scholarly journals Predicting residence time using a continuous‐time discrete‐space model of leatherback turtle satellite telemetry data

Ecosphere ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. e02644 ◽  
Author(s):  
Aimee L. Hoover ◽  
Dong Liang ◽  
Joanna Alfaro‐Shigueto ◽  
Jeffrey C. Mangel ◽  
Peter I. Miller ◽  
...  
Keyword(s):  
Residence Time ◽  
Continuous Time ◽  
Satellite Telemetry ◽  
Discrete Space ◽  
Telemetry Data ◽  
Leatherback Turtle ◽  
Space Model

scholarly journals Mapping TASEP back in time

2021 ◽  
Author(s):  
Leonid Petrov ◽  
Axel Saenz
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Exclusion Process ◽  
Discrete Space ◽  
Baxter Equation ◽  
Simple Exclusion Process ◽  
Open Questions ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

Modelling spatial patterns in harbour porpoise satellite telemetry data using maximum entropy

Ecography ◽  
2010 ◽  
Vol 33 (4) ◽  
pp. 698-708 ◽  
Author(s):  
Susi M. C. Edrén ◽  
Mary S. Wisz ◽  
Jonas Teilmann ◽  
Rune Dietz ◽  
Johan Söderkvist
Keyword(s):  
Maximum Entropy ◽  
Spatial Patterns ◽  
Satellite Telemetry ◽  
Harbour Porpoise ◽  
Telemetry Data

scholarly journals Using approximate Bayesian inference for a “steps and turns” continuous-time random walk observed at regular time intervals

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e8452
Author(s):  
Sofia Ruiz-Suarez ◽  
Vianey Leos-Barajas ◽  
Ignacio Alvarez-Castro ◽  
Juan Manuel Morales
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Time Scale ◽  
Animal Movement ◽  
State Space Model ◽  
Movement Direction ◽  
Time Intervals ◽  
Space Model ◽  
Regular Time ◽  
Approximate Bayesian

The study of animal movement is challenging because movement is a process modulated by many factors acting at different spatial and temporal scales. In order to describe and analyse animal movement, several models have been proposed which differ primarily in the temporal conceptualization, namely continuous and discrete time formulations. Naturally, animal movement occurs in continuous time but we tend to observe it at fixed time intervals. To account for the temporal mismatch between observations and movement decisions, we used a state-space model where movement decisions (steps and turns) are made in continuous time. That is, at any time there is a non-zero probability of making a change in movement direction. The movement process is then observed at regular time intervals. As the likelihood function of this state-space model turned out to be intractable yet simulating data is straightforward, we conduct inference using different variations of Approximate Bayesian Computation (ABC). We explore the applicability of this approach as a function of the discrepancy between the temporal scale of the observations and that of the movement process in a simulation study. Simulation results suggest that the model parameters can be recovered if the observation time scale is moderately close to the average time between changes in movement direction. Good estimates were obtained when the scale of observation was up to five times that of the scale of changes in direction. We demonstrate the application of this model to a trajectory of a sheep that was reconstructed in high resolution using information from magnetometer and GPS devices. The state-space model used here allowed us to connect the scales of the observations and movement decisions in an intuitive and easy to interpret way. Our findings underscore the idea that the time scale at which animal movement decisions are made needs to be considered when designing data collection protocols. In principle, ABC methods allow to make inferences about movement processes defined in continuous time but in terms of easily interpreted steps and turns.

Limit theorems for processes such as the Markov branching process

1975 ◽  
Vol 12 (02) ◽  
pp. 289-297
Author(s):  
Andrew D. Barbour
Keyword(s):  
Markov Process ◽  
Residence Time ◽  
Continuous Time ◽  
Limit Theorems ◽  
Branching Process ◽  
Continuous Mapping ◽  
Random Variables ◽  
Time Parameter ◽  
Image Position ◽  
Independent Identically Distributed

LetX(t) be a continuous time Markov process on the integers such that, ifσis a time at whichXmakes a jump,X(σ)– X(σ–) is distributed independently ofX(σ–), and has finite meanμand variance. Letq(j) denote the residence time parameter for the statej.Iftndenotes the time of thenth jump andXn≡X(tb), it is easy to deduce limit theorems forfrom those for sums of independent identically distributed random variables. In this paper, it is shown how, forμ> 0 and for suitableq(·), these theorems can be translated into limit theorems forX(t), by using the continuous mapping theorem.

A discrete space model for continuous space dispersal processes

2009 ◽  
Vol 4 (2) ◽  
pp. 57-68 ◽  
Author(s):  
David O'Sullivan ◽  
George L.W. Perry
Keyword(s):  
Discrete Space ◽  
Continuous Space ◽  
Space Model

scholarly journals A continuous-time state-space model for rapid quality control of argos locations from animal-borne tags

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Ian D. Jonsen ◽  
Toby A. Patterson ◽  
Daniel P. Costa ◽  
Philip D. Doherty ◽  
Brendan J. Godley ◽  
...  
Keyword(s):  
Quality Control ◽  
State Space ◽  
Continuous Time ◽  
State Space Model ◽  
Space Model

Inconspicuous, recovering, or northward shift: status and management of the white shark (Carcharodon carcharias) in Atlantic Canada

2020 ◽  
Vol 77 (10) ◽  
pp. 1666-1677
Author(s):  
G. Bastien ◽  
A. Barkley ◽  
J. Chappus ◽  
V. Heath ◽  
S. Popov ◽  
...  
Keyword(s):  
Action Plan ◽  
Satellite Telemetry ◽  
White Shark ◽  
Conservation Priorities ◽  
Atlantic Canada ◽  
Telemetry Data ◽  
Carcharodon Carcharias ◽  
Proactive Management ◽  
High Site ◽  
Research Incentives

Although white sharks (Carcharodon carcharias) have been considered rare in Atlantic Canada waters, recent sighting records indicate a potentially increasing presence. We combine historical to present sighting data with satellite telemetry tracks of large juvenile and adult white sharks tagged in US (n = 9) and Atlantic Canada waters (n = 17) to show seasonal white shark presence and distribution in Atlantic Canada, returns by individuals over multiple years, and high site fidelity to the region. Telemetry data indicate that white sharks are a more common and consistent occurrence in Canadian waters than previously thought, presenting two potential scenarios: (i) tagging technology is revealing white shark presence that was historically cryptic and (or) (ii) a northward range expansion of white sharks in the Northwest Atlantic, potentially due to climate change, population recovery, and (or) increasing pinniped prey. Given combined sighting and telemetry data indicate a current need for proactive management of white sharks in Atlantic Canada waters, we propose the basis for a management action plan, addressing conservation priorities, management goals, and research incentives while considering the potential for human–shark interactions.

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