Connectivity modelling in conservation science: a comparative evaluation

Recent work in connectivity modelling, such as dynamic landscape connectivity, has developed in response to spatiotemporal limitations of resistance surfaces.

“Recent work in connectivity modelling, such as dynamic landscape connectivity46, has developed in response to these spatiotemporal limitations of resistance surfaces.”

• cites [46] Zeller, K. A., Lewsion, R., Fletcher, R. J., Tulbure, M. G. & Jennings, M. K. Understanding the importance of dynamic landscape connectivity. Land 9(9), 303. https://doi.org/10.3390/land9090303 (2020). sourceSupported

Circuitscape predictions had the least root-mean-squared error between predicted and simulated connectivity maps.

“Fig. 5b shows that predictions using Circuitscape result in the least root-mean-squared error between the predicted and simulated connectivity maps”

When movement was strongly biased towards a known destination on the resistance surface, Circuitscape predictions typically correlated more strongly than those of resistant kernels.

“However, when the movement was strongly biased towards a known destination on the resistance surface, the connectivity predictions of Circuitscape typically correlated more strongly than those of resistant kernels.”

Resistant kernels and Circuitscape consistently performed most accurately among the three connectivity models in nearly all simulated scenarios.

“Our study shows the latter two of these three models to consistently perform most accurately in nearly all cases, with their abilities varying substantially in different contexts.”

Model choice has a much greater effect on predictive accuracy than movement mechanism (X1) and spatial complexity (X2).

“The variance partitioning now shows destination bias to be the primary factor determining the accuracy of connectivity predictions, approximately thrice as influential as model choice (X4), which in turn has a much greater effect on predictive accuracy than movement mechanism (X1) and spatial complexity (X2).”

Model choice was the dominant factor affecting the accuracy of predicting connectivity.

“The variance partitioning in Fig. 5a shows that the dominant factor in the accuracy of predicting connectivity is the choice of model used.”

Resistant kernels was the most accurate method overall based on linear correlation and spatial overlap between predicted and true connectivity maps.

“Resistant kernels are seen to be the most accurate method overall, based on the linear correlation and spatial overlap between the predicted and true connectivity maps.”

With strong destination bias, the error from resistant kernels and Circuitscape roughly doubled.

“Additionally, in this case the error from these two models roughly doubled, and the spatial overlap in the predictions from Circuitscape increased but still remained less than those from resistant kernels.”

Without destination bias, resistant kernels produced connectivity predictions that correlated and overlapped more strongly with the simulated connectivity scenarios than those given by Circuitscape, across all degrees of spatial complexity.

“Without destination bias, resistant kernels produced connectivity predictions which correlated and overlapped more strongly with the simulated connectivity scenarios than those given by Circuitscape, across all degrees of spatial complexity, suggesting resistant kernels to be the most robust model regarding variation in landscape structure.”

As spatial heterogeneity increases, the three connectivity models display higher error on average.

“on average, as spatial heterogeneity increases, the models display much higher error”

The difference in model performance was much greater at lower levels of spatial complexity.

“The boxplots in Supplementary Figure S2 show that the difference in model performance is much greater at lower levels of spatial complexity.”

Resistant kernels displayed the highest spatial overlap with simulated connectivity maps.

“And as before, resistant kernels display the highest spatial overlap, and Circuitscape the lowest average error.”

• Also stated in: § Analysis results · plain

  “We also find resistant kernels to consistently produce predictions which result in the greatest degree of spatial overlap with the simulated connectivity maps, substantially higher than both Circuitscape and factorial least-cost paths.”

• Also stated in: § Connectivity model performance with destination bias · plain

  “In (c) we find that predictions by resistant kernels overall give the highest overlap, and those by Circuitscape result in the least error, whereas factorial least-cost paths is seen to be the least accurate.”

A lower degree of destination bias gives predictions that are more accurate across all three statistics.

“In (b), we see that a lower degree of destination bias gives predictions which are more accurate across all three statistics.”

As the degree of destination bias increases, model error increases.

“as the degree of destination bias increases, the error increases and the correlation and overlap decrease.”

Destination bias was the main driver of variation in model accuracy across connectivity scenarios, approximately three times as influential as the choice of model used.

“For this analysis, the variance partitioning in Fig. 6a shows destination bias to be the main driver in variation of model accuracy across the different connectivity scenarios, approximately three times as influential as the choice of model used.”

