Draft:Movement Ecology

Movement ecology is a sub discipline of ecology that focuses on studying the movement behavior of individuals and the coordinated movement of groups of individuals. It seeks to understand the effects of both external environmental factors (e.g.: weather, landscape topography, and resource distributions; presence of conspecific and heterospecific predators, competitors, and symbionts) and internal individual-state factors (e.g., hunger, thirst, physiology, and state-of-mind drivers) on when, where and why individuals move to known and unknown places. Although animal movement studies can be traced back to Aristotle (4th century B.C.), and even Jeremiah who described the temporal consistency of bird migratory patterns in the 7th century B.C., a unifying paradigm for studying the movement of organisms was only formulated around 2007. .



Researchers in the field of movement ecology use various technologies, including Global Positioning Systems (GPS), reverse GPS tracking, tri-axial accelerometer and physiological (e.g. temperature ) data retrieved from sensors place on individuals remote sensing, and mathematical modeling, to monitor and analyze the movement tracks of individuals. A review of recent trends in movement ecology included the following graphic on the history of movement ecology research publications, highlighting critical events in this history.

By studying movement ecology, scientists can gain insights into the spatial ecology of organisms, the impacts of habitat fragmentation and climate change on animal movements, and the conservation of migratory species.

DATA SOURCES
The focal dataset in movement ecology is a relocation time series
 * $$\mathcal{T}^{\rm loc}=\{(t;x_t,y_t) | t=0,\cdots,T\}$$

whose properties can either be studied on its own using the methods of time series analysis or in the context of landscape and other (e.g., accelerometer data, an individual's internal state) covariates of the individual's location in time and space. The earliest such time series were collected using radio telemetry and in the 1960's included movement data from wild porcupines and grizzly bears. From the early 2000s, the automated collection of animal movement relocation time series data became increasingly prevalent, collected at increasingly higher frequencies and for increasingly longer periods of time so that today movement ecology has entered the Big data era of science.

In the tradition of data sharing in science the data portal Movebank was established in 2012 as repository for sharing data, particularly in support of studies reporting and analyzing movement data in the scientific literature. . As of April 2024, this repository included more than 8,200 studies containing data on more than 6.3 billion location points.

DERIVED TIME SERIES
The two most important time series in movement ecology that that can be derived from $$\mathcal{T}^{\rm loc}$$ defined above are the step length (SL) and heading direction time series (DH). In terms of using these time series for analyses, the step length time series is more often referred to as the velocity, $$v$$, time series, though this only holds true if the times series is collected using a fixed time interval that sets a fixed frequency, $$F$$, of collection, thereby allowing the speed of movement to be computed using the speed=frequency$$\times$$distance-moved relationship. The quantities velocity, $$v$$ and heading $$\theta$$ are computed from the time series $$\mathcal{T}^{\rm loc}$$ using the following equations
 * $$\mathcal{T}^{v}=\{(t,v_t) | t=1,\cdots,T\}, \quad \mbox{where} \quad v_t = F \sqrt{\left(x_{t}-x_{t-1}\right)^2 + \left(y_t-y_{t-1}\right)^2}$$

and
 * $$\mathcal{T}^{\theta}=\{(t,\theta_t) | t=1,\cdots,T\}, \quad \mbox{where} \quad \theta_t = {\rm arctan}\Bigl(\frac{y_t-y_{t-1}}{x_{t}-x_{t-1}}\Bigr)$$

and the arctan is computed using the atan2 function.

Beyond these two times series, movement ecologists often compute the following quantities that require computing changes in position and or heading from one time step to the next: turning angle ($$\Delta \theta$$, change in heading), persistent velocity ($$v^P = v \cos \theta$$, which is maximized when there is no change in heading, or minimized and negative when direction is reversed) and tangential velocity ($$v^T= v \sin \theta$$, which is maximized when a complete right or left turn is made).

MOVEMENT MODES AND PATH SEGMENTATION
Identifying the current behavioral movement state or movement mode is a central theme of many movement ecology studies. Various types of path segmentation methods are used to identify the behavioral states associated with points along the movement track time series $$\mathcal{T}^{\rm loc}$$. The most popular two methods are behavioral change point analysis (BCPA  ) and hidden Markov models (HMM   ).

More recently, a hierarchical track structure approach has been proposed as a way to use information theory to assess the performance of hierarchical path segmentation methods