Michael Lavine, J. Roger Brothers, Kenneth J. Lohmann, and Isaac Lavine

The scientific exploration of whether and how migratory animals return to their birth areas goes back at least to John James Audubon, who tied silver threads to the legs of young songbirds and observed their return in the following year. Different species use different cues to find their way home. Some Monarch butterflies spend the summer in eastern North America and the winter in Mexico, while others summer throughout the western U.S. and winter in a small part of California around Santa Cruz and San Diego.

Monarchs appear to migrate by using a combination of the Earth’s magnetic field and the position of the sun, while salmon spend much of their adult lives in the ocean but return to their birth streams to spawn. As infants, or fry, they learn the odor specific to their natal streams. As adults, they use the Earth’s magnetic field to find the general location of their home streams, then follow that odor upstream to where they spawn.

The loggerhead turtle, Caretta caretta, is another species that returns home to reproduce. Adults lay eggs in nests on the south Atlantic coast of the U.S., from Florida to North Carolina. When baby loggerheads hatch, they crawl across the beach, swim out to the Gulf Stream, and enter the North Atlantic gyre. Their survival depends on staying in the gyre, where conditions are favorable. Straying too far north leads them into dangerously cold water, while straying too far south creates the risk of being caught in the South Atlantic gyre and swept too far from their home territory. After several years in the gyre, they return home to nest.

A series of biological experiments has shown that loggerheads, and other sea turtles, use the Earth’s magnetic field to find their way home. These experiments also show the power of statistical graphics to tell a story without the need for complex statistical models.

One of the early experiments was by Lohmann, et al. (2001), who captured hatchling loggerheads that had never been in the ocean and put them in a tank surrounded by a coil that could produce a magnetic field similar to that at pre-selected locations on the globe. Figure 1 shows the results.

Figure 1. Reproduced from Lohmann, et al. (2001), summarizing their results.

The circles represent three locations—one near northern Florida, one near Portugal, and one in the middle of the North Equatorial Current—whose magnetic fields were simulated in the turtle tank. Each dot in a circle represents a turtle that was exposed to that magnetic field. The dot shows the turtle’s mean swimming direction. The arrow is the overall mean of all turtles in that field and the dashed lines enclose a 95% confidence interval for the overall mean.

Turtles exposed to the Florida field tend to swim east, or what would be toward the gyre; those exposed to the Portugal field tend to swim south; and those exposed to the Equatorial Current field tend to swim west. In all cases, the mean swimming direction is consistent with loggerheads’ migratory pattern.

The experiment shows that turtles can detect the Earth’s magnetic field; they use that information to determine which way to swim; and some of their ability must be inherited, not learned, because it occurs in hatchlings that have never been to sea. (Loggerheads may learn to navigate even better after they have been to sea, but that possibility was not addressed by this experiment.) Lohmann, et al., say:

One possible interpretation of the results is that hatchlings inherit a large-scale magnetic map that enables them to continuously approximate their position anywhere in the North Atlantic. However, hatchlings might instead emerge from their nests programmed only to swim in specific directions if and when they encounter magnetic fields resembling those in a few crucial oceanic regions where the risk of displacement from the gyre is high. Thus, young turtles might remain within the gyre and advance blindly along their migratory route without any real conception of their geographic position and without the ability to determine their position relative to a goal.

A subsequent experiment by some of the same biologists (Lohmann, et al., 2004) tried to infer more detail about how turtles use magnetic cues for navigation. This time the experiment was conducted on green sea-turtles, Chelonia mydas. The experimenters captured juvenile turtles, several years old, at their feeding grounds near Melbourne Beach, Florida (marked “Test site” in Figure 2). Then the turtles were exposed to the magnetic field of a site either slightly to the north or slightly to the south, marked as blue dots in Figure 2. Again, the black dots in the circles represent the mean swimming directions of individual turtles.

Figure 2. Summary of results from Lohmann, et al. (2004).

Those exposed to the northern magnetic field swam south, while those exposed to the southern field swam north. According to Lohmann, et al. (2004):

These results indicate that juvenile turtles have a magnetic map sense that helps them navigate to specific targets. …. Turtles may possess a map in which magnetic cues provide only one coordinate, with another environmental feature (which could be the coastline in this case) providing the second. The turtles may swim along the coastline until they encounter a magnetic parameter that marks a specific coastal location. Alternatively, turtles might detect two magnetic elements (such as inclination and intensity) and rely on bicoordinate magnetic navigation.