Factorial least-cost paths was the least accurate of the three models in the second investigation, having the highest error and lowest correlation and spatial overlap.

“In Fig. 6c, we see factorial least-cost paths to still be the least accurate by all three metrics.”

• Also stated in: § Analysis results · plain

  “Centrally, factorial least-cost paths proved the least accurate of the three models, being consistent in having the highest error and lowest correlation and spatial overlap.”

• Also stated in: § Connectivity model performance with destination bias · plain

  “In (c) we find that predictions by resistant kernels overall give the highest overlap, and those by Circuitscape result in the least error, whereas factorial least-cost paths is seen to be the least accurate.”

As spatial heterogeneity becomes more complex, the correlation and overlap of factorial least-cost paths and Circuitscape increase.

“As the spatial heterogeneity becomes more complex, on average, all three models display higher error; simultaneously, the correlation and overlap of factorial least-cost paths and Circuitscape increases, while that of resistant kernels remains consistently high across the variation in spatial complexity.”

As the degree of destination bias increases, model overlap decreases.

“as the degree of destination bias increases, the error increases and the correlation and overlap decrease.”

As spatial heterogeneity increases, the three connectivity models display substantially higher spatial overlap on average.

“but also substantially higher overlap”

Spatial heterogeneity has little effect on the degree of linear correlation between predicted and true connectivity maps.

“with little effect seen on the degree of linear correlation.”

The effects of spatial scaling and autocorrelation were not major factors affecting the accuracy of the three connectivity models.

“Comparatively, the variance partitioning suggests that the effects of spatial scaling and autocorrelation are not seen to be major factors affecting the accuracy of the three connectivity models”

As the degree of destination bias increases, model correlation decreases.

“as the degree of destination bias increases, the error increases and the correlation and overlap decrease.”

Circuitscape had the lowest average error.

“And as before, resistant kernels display the highest spatial overlap, and Circuitscape the lowest average error.”

• Also stated in: § Connectivity model performance with destination bias · plain

  “In (c) we find that predictions by resistant kernels overall give the highest overlap, and those by Circuitscape result in the least error, whereas factorial least-cost paths is seen to be the least accurate.”

• Also stated in: § Connectivity model performance with destination bias · plain

  “| Circuitscape | 0.0127 | 0.5276 | 0.4801 |”

There was very strong interaction between model accuracy and the choice of resistance surface.

“Moreover, the four-way analysis of variance (Supplementary Table S1) shows very strong interaction between model accuracy and the choice of resistance surface.”

The results of the simulation analysis show particular patterns in model performance which remain constant across the various combinations of movement mechanism, spatial scaling, autocorrelation, destination bias and spatial complexity.

“The results of our simulation analysis show particular patterns in model performance which remain constant across the various combinations of movement mechanism, spatial scaling, autocorrelation, destination bias and spatial complexity.”

The comparative predictive abilities of resistant kernels and Circuitscape vary primarily according to the degree to which movement is inclined towards a known destination, and to a lesser degree according to the spatial complexity of the resistance surface.

“In terms of the other two statistics measuring accuracy - root-mean-squared error and linear correlation - the comparative predictive abilities of resistant kernels and Circuitscape vary according to two factors: primarily, the degree to which movement is inclined towards a known destination; and to a lesser degree, the spatial complexity of the resistance surface.”

The connectivity models are overall much less accurate if movement is influenced only by landscape resistance values, without any limit on dispersal capabilities or mortality risk.

“Figure 5d shows that these connectivity models are overall much less accurate if the movement is influenced only by landscape resistance values (which is parameterised by the attraction mechanism), without any limit on dispersal capabilities or mortality risk.”

For higher levels of destination bias, Circuitscape predictions produced the strongest linear correlations with the simulated connectivity maps.

“However, the boxplot diagram in Supplementary Figure S4(b) shows that, for higher levels of destination bias, the connectivity predictions by Circuitscape produce the strongest linear correlations with the simulated connectivity maps; this results in the overall higher correlation seen with Circuitscape in Table 3.”

Other movement parameters in Pathwalker did not affect model performance to the same extent as destination bias and spatial heterogeneity.

“Other movement parameters in Pathwalker did not affect model performance to same the extent as destination bias and spatial heterogeneity.”

