R. Murekatete:

"Sensitivity, Variation, and Application of Least-Cost Path Models in Landscape Connectivity Analysis and Corridor Planning";

Supervisor, Reviewer: T. Shirabe, S. Georganos, U. Mörtberg, F. Karimipour, A. Mansourian, G. Navratil; KTH, Geoinformatics, 2022; oral examination: 2022-06-10.

In recent decades, Rwanda has been affected by the loss and fragmentation of natural habitats for native species of animals and plants. As a consequence, landscape connectivity-i.e., the degree to which a landscape facilitates or impedes the movement of organisms between resource patches-has considerably weakened or is even completely lost, causing detrimental effects on biodiversity, notably the reduction of populations of key native species. In order to counter this problem, one potential solution currently being explored by local planners in Rwanda consists of establishing conservation corridors for organisms to move safely between their habitat remnants. Specifically, this thesis was inspired by a project initiated by the Dian Fossey Gorilla Fund International, a conservation non-governmental organization (NGO) based in Rwanda, which consists of establishing a conservation corridor for pollinators.

For their capabilities of storing, processing, and visualizing landscape data, geographic information systems (GIS) have been increasingly popular among conservation biologists and practitioners. Of particular relevance to connectivity analysis and corridor planning is the least-cost path model. A typical use of this model is such that one first estimates the cost for a certain action (e.g., movement by an organism or acquisition by a government) at each location of a given landscape and represents the results in the form of a raster surface, and then measures the degrees of connectivity between patches of interest in terms of effective distances, which are equated with least-cost path distances over the raster cost surface. While the least-cost path model is easy to use and available in virtually any commercial raster-based GIS, we observe that users of it often overlook some important assumptions, the violation of which might greatly affect the validity of the modelīs outcome.

The goal of this thesis is to provide a scientific contribution to landscape connectivity analysis and conservation corridor planning by 1) investigating the potential misuse or abuse of the conventional least-cost path model when sufficient information is not available on the underlying cost surface, 2) proposing an alternative model under such a circumstance and 3) demonstrating its relevance to conservation practice. More specifically, for the model to work, it is explicitly or implicitly assumed that, the optimality of a path is evaluated as the sum of the cost-weighted lengths of all its segments-cost-weighted, i.e., multiplied by their underlying cost values. The validity of this assumption must be questioned, however, if cost values are measured on a scale-e.g., an ordinal scale of measurement in Stevensīs typology-that does not permit arithmetic operations. In a typical practice of landscape connectivity analysis and corridor planning, the raster cost surface is created by transforming one or more sets of values (e.g., land cover type, land ownership, and elevation) attributed to cells into another set of such values (representing cost) through a function reflecting one or more criteria. A question arises: how certain can one be about the correctness of such a cost estimation function?

There are at least four issues in the application of the least-cost path model to landscape connectivity analysis and corridor planning under uncertainty. First, while it is generally anticipated that different cost estimation functions lead to different least-cost paths (hence to different effective distances or different corridor locations), little is known on how such differences arise (or do not arise). Second, while it is generally recognized that the location and length of a least-cost path are both sensitive to the spatial resolution of the raster cost surface, little is known if they are always sensitive in the same way and to the same degree and if not, what makes them more (or less) sensitive. Third, when it is difficult to establish a fully connected corridor between target habitat areas (e.g., because of surrounding anthropogenic activities), the least-cost path (which is by definition fully connected) may not be useful at least in its original form. Lastly, even if the conventional least-cost path model may have inconsistent results in theory, it may well be continued to be used in practice, unless there is a sound alternative to it.

