Nonlinear reaction–diffusion process models improve inference for population dynamics

Lu, Xinyi; Williams, Perry J.; Hooten, Mevin B.; Powell, James A.; Womble, Jamie N.; Bower, Michael R.

doi:10.1002/env.2604

Cited by 16 publications

(80 citation statements)

References 29 publications

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“…Each image covered ∼60 m × 90 m area of the water's surface. We used only non-overlapping images for analyses (Lu et al, 2020).…”

Section: Data Collectionmentioning

confidence: 99%

“…Note that modeling on this 400 m spatial resolution matches the resolution of the design-based surveys. Due to the finer spatial resolution, the aerial photographic survey counts were aggregated to the 400 m scale, following Lu et al (2020).…”

Section: Model Specificationmentioning

confidence: 99%

“…The growing and expanding population colonized previously occupied areas, as well as newly available habitat that was historically glaciated (e.g., Glacier Bay; Williams et al, 2019). Across Southeast Alaska, the sea otter population is likely decades from reaching carrying capacity (Tinker et al, 2019;Lu et al, 2020); even in Glacier Bay, the most densely populated area, evidence suggests carrying capacity may not be reached for 30 years (Lu et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…Our approach involved integrating the mechanistic model of population growth and spread in a Bayesian hierarchical framework to estimate process parameters and uncertainty (Wikle and Hooten, 2010). This approach has previously been applied on much smaller spatial scales to model sea otter recolonization and population dynamics in Glacier Bay from a single epicenter (Williams et al, 2017b(Williams et al, , 2019Lu et al, 2020). Here, we applied it across seven population epicenters (or reintroduction sites) to learn about changes in distribution and abundance of sea otters in a region with spatially-variable management regimes.…”

Section: Introductionmentioning

confidence: 99%

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Diffusion modeling reveals effects of multiple release sites and human activity on a recolonizing apex predator

Eisaguirre

Williams

et al. 2021

Preprint

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Background: Reintroducing predators is a promising conservation tool to help remedy human-caused ecosystem changes. However, the growth and spread of a reintroduced population is a spatiotemporal process that is driven by a suite of factors, such as habitat change, human activity, and prey availability. Sea otters (Enhydra lutris) are apex predators of nearshore marine ecosystems that had declined nearly to extinction across much of their range by the early 20th century. In Southeast Alaska, which is comprised of a diverse matrix of nearshore habitat and managed areas, reintroduction of 413 individuals in the late 1960s initiated the growth and spread of a population that now exceeds 25,000. Methods: Periodic aerial surveys in the region provide a time series of spatially-explicit data to investigate factors influencing this successful and ongoing recovery. We integrated an ecological diffusion model that accounted for spatially-variable motility and density-dependent population growth, as well as multiple population epicenters, into a Bayesian hierarchical framework to help understand the factors influencing the success of this recovery. Results: Our results indicated that sea otters exhibited higher residence time as well as greater equilibrium abundance in Glacier Bay, a protected area, and in areas where there is limited or no commercial fishing. Asymptotic spread rates suggested sea otters colonized Southeast Alaska at rates of 1-8 km/yr with lower rates occurring in areas correlated with higher residence time, which primarily included areas near shore and closed to commercial fishing. Further, we found that the intrinsic growth rate of sea otters may be higher than previous estimates suggested. Conclusions: This study shows how predator recolonization can occur from multiple population epicenters. Additionally, our results suggest spatial heterogeneity in the physical environment as well as human activity and management can influence recolonization processes, both in terms of movement (or motility) and density dependence.