While the two earlier experiments manipulated magnetic fields in tanks, a more recent study by Brothers and Lohmann (2015) used naturally occurring data. The Earth’s magnetic field changes over time, with isolines converging (getting closer together) in some places and diverging in others. Brothers and Lohmann examined whether those changes are related to changes in where loggerheads nest. If turtles use the magnetic field to navigate, then, where isolines converge, nesting density should increase. Similarly, where isolines diverge, nesting density should decrease.

The International Geomagnetic Reference Field model 11 provides estimates of the Earth’s magnetic field over time, while Florida’s Statewide Nesting Beach Survey records the number of loggerhead nests each year in each county along the coast of Florida. Because loggerheads typically spend two to three years in the ocean between trips to nest sites, Brothers and Lohmann examined the relationship between X = 2-yr change in magnetic field and Y = 2-yr change in nest density.

Figure 3 is a plot of Y vs. X and shows a clear positive relationship—where isolines converge, nests get denser, providing further confirmation that turtles find their nest sites at least partly through magnetism. For this plot, we used X = 2-yr change in magnetic field inclination; using X = 2-yr change in magnetic field strength results in a nearly identical plot.

Figure 3. Relationship between percent change in nesting density and inclination convergence index. Each dot is a two-year time period in a Florida county.

Brothers and Lohmann found that turtles do not rely solely on magnetism:

Successful nesting requires deposition of eggs in a location suitable for incubation. Factors such as beach erosion, sand quality, visual cues, and predation are known to influence where turtles nest on a local scale. Because these and other environmental conditions also affect the likelihood that a nest will yield viable hatchings, natural selection is likely to act against turtles that choose nesting locations by relying on magnetic cues to the exclusion of all else. Moreover, sensory cues other than geomagnetism are likely to help guide natal homing, especially once turtles have arrived in the vicinity of the nesting area.

Another interesting phenomenon is revealed by plotting the data separately for each county, as in Figure 4, where the counties are arranged from Nassau in the north to Miami-Dade in the south. This shows steadily decreasing scatter going south along the coast. At present, we do not know why this occurs.

Figure 4. Relationship between percent change in nesting density and inclination convergence index split by county. Each dot is a two-year time period.

We have seen that good statistical graphics can help tell a good story and suggest an interesting phenomenon to investigate. If we were to continue this analysis using a statistical model, we would need to account for the heteroscedasticity seen in Figure 3. We would also need to decide whether to include the magnetic field’s inclination, or strength, or both, as well as investigate whether the model errors are correlated spatially or temporally.

Learning how turtles navigate required good biological experiments aided by statistical graphics. We thank the biologists for conducting the experiments and we thank Caretta caretta for providing an interesting problem to study.

Further Reading

On Loggerheads

Brothers, J. Rogers and Kenneth J. Lohmann. 2015. Evidence for Geomagnetic Imprinting and Magnetic Navigation in the Natal Homing of Sea Turtles, Current Biology 25:392–396.

Lohmann, et al. 2001. Regional Magnetic Fields as Navigational Markers for Sea Turtles, Science 294:364–366.

Lohmann, et al. 2004. Geomagnetic Map Used in Sea-Turtle Navigation, Nature 428:909–910.

On Other Species

Monarch butterflies.

Salmon.

On Angular Statistics

Fisher, N.I. 1993. Statistical Analysis of Circular Data, University Press: Cambridge.

R package (PDF download).

About the Authors

Michael Lavine was a professor of statistics at Duke University from 1987 through 2008 and is now professor of statistics and director of the Statistical Consulting and Collaboration Center at the University of Massachusetts Amherst. He is author of the free graduate-level text Introduction to Statistical Thought. He has wide interests in statistical methodology and applications, and is subject matter editor for statistical articles in Ecology and Ecological Monographs.

Kenneth J. Lohmann is the Charles P. Postelle, Jr. Distinguished Professor in the Biology Department at the University of North Carolina (UNC). He is on the advisory board of the Galapagos Science Center and a Fellow of the American Association for the Advancement of Science. His research interests include the behavior, sensory biology, neuroethology, and conservation of marine animals.

Isaac Lavine holds a BS degree in mathematics and chemical engineering from Lafayette. He plans to enter a statistics PhD program in the fall of 2016.

J. Roger Brothers is a graduate student in the biology department of UNC-CH.

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