The issues raised above are addressed through four studies corresponding to four respective papers which are appended to this thesis. While the first three studies use artificial landscape data generated by computers with varying spatial and non-spatial characteristics, the fourth study uses data on a real landscape. The first study (Paper 1) evaluates how the locations and lengths of least-cost paths (the latter of which are referred to as least-cost distances) vary with change in cost estimation parameters. This is done through a series of computational experiments, in which each of the artificial landscapes is converted into different cost surfaces by systematically varying parameters of a cost-estimation function, on which least-cost paths are generated. The locations and lengths of those paths are statistically analyzed to find sources of their variation. The second study (Paper 2) investigates how the least-cost distance is affected by the spatial resolution of the corresponding cost surface. This is also done through a series of computational experiments, in which each of the artificial landscapes is converted into a cost surface, which is, in turn, converted into different cost surfaces (different, i.e., only in their spatial resolutions) by systematically aggregating grid cells. Then, the statistical behavior of the ratio of the least-cost distance measured on a lower-resolution cost surface to that measured on a higher-resolution cost surface is analyzed. The third study (Paper 3) proposes the mini-max path model as an alternative to the least-cost path model. Unlike the conventional model (in which the optimality of a path is based on the sum of its length multiplied by the underlying cost values), the alternative model determines the optimality of a path using the length of a segment(s) of the path that intersects the cells having the maximum cost value (with a special tie-breaking rule). The performances of the two models are tested in one of the following two assumptions at a time: the cost values are measured on an ordinal scale or on a ratio scale. The fourth study (Paper 4) applies the model proposed in the third study to an ongoing conservation project of the Dian Fossey Gorilla Fund International that plans to design a `stepping-stoneī corridor-which is not fully connected but takes the form of a sequence of fragmented forest patches-between two core habitat areas of pollinator birds between two protected areas in Rwanda. The project does not have complete information on the study area and the target species and thus the project staff can only rank land cover types in terms of their suitability/cost for being part of the corridor. The utility of the model is tested with different assumptions on the behavior of the birds (e.g., minimum stepping stone size) as well as on the cost associated with the implementation of the corridor (e.g., cost for planting shrubs along the corridor to encourage the birds to use it).

The first study finds that the same pair of terminal cells may well be connected by different least-cost paths on different cost surfaces though derived from the same landscape data. The variation among those paths is highly sensitive to the forms of spatial and non-spatial distributions of landscape elements (which cannot be controlled by users of the least-cost path model) as well as by those of cost values derived from them (which may be, at least indirectly, controlled by users of the model). The second study finds that least-cost distances measured on lower-resolution cost surfaces are generally highly correlated with-and useful predictors of-effective distances measured on higher-resolution cost surfaces. This relationship tends to be weakened when linear barriers to connectivity (e.g., roads and rivers) exist, but strengthened as distances increase and/or when linear barriers (if any) are detected by other presumably more accessible and affordable sources such as vector line data. The third study confirms the effectiveness of the conventional least-cost path model on ratio-scaled cost surfaces but finds that the alternative mini-max path model is mathematically sounder if the cost values are measured on an ordinal scale and practically useful if the problem is concerned not with the minimization of cost but with the maximization of some desirable condition such as suitability. The fourth study demonstrates the utility of the mini-max path model by effectively casting the stepping stone corridor problem as a special case of it. The model allows for a rapid first delineation of candidate routes for stepping stone corridors and facilitates the early exploratory stages of conservation projects.

Major implications of this thesis to the research and practice in landscape connectivity analysis and conservation corridor planning with raster-based GIS are summarized as follows.

- When sufficient information is available for quantification of cost values, the conventional least-cost path model is a reasonable approach to use.

- However, it is worth trying or at least acknowledging alternatives that do not rely on the quantitative-cost assumption if the value of each cell only indicates the ordinal category of cost of intersecting that cell. Note in particular that information used for cost estimation in practice (e.g., expert opinions or public surveys) are often of subjective and qualitative nature.

- The highest-resolution data may not always be most effective-much less, most cost-effective-for the task being undertaken. The choice of spatial resolution of the input raster data can significantly affect the output of the least-cost path model. Thus it should be consistent to the amount of spatial details needed, which should be estimated based on adequate ecological and geographical knowledge on the landscape and species being studied.

- It is not always obvious that a given spatial planning task can be effectively cast as an instance of an existing spatial optimization model. Therefore, knowledge exchange and collaboration are important between conservation biology and GIScience.