Factorial least-cost paths was the least accurate model in all three accuracy statistics.

“whereas the factorial least-cost paths model is the least accurate in all three statistics.”

In comparison with the first study, the presence of destination bias results in a stronger link between higher spatial complexity and greater model accuracy.

“And in comparison with the first study, the presence of destination bias results in a stronger link between higher spatial complexity and greater model accuracy, as inferred from Fig. 6d.”

The choice of connectivity model, along with the degree of destination bias in the movement and spatial complexity of the landscape, had the greatest impact on the accuracy of connectivity predictions.

“The results of our study show that the choice of connectivity model, along with the degree of destination bias in the movement and spatial complexity of the landscape, had the greatest impact on the accuracy of connectivity predictions.”

Aspects of movement behaviour such as autocorrelation and the spatial scale of response to the landscape had relatively little overall effect on accuracy.

“Comparatively, aspects of movement behaviour such as autocorrelation and the spatial scale of response to the landscape had relatively little overall effect.”

The factorial least-cost path algorithm was substantially less accurate than Circuitscape and resistant kernels across nearly all scenarios.

“We found the factorial least-cost path algorithm to be substantially less accurate than Circuitscape and resistant kernels across nearly all scenarios.”

The degree to which a connectivity model prediction matches observed movement paths does not necessarily demonstrate the model's accuracy relative to other methods.

“As a result, the degree to which a connectivity model prediction matches observed movement paths does not necessarily demonstrate the model’s accuracy relative to other methods.”

Pathwalker and other recent agent-based approaches like HexSim and RangeShifter combine the spatially-explicit approach of resistance-based algorithms with the detail and flexibility given to simulating movement behaviour enabled by agent-based modelling.

“Pathwalker, and other recent agent-based approaches like HexSim and RangeShifter40,41, combine the spatially-explicit approach of resistance-based algorithms with the detail and flexibility given to simulating movement behaviour enabled by agent-based modelling.”

• cites [40] Schumaker, N. H. & Brookes, A. HexSim: A modeling environment for ecology and conservation. Landscape Ecol. 33(2), 197–211 (2018). sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

• cites [41] Bocedi, G., Palmer, S. C. F., Malchow, A.-K., Zurell, D. & Watts, K. RangeShifter 2.0: An extended and enhanced platform for modelling spatial eco-evolutionary dynamics and species’ responses to environmental changes. Ecography 44(10), 1453–1462 (2021). sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

Ecological processes in reality do not follow a neat distinction between 'nature' and 'society'.

“Since ecological processes in reality do not follow a neat distinction between ‘nature’ and ‘society’7,47,48, traditional movement models which ignore the complexities of human influence on animal behaviour for the sake of theoretical and algorithmic simplicity are growing increasingly unreliable49–51.”

• cites [7] Lorimer, J. Wildlife in the Anthropocene: conservation after nature. (U of Minnesota Press, 2015). sourceNot checked — no full text of the source
• cites [47] Cronon, W. The trouble with wilderness: or, getting back to the wrong nature. Environ. Hist. 1(1), 7–28 (1996). sourceNot checked — no full text of the source
• cites [48] Ingold, T. The Perception of the Environment: Essays on Livelihood, Dwelling and Skill (Routledge, 2021). sourceNot checked — no full text of the source

Traditional movement models which ignore the complexities of human influence on animal behaviour for the sake of theoretical and algorithmic simplicity are growing increasingly unreliable.

“Since ecological processes in reality do not follow a neat distinction between ‘nature’ and ‘society’7,47,48, traditional movement models which ignore the complexities of human influence on animal behaviour for the sake of theoretical and algorithmic simplicity are growing increasingly unreliable49–51.”

• cites [49] Boettiger, A. N. et al. Inferring ecological and behavioral drivers of African elephant movement using a linear filtering approach. Ecology 92(8), 1648–1657 (2011). sourceNot checked — no full text of the source
• cites [50] Pooley, S. et al. An interdisciplinary review of current and future approaches to improving human-predator relations. Conserv. Biol. 31(3), 513–523. https://doi.org/10.1111/cobi.12859 (2017). sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

• cites [51] Benson, E. S. Minimal animal: Surveillance, simulation, and stochasticity in wildlife biology. Antennae 30, 39 (2014).Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

There remain significant limitations to methods such as Circuitscape, factorial least-cost paths and resistant kernels in their ability to understand and predict the pathways central to animal movement.

