Pattern Formation in Intertidal Oyster Reefs

By Lina Sorg

Spatial patterns are present in numerous ecological systems, including vegetation, mussel beds, and sea grasses. Researchers believe that scale-dependent feedbacks are responsible for some of these patterns, which span a variety of spatial scales.

Oyster reef networks are a particularly fascinating example of pattern formation in nature. Oysters tend to aggregate in large, colonial reef communities. These reefs are comprised of a bottom layer of sediment, a middle layer of shell and rubble that acts as a substrate to which the oysters can adhere, and a top layer of live oysters. Oyster larvae settle on the hard substrate and do not move, thus allowing the reefs to develop and propagate.

Scientists frequently refer to oysters as “ecosystem engineers” because they significantly impact their own habitat. They attenuate erosion, improve water quality through filtration, provide refuge for other species, and have commercial value. Unfortunately, oyster populations have diminished greatly in the last 100 years, prompting restoration efforts. Many guidelines exist for artificial reef construction that pertain to reef height; salinity/turbidity; geometry/orientation; and flow, which provides the main source of larvae and nutrients. During a virtual minisymposium presentation at the 2020 SIAM Conference on Mathematics of Planet Earth, which is taking place this week, Sofya Zaytseva of the University of Georgia explored the mathematics of pattern formation in intertidal oyster reefs. She focused particularly on flow and geometry/orientation.

Existing literature identifies three different configurations for oyster reefs, based on their orientation. Fringe reefs run parallel to water flow; string reefs run perpendicular to water flow; and patch reefs are smaller, rounded, and have no specific direction (see Figure 1). While much observational evidence exists about these three reef types, most observations are primarily anecdotal.

The goal of Zaytseva’s project is to thus conduct a comprehensive study based on a specific location. She selected a spot near Wachapreague, Va., as the surrounding bay houses a natural network of oysters that have not been harvested or restored. These intertidal reefs are visible on Google Earth during low tide, so Zaytseva and her team flew a drone over the area to collect high-resolution images (see Figure 2). “Even here we have a really diverse set of configurations,” she said. The reefs’ varying shapes and sizes make Wachapreague a good place of study.

The first portion of Zaytseva’s project involved extracting parts of the images that corresponded to the reefs, delineating each reef, and assembling individual polygon features that identify the reefs’ boundaries. The two major categories of image classification are unsupervised and supervised classification; Zaytseva opted for unsupervised classification to reduce bias. Color itself was not enough, so she turned to texture as an additional measure to provide contrast. For example, reefs comprise a higher variability of pixels in the drone images and thus have more texture than water or sediment. Calculating texture therefore separates the oysters from the sediment, which makes the corresponding algorithm more effective. Ultimately, Zaytseva delineated 6,160 oyster reefs.

Next, Zaytseva examined the reefs’ geometric attributes and employed cluster analysis to classify the reefs into types based on their shape, size, and orientation to the main channel. Hierarchical clustering revealed three distinct groups—parallel, perpendicular, and round—as the optimal way to partition the data based on the geometry. These groups were consistent with the fringe, string, and patch configurations in existing literature.

The next part of Zaytseva’s study explores the scale-dependent feedbacks that researchers believe are present in oyster reefs. When the tide comes in, erosion occurs on the reef crest. This erosion helps maintain a suitable substrate for oyster settlement and maximizes filtration efforts, both of which are shore-range positive feedbacks. However, erosion also deposits sediment behind the reef, which inhibits the development of directly adjacent reefs; this is a long-range negative feedback. Reef width and inter-reef distance provide more information on these feedbacks.

Zaytseva is presently using additional data on depth and tidal currents to understand reef geometry and distribution. “We really want to understand what is driving this diversity,” she said. She notes the water flow at each point in space and utilizes it to obtain the average speed and direction during the flood and ebb cycles.

Features such as depth, flow speed, average direction, orientation to flow, distance to main channel, and distance to the source of greatest flow—during both the ebb and flood cycles—are important to the reef development process. Zaytseva set out to determine whether a combination of these features can help predict the shape, size, orientation, spacing, and type of reef. She began with some exploratory data analysis and drew conclusions about the positioning, orientation, and shape of large versus small reefs and elongated versus round reefs, including the fact that reefs tend to orient in two dominant directions. These observations confirm the findings of existing literature. However, the large number of small, round reefs obscure the other data, as the noise from image gathering and classification is distracting. This noise makes it difficult to identify patterns in data and discern interactions between the geometry and drivers.

To handle the noise, Zaytseva adapts a machine learning approach. Her large data set has many features, and their relationships to response variables is not straightforward. She chose to use regression models and decision trees because they tend to be more straightforward and interpretable. Zaytseva specifically employs regularized regression, which is an alternative to classical regression and better for handling correlated features and performing feature selection. It also corrects for the over-fitting that sometimes occurs with classical regression models. This portion of her project is currently ongoing, so Zaytseva is still training the data and does not yet have concrete results.

Ultimately, Zaytseva emphasized that the relationship between oyster reef geometry, flow, and bathymetry is complicated. She and her team utilize a machine learning approach to build predictive models and glean a better understanding of patterns in their data. “We want to gain insight to help with oyster restoration efforts,” she said.

Lina Sorg is the managing editor of SIAM News.