Basis Function Models for Animal Movement

Hooten, Mevin B.; Johnson, Devin S.

doi:10.1080/01621459.2016.1246250

Cited by 30 publications

(54 citation statements)

References 77 publications

(116 reference statements)

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“…Hooten and Johnson (2017a) proposed movement models as convolutions with white noise

μ false(t false) = {boldμ}_{0} + \int_{t_{1}}^{t_{n}} H false(t, normalτ false) d b false(normalτ false),

where μ ( t ) is a 2 × 1 vector that represents the true unobserved animal position at time t (

t_{1} \leq t \leq t_{n}

, where

t_{1}

and

t_{n}

bound the temporal period of interest) and d b (τ) is a two‐dimensional–scaled white noise process (scaled by

σ_{μ}^{2}

). The matrix H ( t , τ) in Equation is a 2 × 2 diagonal matrix with diagonal elements equal to

h false(t, normalτ false) = \int_{τ}^{t_{n}} g false(t, \overset{τ}{true} false) d \overset{false~}{normalτ}

(also called a “basis function;” e.g.…”

Section: General Statistical Frameworkmentioning

confidence: 99%

“…a Gaussian function with location t ). Different choices for g ( t , τ) represent different hypotheses about the ecology of the species under the study (see Figure in Hooten & Johnson, 2017a). For example, both Brownian motion and integrated Brownian motion (i.e.…”

Section: General Statistical Frameworkmentioning

confidence: 99%

“…Warping functions have traditionally been expressed as smooth stochastic functions in the time domain, such as Gaussian processes (e.g. Hooten & Johnson, 2017a). The derivative of the warping function (i.e.…”

Section: General Statistical Frameworkmentioning

confidence: 99%

“…The process convolution in Equation is actually a two‐level nested convolution with the first level resulting in Brownian motion and the second performing the inertial smoothing (Hooten and Johnson, 2017a, 2017b). However, that nested convolution can be expressed as a single process convolution with white noise to obtain the covariance for the Gaussian process model in Equation .…”

Section: General Statistical Frameworkmentioning

confidence: 99%

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Animal movement models for migratory individuals and groups

et al. 2018

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Animals often exhibit changes in their behaviour during migration. Telemetry data provide a way to observe geographic position of animals over time, but not necessarily changes in the dynamics of the movement process. Continuous‐time models allow for statistical predictions of the trajectory in the presence of measurement error and during periods when the telemetry device did not record the animal's position. However, continuous‐time models capable of mimicking realistic trajectories with sufficient detail are computationally challenging to fit to large datasets. Furthermore, basic continuous‐time model specifications (e.g. Brownian motion) lack realism in their ability to capture nonstationary dynamics. We present a unified class of animal movement models that are computationally efficient and provide a suite of approaches for accommodating nonstationarity in continuous trajectories due to migration and interactions among individuals. Our approach uses process convolutions to allow for flexibility in the movement process while facilitating implementation and incorporating location uncertainty. We show how to nest convolution models to incorporate interactions among migrating individuals to account for nonstationarity and provide inference about dynamic migratory networks. We demonstrate these approaches in two case studies involving migratory birds. Specifically, we used process convolution models with temporal deformation to account for heterogeneity in individual greater white‐fronted goose migrations in Europe and Iceland, and we used nested process convolutions to model dynamic migratory networks in sandhill cranes in North America. The approach we present accounts for various forms of temporal heterogeneity in animal movement and is not limited to migratory applications. Furthermore, our models rely on well‐established principles for modelling‐dependent data and leverage modern approaches for modelling dynamic networks to help explain animal movement and social interaction.