In recent decades, Rwanda has been affected by the loss and fragmentation of natural habitats for native species of animals and plants. As a consequence, landscape connectivity-i.e., the degree to which a landscape facilitates or impedes the movement of organisms between resource patches-has considerably weakened or is even completely lost, causing detrimental effects on biodiversity, notably the reduction of populations of key native species. In order to counter this problem, one potential solution currently being explored by local planners in Rwanda consists of establishing conservation corridors for organisms to move safely between their habitat remnants. Specifically, this thesis was inspired by a project initiated by the Dian Fossey Gorilla Fund International, a conservation non-governmental organization (NGO) based in Rwanda, which consists of establishing a conservation corridor for pollinators.

For their capabilities of storing, processing, and visualizing landscape data, geographic information systems (GIS) have been increasingly popular among conservation biologists and practitioners. Of particular relevance to connectivity analysis and corridor planning is the least-cost path model. A typical use of this model is such that one first estimates the cost for a certain action (e.g., movement by an organism or acquisition by a government) at each location of a given landscape and represents the results in the form of a raster surface, and then measures the degrees of connectivity between patches of interest in terms of effective distances, which are equated with least-cost path distances over the raster cost surface. While the least-cost path model is easy to use and available in virtually any commercial raster-based GIS, we observe that users of it often overlook some important assumptions, the violation of which might greatly affect the validity of the modelīs outcome.

The goal of this thesis is to provide a scientific contribution to landscape connectivity analysis and conservation corridor planning by 1) investigating the potential misuse or abuse of the conventional least-cost path model when sufficient information is not available on the underlying cost surface, 2) proposing an alternative model under such a circumstance and 3) demonstrating its relevance to conservation practice. More specifically, for the model to work, it is explicitly or implicitly assumed that, the optimality of a path is evaluated as the sum of the cost-weighted lengths of all its segments-cost-weighted, i.e., multiplied by their underlying cost values. The validity of this assumption must be questioned, however, if cost values are measured on a scale-e.g., an ordinal scale of measurement in Stevensīs typology-that does not permit arithmetic operations. In a typical practice of landscape connectivity analysis and corridor planning, the raster cost surface is created by transforming one or more sets of values (e.g., land cover type, land ownership, and elevation) attributed to cells into another set of such values (representing cost) through a function reflecting one or more criteria. A question arises: how certain can one be about the correctness of such a cost estimation function?

There are at least four issues in the application of the least-cost path model to landscape connectivity analysis and corridor planning under uncertainty. First, while it is generally anticipated that different cost estimation functions lead to different least-cost paths (hence to different effective distances or different corridor locations), little is known on how such differences arise (or do not arise). Second, while it is generally recognized that the location and length of a least-cost path are both sensitive to the spatial resolution of the raster cost surface, little is known if they are always sensitive in the same way and to the same degree and if not, what makes them more (or less) sensitive. Third, when it is difficult to establish a fully connected corridor between target habitat areas (e.g., because of surrounding anthropogenic activities), the least-cost path (which is by definition fully connected) may not be useful at least in its original form. Lastly, even if the conventional least-cost path model may have inconsistent results in theory, it may well be continued to be used in practice, unless there is a sound alternative to it.

