EECS Project: Learning the governing equations of ecological dynamics
Apply scientific machine learning methods to time-series from a three-year ecological field experiment to help disentangle the role of predator-prey interactions in driving the abundance dynamics of a species-rich community in the Oregon marine intertidal.
Scientific machine learning methods — which include the use of neural networks, symbolic regression, neural ordinary differential equations, and universal differential equations --- are a rapidly-developing means to learn the governing equations of both simple and complex system dynamics from data. Using these methods, the goal of the project will be to infer the equations (the model) that describes and predicts how predator-prey interactions influence population dynamics in the Oregon marine intertidal. The data for doing so comes from a unique field experiment in which species abundances and the feeding rates of a focal intertidal predator, the whelk Nucella ostrina, was monitored on a monthly basis for a total of three years. Progress towards achieving the goals of this project will serve as novel comparison to traditional (non-machine learning) methods of inferring and characterizing species interactions, and will lead to a better, predictive understanding of how complex ecological systems respond to the extrinsic and intrinsic perburbations.
Understanding how and why species abundances vary in space and over time represents a fundamental and pressing challenge for the field of Ecology. Many processes influence species abundances, including both extrinsic disturbances such as weather events, seasonality, and climate change, and intrinsic processes such as birth-death events, predator-prey interactions, and competition for limited resources. These multi-dimensional processes inherent to species-rich ecological communities mirror the processes that underlie complex adaptive systems in general.
The experiment was conducted at Yachats Beach, OR. In July 2013, we established 18 randomly-located patches in the mussel bed of this site by scraping away all living material within them. Each patch was created as a square, 1.5 x 1.5 meters in size, had large bolts drilled into two opposing corners so that it could be relocated over time. The 18 patches are labelled by letters: A, B, C,...,F, G, AB, AC,..., AE (there is no AA patch). Within each patch we established 9 randomly-located quadrats, each 25 x 35 cm large, by placing small bolts in two opposing corners. The quadrats are numbered 1-9 (hence AC9 refers to the 9th quadrat in patch AC).
The patches differ from each other in various ways, both for deterministic and stochastic reasons. For example, they differ in their aspect and immediate surroundings, which affect how forcefully waves crash onto them. They also differ in their tidal height and hence how long they are submerged for each high tide. In this regard, all that we have data on is their tidal heights, hence in most regards we must assume the patches to be random samples of the intertidal from the population of potential intertidal locations that we could have sampled.
For the next ~3 years, we returned to the site each month to survey species' ensuing population dynamics. That is, we followed the system's patterns of succession. (A handful of months were missed due to dangerous wave conditions.)
Each month, two types of surveys were performed:
Each of the 18 x 9 = 162 quadrats was photographed. We then used ImageJ to locate (x-y coordinates) and count the individuals of every identifiable "species" in (a subset of) the pictures. Unfortunately, because of the amount of time required to process each picture, only 3 of the 9 quadrats in each patch were processed over the entire duration of the time-series. (Other EECS teams are working on automating the process.) Therefore, the in-hand data consist of counts in each of 18 x 3 = 54 quadrats per survey. (In each patch, the 3 focal quadrats are always the same 3 quadrats for the entire time series.)
Focal species -- There are 27 type categories of "species". However, the primary (prey) species of interest are the acorn barnacle Balanus glandula (Bg, Type 1), the gooseneck barnacle Pollicipes polymerus (Pp, Type 11), and the mussel Mytilus trossulus (Mt, the combination of Type 7 and Type 15). These are the most abundant species in the patches. They are also the primary prey to the focal predator species, two Nucella whelks, whose feeding we have data on.
Each month, we also performed feeding surveys of two predatory snails (whelks), Nucella ostrina and Nucella canaliculata, in the patches. Each survey was performed at the patch scale (not quadrat-specific) and consisted of a careful examination of every found individual to see whether it was feeding or not feeding. (We typically tried to survey the whole patch, but often -- due to time or waves -- could only survey a fraction of the patch and the whelks within that fraction).
On the basis of the size of the whelk, the identity and size of its prey item, and temperature, we can back-calculate the "detection time" of each observed feeding event (i.e. the length of time that the whelk would, on average, take to feed on a prey item, which determines how likely we are to detect a feeding event). Using these detection times (
Focal species -- Nucella ostrina is far more abundant that Nucella canaliculata, thus it's the former species' feeding behaviour that is of primary interest.
Temperature is an important biological variable, dicating process rates at individual physiological scales (e.g., metabolic rates) to community and ecosystem scales (e.g., predator feeding rates). We measured temperature using several TidBit data-loggers positioned at various locations around the site (both just below the lowest patch and just above the highest patch). Measurements were taken every 15 minutes, thus encompass both low-tide (exposed => air) and high-tide (submerged => water) temperatures.
The overarching questions are, (how) can we (best) describe and explain (1) the population growth rates of the species (as a function of their own abundance, the abundance of the other species, temperature, time (season), and/or space)?, and/or (2) the feeding rates of Nucella ostrina (as a function of their prey species' abundances, their own abundance, temperature, time (season), and/or space)?
While many "traditional" statistical methods have been tried, they all rely on knowing/assuming the "right" predator-prey population-dynamics model (or set of hypothesized models) a priori and fitting it to the data to estimate parameters. However, recent work (here and here), suggests the prospect of learning the "right" model from the data itself.
- PySR: parallel symbolic regression built on Julia, and interfaced by Python
- YouTube: Automated Discovery of Mechanistic Models via Universal Differential Equations
- YouTube: Discovering Symbolic Models from Deep Learning with Inductive Biases (Paper Explained)
- DiffEqFlux.jl – A Julia Library for Neural Differential Equations
Mark Novak ([email protected])