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“…Each image covered ∼60 m × 90 m area of the water's surface. We used only non-overlapping images for analyses (Lu et al, 2020).…”

Section: Data Collectionmentioning

confidence: 99%

Section: Model Specificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Diffusion modeling reveals effects of multiple release sites and human activity on a recolonizing apex predator

Eisaguirre

Williams

et al. 2021

Preprint

Self Cite

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show abstract

“…We used Partial Differential Equations (PDE) known as ecological diffusion to describe diffusion and growth dynamics. The ecological diffusion PDE describing the variation of density of individuals at location x at time t, N(x,t) over time, in two dimensions with logistic growth (see also Lu et al 2019), can be written as follows:…”

Section: State Processmentioning

confidence: 99%

A mechanistic–statistical species distribution model to explain and forecast wolf (Canis lupus) colonization in South-Eastern France

Louvrier

Papaïx

Duchamp³

et al. 2020

Spatial Statistics

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Species distribution models (SDMs) are important statistical tools for ecologists to understand and predict species range. However, standard SDMs do not explicitly incorporate dynamic processes like dispersal. This limitation may lead to bias in inference about species distribution.Here, we adopt the theory of ecological diffusion that has recently been introduced in statistical ecology to incorporate spatio-temporal processes in ecological models. As a case study, we considered the wolf (Canis lupus) that has been recolonizing Eastern France naturally through dispersal from the Apennines since the early 90's. Using partial differential equations for modelling species diffusion and growth in a fragmented landscape, we develop a mechanisticstatistical spatio-temporal model accounting for ecological diffusion, logistic growth and imperfect species detection. We conduct a simulation study and show the ability of our model to i) estimate ecological parameters in various situations with contrasted species detection probability and number of surveyed sites and ii) forecast the distribution into the future. We found that the growth rate of the wolf population in France was explained by the proportion of forest cover, that diffusion was influenced by human density and that species detectability increased with increasing survey effort. Using the parameters estimated from the 2007-2015 period, we then forecasted wolf distribution in 2016 and found good agreement with the actual detections made that year. Our approach may be useful for managing species that interact with human activities to anticipate potential conflicts.

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Species distribution modeling of northern sea otters (Enhydra lutris kenyoni) in a data‐limited ecosystem

Hasan,

Gorman,

Coletti

et al. 2024

Ecology and Evolution

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Species distribution models (SDMs) are used to map and predict the geographic distributions of animals based on environmental covariates. Typically, SDMs require high‐resolution habitat data and time series information on animal locations. For data‐limited regions, defined as having scarce habitat or animal survey data, modeling is more challenging, often failing to incorporate important environmental attributes. For example, for sea otters (Enhydra lutris), a federally protected keystone species with variable population trends across the species' range, predictive modeling of distributions has been successfully conducted in areas with robust sea otter population and habitat data. We used open‐access data and employed a presence‐only model, maximum entropy (MaxEnt), to investigate subtidal habitat associations (substrate and algal cover, bathymetry, and rugosity) of northern sea otters (E. lutris kenyoni) for a data‐limited ecosystem, represented by Kachemak Bay, Alaska. Habitat association results corroborated previous findings regarding the importance of bathymetry and understory kelp as predictors of sea otter presence. Novel associations were detected as filamentous algae and shell litter were positively and negatively associated with northern sea otter presence, respectively, advancing existing knowledge of sea otter benthic habitat associations useful for predicting habitat suitability. This study provides a quantitative framework for conducting species distribution modeling with limited temporal and spatial animal distribution and abundance data. Utilizing drop camera information, our novel approach allowed for a better understanding of habitat requirements for a stable northern sea otter population, including bathymetry, understory kelp, and filamentous algae as positive predictors of sea otter presence in Kachemak Bay, Alaska.

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Nonlinear reaction–diffusion process models improve inference for population dynamics

Cited by 16 publications

References 29 publications

Diffusion modeling reveals effects of multiple release sites and human activity on a recolonizing apex predator

Diffusion modeling reveals effects of multiple release sites and human activity on a recolonizing apex predator

A mechanistic–statistical species distribution model to explain and forecast wolf (Canis lupus) colonization in South-Eastern France

Species distribution modeling of northern sea otters (Enhydra lutris kenyoni) in a data‐limited ecosystem

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