The issues raised above are addressed through four studies corresponding to four respective papers which are appended to this thesis. While the first three studies use artificial landscape data generated by computers with varying spatial and non-spatial characteristics, the fourth study uses data on a real landscape. The first study (Paper 1) evaluates how the locations and lengths of least-cost paths (the latter of which are referred to as least-cost distances) vary with change in cost estimation parameters. This is done through a series of computational experiments, in which each of the artificial landscapes is converted into different cost surfaces by systematically varying parameters of a cost-estimation function, on which least-cost paths are generated. The locations and lengths of those paths are statistically analyzed to find sources of their variation. The second study (Paper 2) investigates how the least-cost distance is affected by the spatial resolution of the corresponding cost surface. This is also done through a series of computational experiments, in which each of the artificial landscapes is converted into a cost surface, which is, in turn, converted into different cost surfaces (different, i.e., only in their spatial resolutions) by systematically aggregating grid cells. Then, the statistical behavior of the ratio of the least-cost distance measured on a lower-resolution cost surface to that measured on a higher-resolution cost surface is analyzed. The third study (Paper 3) proposes the mini-max path model as an alternative to the least-cost path model. Unlike the conventional model (in which the optimality of a path is based on the sum of its length multiplied by the underlying cost values), the alternative model determines the optimality of a path using the length of a segment(s) of the path that intersects the cells having the maximum cost value (with a special tie-breaking rule). The performances of the two models are tested in one of the following two assumptions at a time: the cost values are measured on an ordinal scale or on a ratio scale. The fourth study (Paper 4) applies the model proposed in the third study to an ongoing conservation project of the Dian Fossey Gorilla Fund International that plans to design a `stepping-stoneī corridor-which is not fully connected but takes the form of a sequence of fragmented forest patches-between two core habitat areas of pollinator birds between two protected areas in Rwanda. The project does not have complete information on the study area and the target species and thus the project staff can only rank land cover types in terms of their suitability/cost for being part of the corridor. The utility of the model is tested with different assumptions on the behavior of the birds (e.g., minimum stepping stone size) as well as on the cost associated with the implementation of the corridor (e.g., cost for planting shrubs along the corridor to encourage the birds to use it).

The first study finds that the same pair of terminal cells may well be connected by different least-cost paths on different cost surfaces though derived from the same landscape data. The variation among those paths is highly sensitive to the forms of spatial and non-spatial distributions of landscape elements (which cannot be controlled by users of the least-cost path model) as well as by those of cost values derived from them (which may be, at least indirectly, controlled by users of the model). The second study finds that least-cost distances measured on lower-resolution cost surfaces are generally highly correlated with-and useful predictors of-effective distances measured on higher-resolution cost surfaces. This relationship tends to be weakened when linear barriers to connectivity (e.g., roads and rivers) exist, but strengthened as distances increase and/or when linear barriers (if any) are detected by other presumably more accessible and affordable sources such as vector line data. The third study confirms the effectiveness of the conventional least-cost path model on ratio-scaled cost surfaces but finds that the alternative mini-max path model is mathematically sounder if the cost values are measured on an ordinal scale and practically useful if the problem is concerned not with the minimization of cost but with the maximization of some desirable condition such as suitability. The fourth study demonstrates the utility of the mini-max path model by effectively casting the stepping stone corridor problem as a special case of it. The model allows for a rapid first delineation of candidate routes for stepping stone corridors and facilitates the early exploratory stages of conservation projects.

Major implications of this thesis to the research and practice in landscape connectivity analysis and conservation corridor planning with raster-based GIS are summarized as follows.

- When sufficient information is available for quantification of cost values, the conventional least-cost path model is a reasonable approach to use.

- However, it is worth trying or at least acknowledging alternatives that do not rely on the quantitative-cost assumption if the value of each cell only indicates the ordinal category of cost of intersecting that cell. Note in particular that information used for cost estimation in practice (e.g., expert opinions or public surveys) are often of subjective and qualitative nature.

- The highest-resolution data may not always be most effective-much less, most cost-effective-for the task being undertaken. The choice of spatial resolution of the input raster data can significantly affect the output of the least-cost path model. Thus it should be consistent to the amount of spatial details needed, which should be estimated based on adequate ecological and geographical knowledge on the landscape and species being studied.

- It is not always obvious that a given spatial planning task can be effectively cast as an instance of an existing spatial optimization model. Therefore, knowledge exchange and collaboration are important between conservation biology and GIScience.

Landscape connectivity, Conservation corridor, Stepping stones, Effective distance, Geographic Information Systems, Raster data, Land evaluation, Suitability analysis, Cost surface, Suitability surface, Ordinal scale, Least-cost path, Spatial resolution

Created from the Publication Database of the Vienna University of Technology.