Spatiotemporal mapping of Karenia brevis blooms

Measurement of cell concentrations

Measurements of Karenia brevis cell abundance have been compiled by the Fish and Wildlife Research Institute, Florida Fish and Wildlife Conservation Commission, for more than seventy years. Blooms are most frequent along the southwest Florida coast, between Anna Maria Island (N lat 27.54) and Marco Island (N lat 25.80), where newly 120,000 samples have been collected. The sampling rate has varied greatly over this period:

The 1954-57 period of intense sampling, funded by the federal government, followed very severe blooms along the Southwest Florida coast in the late 1940s and early 1950s. Sampling rates were greatly decreased in following years due to lack of funds, except for the uptick in the late-1970s. This was the result of studies proving that fish kills accompanying blooms in 1976-78 were caused by brevetoxins produced by K. brevis (then known as Gymnodinium breve), not oxygen deprivation due decaying organic matter. The very severe 1994-96 bloom resulted in action by the Florida Legislature establishing a routine, proactive sampling protocol that continues today.

Data processing: separating signal from noise

Blooms of K. brevis are inherently heterogeneous; even in the midst of a severe bloom, samples taken from the same general area can have cell concentrations ranging from zero to millions of cells per liter. This is caused by current and wind forcing, vertical migration, and localized nutrient sources. As a result, time series of sample cell concentrations form a cloud of points, not a line. The first step to understanding the temporal structure of a bloom is the removal of the noise hiding that structure. This was done with a three-stage cascaded filter:

1. A simple average of the daily measurements to remove sub-daily spatial patchiness;
2. A seven-day, centered moving average acting as a notch filter to remove the weekly sampling protocol artifact; and
3. A 21-day, centered moving average filter to remove transient, short-term events while preserving the lower-frequency oscillations that represent the true temporal structure of the bloom.

Here is the result of this process:

The two peaks are separated by about 100 days. This periodicity is visually evident across all the blooms in the dataset and confirmed by wavelet analysis.

The time-delay logistic equation

This equation was developed by Hutchinson in 1948 as a modification to the traditional logistic equation that creates a sigmoid curve representing exponential population growth that is initially exponential (no resource limitation) and laters slows so as to asymptotically approach an upper bound representing system carrying capacity. The equation recognizes that populations don’t actually behave this way, instead increasing too rapidly so as to overshoot carrying capacity, then decreasing too rapidly so as to drop below carrying capacity. The result is a population oscillation that may be either damped or sustained indefinitely. Sustained oscillations often take the form of limit cycles, where populations rise to levels far in excess of carrying capacity and then crash by orders of magnitude, sometimes repeating the process several times. It appears that K. brevis blooms behave this way (Kurtz, et al, 2024).

 

 

 

---