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“…Hooten and Johnson (2017a) proposed movement models as convolutions with white noise

μ false(t false) = {boldμ}_{0} + \int_{t_{1}}^{t_{n}} H false(t, normalτ false) d b false(normalτ false),

where μ ( t ) is a 2 × 1 vector that represents the true unobserved animal position at time t (

t_{1} \leq t \leq t_{n}

, where

t_{1}

and

t_{n}

bound the temporal period of interest) and d b (τ) is a two‐dimensional–scaled white noise process (scaled by

σ_{μ}^{2}

). The matrix H ( t , τ) in Equation is a 2 × 2 diagonal matrix with diagonal elements equal to

h false(t, normalτ false) = \int_{τ}^{t_{n}} g false(t, \overset{τ}{true} false) d \overset{false~}{normalτ}

(also called a “basis function;” e.g.…”

Section: General Statistical Frameworkmentioning

confidence: 99%

Section: General Statistical Frameworkmentioning

confidence: 99%

Section: General Statistical Frameworkmentioning

confidence: 99%

Section: General Statistical Frameworkmentioning

confidence: 99%

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Animal movement models for migratory individuals and groups

et al. 2018

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“…Johnson et al (2008) imposed additional smoothness on the resulting stochastic processes by letting a stationary form of Brownian motion (i.e., the Ornstein-Uhlenbeck process) describe the velocity process and then integrating it a second time to result in the position process. This idea to use an integrated form of Brownian motion inspired a class of generalized models using basis function specifications to yield different amounts and types of smoothness in the process to model more realistic animal movement trajectories (Hooten and Johnson 2017b). In this special issue, there are four articles focused on modeling trajectories in continuous time.…”

Section: Continuous-time Modelsmentioning

confidence: 99%

Guest Editor’s Introduction to the Special Issue on “Animal Movement Modeling”

Hooten

King

Langrock

2017

JABES

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Predicting functional responses in agro‐ecosystems from animal movement data to improve management of invasive pests

Wilber

Chinn

Beasley

et al. 2019

Ecological Applications

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Functional responses describe how changing resource availability affects consumer resource use, thus providing a mechanistic approach to prediction of the invasibility and potential damage of invasive alien species (IAS). However, functional responses can be context dependent, varying with resource characteristics and availability, consumer attributes, and environmental variables. Identifying context dependencies can allow invasion and damage risk to be predicted across different ecoregions. Understanding how ecological factors shape the functional response in agro‐ecosystems can improve predictions of hotspots of highest impact and inform strategies to mitigate damage across locations with varying crop types and availability. We linked heterogeneous movement data across different agro‐ecosystems to predict ecologically driven variability in the functional responses. We applied our approach to wild pigs (Sus scrofa), one of the most successful and detrimental IAS worldwide where agricultural resource depredation is an important driver of spread and establishment. We used continental‐scale movement data within agro‐ecosystems to quantify the functional response of agricultural resources relative to availability of crops and natural forage. We hypothesized that wild pigs would selectively use crops more often when natural forage resources were low. We also examined how individual attributes such as sex, crop type, and resource stimulus such as distance to crops altered the magnitude of the functional response. There was a strong agricultural functional response where crop use was an accelerating function of crop availability at low density (Type III) and was highly context dependent. As hypothesized, there was a reduced response of crop use with increasing crop availability when non‐agricultural resources were more available, emphasizing that crop damage levels are likely to be highly heterogeneous depending on surrounding natural resources and temporal availability of crops. We found significant effects of crop type and sex, with males spending 20% more time and visiting crops 58% more often than females, and both sexes showing different functional responses depending on crop type. Our application demonstrates how commonly collected animal movement data can be used to understand context dependencies in resource use to improve our understanding of pest foraging behavior, with implications for prioritizing spatiotemporal hotspots of potential economic loss in agro‐ecosystems.

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Basis Function Models for Animal Movement

Cited by 30 publications

References 77 publications

Animal movement models for migratory individuals and groups

Animal movement models for migratory individuals and groups

Guest Editor’s Introduction to the Special Issue on “Animal Movement Modeling”

Predicting functional responses in agro‐ecosystems from animal movement data to improve management of invasive pests

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