Combining network theory and reaction–advection–diffusion modelling for predicting animal distribution in dynamic environments

Prima, Marie‐Caroline; Duchesne, Thierry; Fortin, A.; Rivest, Louis‐Paul; Fortin, Daniel

doi:10.1111/2041-210x.12997

Cited by 11 publications

(15 citation statements)

References 37 publications

(100 reference statements)

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“…We used a reaction–advection–diffusion model to predict relative intensity of node use in each experimental site (Prima et al, ). The model integrates both the spatial and temporal dynamics of animal movement to estimate the relative intensity of space use and it requires two input parameters: a weighted graph reflecting selection during inter‐patch movements and average residency time in network nodes.…”

Section: Methodsmentioning

confidence: 99%

“…where

N

is the number of nodes in the network,

u_{i} false(t false)

is the density in node

i

at time

t

\frac{d false(u_{i} ()(, t) false)}{normald t}

is the instantaneous rate of change in

u_{i} false(t false)

T_{i}

is the average residency time in node

i

and

{w_{italicji}}_{normals normalt normala normaln normald normala normalr normald normali normalz normale normald}

is the standardized score for the link from node

j

to node

i

(Prima et al, ). We then standardized predicted densities at the end of the simulation to estimate relative intensity of node use in both pre‐ and post‐disturbance networks using,

I_{i} false(t false) = \frac{u_{i} false(t false)}{\sum_{j = 1}^{N} u_{j} false(t false)},

…”

Section: Methodsmentioning

confidence: 99%

“…We used a reaction-advection-diffusion model to predict relative intensity of node use in each experimental site (Prima et al, 2018).…”

Section: Predictions Of Spatial Network and Space Usementioning

confidence: 99%

“…dt is the instantaneous rate of change in u i (t), T i is the average residency time in node i and w ji standardized is the standardized score for the link from node j to node i (Prima et al, 2018). We then standardized predicted densities at the end of the simulation to estimate relative intensity of node use in both pre-and post-disturbance networks using, where I i (t) is the relative intensity of use for node i at time t.…”

Section: Model Simulationmentioning

confidence: 99%

“…Robustness should vary among graph topologies depending on how constituents are altered (Albert, Jeong, & Barabasi, 2000). The minimum planar graph, for example, is stable against node removal because alternate paths are generally available across the network (Prima, Duchesne, Fortin, Rivest, & Fortin, 2018;Reunanen, Fall, & Nikula, 2012). Networks of greater complexity than the minimum planar graph often provide a more realistic description of the spatial dynamics of animal populations, while displaying different reliance to disturbance (Almpanidou et al, 2014;Fox & Bellwood, 2014;Rhodes, Wardell-Johnson, Rhodes, & Raymond, 2006).…”

Section: Introductionmentioning

confidence: 99%

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A landscape experiment of spatial network robustness and space‐use reorganization following habitat fragmentation

et al. 2019

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Network theory increasingly informs wildlife conservation in disturbed landscapes, but with concern increasingly expressed about its application to real‐world situations. The theory predicts that the connectivity of scale‐free networks should be particularly sensitive to the disturbance of highly connected nodes (i.e. hubs). This expectation relies on complete patch removal, thus restraining its application to the last of several steps involved in habitat fragmentation, and overlooks potential reconnection of patches after disturbance (i.e. rewiring). We performed a landscape‐scale experiment to evaluate the robustness of scale‐free spatial networks of woodland caribou (Rangifer tarandus caribou) to logging activity. We built caribou networks before and after disturbance using a mechanistic model of inter‐patch movements and differentiated networks disturbed in their hubs and non‐hubs. We applied a reaction–advection–diffusion model to networks before and after disturbance to account for the spatio‐temporal dynamics of caribou movement within the networks and anticipate their space use. We validated network and space‐use predictions using empirical estimates from GPS relocations of caribou. Using the validated predictions, we compared topological network measures before and after disturbance to quantify changes in connectivity within the networks according to the type of disturbed nodes (i.e. hubs or non‐hubs) and assessed space‐use reorganization. We used control networks, for which no disturbance occurred in the before–after timeframe of the study, in the latter analysis to get a baseline rate of change. Disturbances due to logging activity typically resulted in fragmentation and shrinkage instead of complete patch removal. Independently to the type of disturbed nodes, caribou rewired their network using remnant patches from the fragmentation process. Consequently, topological network measures generally did not differ between before and after disturbance, such that caribou networks displayed some robustness to logging activity due to the rewiring process. Space‐use reorganization was greater, however, when hubs were disturbed in comparison with non‐hubs and controls. Even though caribou rewired their networks, they revisited less patches after the disturbance of hubs. A naive application of network theory (i.e. without potential rewiring and using complete patch removal), to assess spatial network robustness, may be inappropriate during most steps of the fragmentation process because of the rewiring process. Indeed, network rewiring facilitated by the presence of remnant patches can enhance spatial network robustness, in comparison with no rewiring. In addition, species‐specific functional connectivity should be accounted for when anticipating the rewiring process and animal space use within disturbed networks. A free Plain Language Summary can be found within the Supporting Information of this article.

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Section: Methodsmentioning

confidence: 99%

“…where

N

is the number of nodes in the network,

u_{i} false(t false)

is the density in node

i

at time

t

\frac{d false(u_{i} ()(, t) false)}{normald t}

is the instantaneous rate of change in

u_{i} false(t false)

T_{i}

is the average residency time in node

i

and

{w_{italicji}}_{normals normalt normala normaln normald normala normalr normald normali normalz normale normald}

is the standardized score for the link from node

j

to node

i

(Prima et al, ). We then standardized predicted densities at the end of the simulation to estimate relative intensity of node use in both pre‐ and post‐disturbance networks using,