“Although such methods have grown in sophistication since the first least-cost path algorithms used in ecology two decades ago, there remain significant limitations to methods such as Circuitscape, factorial least-cost paths and resistant kernels, in their ability to understand and predict the pathways central to animal movement.”

Key contextual details pose a particular challenge to the minimalist assumptions used in resistance surfaces and the major resistance-based connectivity models.

“As demonstrated in the above literature, these key contextual details pose a particular challenge to the minimalist assumptions used in resistance surfaces and the major resistance-based connectivity models.”

Before the emergence of landscape resistance as a framework for mapping connectivity, some agent-based models did incorporate more detailed aspects of individual movement choice.

“Before the emergence of landscape resistance as a framework for mapping connectivity, some agent-based models did incorporate more detailed aspects of individual movement choice38,39, but the lack of spatial complexity in these earlier methods greatly limited their effective application to conservation science.”

• cites [38] Kareiva, P. M. & Shigesada, N. Analyzing insect movement as a correlated random walk. Oecologia 56(2), 234–238 (1983). sourceNot checked — no full text of the source
• cites [39] Schumaker, N.H. Using landscape indices to predict habitat connectivity. Ecology (1996), pp. 1210–1225. sourceNot checked — no full text of the source

For the majority of conservation applications, resistant kernels is the most appropriate connectivity model, except when movement is strongly directed towards a known location.

“For the majority of conservation applications, we infer resistant kernels to be the most appropriate model, except for when the movement is strongly directed towards a known location.”

Spatial variability in movement behaviour can result in radically different estimates of landscape resistance and connectivity.

“For example, seasonal variability in the landscape can substantially alter movement patterns42,43, and spatial variability in movement behaviour can result in radically different estimates of landscape resistance and connectivity44,45.”

• cites [44] Vergara, M., Cushman, S. A. & Ruiz-González, A. Ecological differences and limiting factors in different regional contexts: landscape genetics of the stone marten in the Iberian Peninsula. Landscape Ecol. 32(6), 1269–1283 (2017). sourceNot checked — no full text of the source
• cites [45] Reddy, P. A., Puyravaud, J.-P., Cushman, S. A. & Segu, H. Spatial variation in the response of tiger gene ow to landscape features and limiting factors. Anim. Conserv. 22(5), 472–480 (2019). sourceNot checked — no full text of the source

Spatiotemporal variation and contextual details often lie at the heart of shaping movement and connectivity.

“These factors often lie at the heart of shaping movement and connectivity.”

The assumption that animals are automatons moving through a static landscape, according to a simplistic set of cost-benefit movement rules, reduces the rich dynamics of both animal and landscape to an extent that often renders such models ineffective for application to conservation practice and policy.

“Namely, the assumption that animals are automatons moving through a static landscape, according to a simplistic set of cost-benefit movement rules, reduces the rich dynamics of both animal and landscape to an extent that often renders such models ineffective for application to conservation practice and policy.”

Individual-based methods address some important drivers of connectivity which are missing in the simplistic assumptions used by Circuitscape, resistant kernels and factorial least-cost paths.

“Because landscape connectivity is a phenomenon which arises from the cumulative movement routes of individual organisms, these individual-based methods thus address some important drivers of connectivity which are missing in the simplistic assumptions used by Circuitscape, resistant kernels and factorial least-cost paths.”

• AssumptionRests on an assumption: Landscape connectivity arises from the cumulative movement routes of individual organisms.

Resistant kernels is the most robust model regarding variation in landscape structure.

“Without destination bias, resistant kernels produced connectivity predictions which correlated and overlapped more strongly with the simulated connectivity scenarios than those given by Circuitscape, across all degrees of spatial complexity, suggesting resistant kernels to be the most robust model regarding variation in landscape structure.”

Empirical connectivity analyses are limited in their ability to comparatively evaluate the performance of different connectivity models.

“Thus, although empirical connectivity analyses can give tremendous insight in many contexts, they are limited in their ability to comparatively evaluate the performance of different connectivity models.”

Movement from an area of higher to lower resistance is much more likely than the reverse.

“Furthermore, as noted in21, Circuitscape assumes a directional symmetry of resistance between adjacent pixels, despite movement from an area of higher to lower resistance being much more likely than the reverse.”

