers and policymakers prepare for changes in species range.
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Jillian Kunze is the associate editor of SIAM News. |