• cites [21] McRae, B. H., Dickson, B. G., Keitt, T. H. & Shah, V. B. Using circuit theory to model connectivity in ecology, evolution, and conservation. Ecology 89(10), 2712–2724. https://doi.org/10.1890/07-1861.1. (2008). sourceNot checked — no full text of the source

Models such as Circuitscape which require knowledge of a location or region towards which movement is inclined are limited in effectiveness because precise destination knowledge is often difficult to obtain.

“This limits the effectiveness of models such as Circuitscape which require knowledge of a location, or region, towards which the movement is inclined.”

• AssumptionRests on an assumption: In many applications of connectivity modelling, knowledge of the precise destination of movement is often very difficult to obtain, particularly with dispersing animals.

The precise least-cost path (or corridor) between two locations on a resistance surface may dramatically not reflect the actual pathways of animal movement.

“This demonstrates that, despite being a widely used approach to modelling connectivity, the precise least-cost path (or corridor) between two locations on a resistance surface may dramatically not reflect the actual pathways of animal movement.”

Seasonal variability in the landscape can substantially alter movement patterns.

“For example, seasonal variability in the landscape can substantially alter movement patterns42,43, and spatial variability in movement behaviour can result in radically different estimates of landscape resistance and connectivity44,45.”

• cites [42] Kaszta, Ż, Cushman, S. A. & Slotow, R. Temporal non-stationarity of path- selection movement models and connectivity: An example of African elephants in Kruger national park. Front. Ecol. Evol. 9, 207 (2021). sourceNot checked yet

  Checked before — its earlier verdict is held back until a new check runs.

• cites [43] Osipova, L. et al. Using step-selection functions to model landscape connectivity for African elephants: Accounting for variability across individuals and seasons. Anim. Conserv. 22(1), 35–48 (2019). sourceNot checked — no full text of the source

The dynamic presence of other nonhuman animals can be a major force in shaping movement behaviour and the resulting connectivity pathways, particularly with dispersing individuals.

“Similarly, the dynamic presence of other nonhuman animals can be a major force in shaping movement behaviour and the resulting connectivity pathways, particularly with dispersing individuals55.”

• cites [55] Elliot, N. B., Cushman, S. A., Macdonald, D. W. & Loveridge, A. J. The devil is in the dispersers: Predictions of landscape connectivity change with demography. J. Appl. Ecol. 51(5), 1169–1178 (2014). sourceNot checked — no full text of the source

Circuitscape assumes a directional symmetry of resistance between adjacent pixels.

“Furthermore, as noted in21, Circuitscape assumes a directional symmetry of resistance between adjacent pixels, despite movement from an area of higher to lower resistance being much more likely than the reverse.”

• cites [21] McRae, B. H., Dickson, B. G., Keitt, T. H. & Shah, V. B. Using circuit theory to model connectivity in ecology, evolution, and conservation. Ecology 89(10), 2712–2724. https://doi.org/10.1890/07-1861.1. (2008). sourceNot checked — no full text of the source

The lack of spatial complexity in earlier agent-based methods greatly limited their effective application to conservation science.

“Before the emergence of landscape resistance as a framework for mapping connectivity, some agent-based models did incorporate more detailed aspects of individual movement choice38,39, but the lack of spatial complexity in these earlier methods greatly limited their effective application to conservation science.”

Resistance-based connectivity models assume landscape resistance and animal movement behaviour remain unchanging as the animal moves through space and time.

“However, many fundamental drivers of movement are still left unaccounted for: resistance-based connectivity models assume landscape resistance and animal movement behaviour to remain unchanging as the animal moves through space and time, and thus they ignore spatiotemporal variation and other key contextual details.”

All three models are limited in their effective application and predictive abilities by their simplistic assumptions of animal movement.

“Despite their widespread usage in conservation science, all three models are limited in their effective application and predictive abilities by their simplistic assumptions of animal movement.”

Connectivity models such as resistant kernels are likely to be more appropriate in a wider range of contexts because knowledge of precise destinations is usually very difficult to obtain.

“In practice however, knowledge of precise destinations are usually very difficult to obtain; connectivity models such as resistant kernels are thus likely to be more appropriate in a wider range of contexts.”

• AssumptionRests on an assumption: In many applications of connectivity modelling, knowledge of the precise destination of movement is often very difficult to obtain, particularly with dispersing animals.