Thomas R. Etherington

Least-cost path length versus accumulated-cost as connectivity measures

Least-cost modelling has become a popular method for measuring connectivity. By representing the landscape as a cost-surface, least-cost paths can be calculated that represent the route of maximum efficiency between two locations as a function of the distance travelled and the costs traversed. Both the length and the accumulated-cost of a least-cost path have been used as measures of connectivity between pairs of locations. However, we are concerned that in some situations the length of a least-cost path may provide a misleading measure of connectivity as it only accounts for the distance travelled while ignoring the costs traversed, and results in a measure that may be little better than Euclidean distance. Through simulations using fractal landscapes we demonstrate that least-cost path length is often highly correlated with Euclidean distance. This indicates that least-cost path length provides a poor measure of connectivity in many situations, as it does not capture sufficient information about the ecological costs to movement represented by the cost-surface. We recommend that in most situations the accumulated-cost of a least-cost path provides a more appropriate measure of connectivity between locations as it accounts for both the distance travelled and costs traversed, and that the generation of vector least-cost paths should be reserved for visualisation purposes.

NLMpy: a python software package for the creation of neutral landscape models within a general numerical framework

Summary Neutral landscape models (NLMs) are widely used to model ecological patterns and processes across landscapes. However, the ability to generate NLMs is often made available through standalone bespoke software packages that have platform limitations. We have developed a python package that brings together some of the more popular NLM algorithms using a general numerical framework. The resulting NLMpy package: (i) allows for the creation of NLMs directly within a python modelling workflow or by other modelling software capable executing a python script, (ii) enables the first opportunity to create a NLM that combines different algorithms, (iii) provides easy integration with geographic information system data and (iv) creates a framework for developing other NLMs.

Least-cost modelling on irregular landscape graphs

Least-cost modelling is becoming widely used in landscape ecology to examine functional connectivity. Traditionally the least-cost modelling algorithm creates a regularly structured landscape graph for connectivity analysis by converting all the cells from a cost-surface into vertices in a landscape graph. However, use of a regular landscape graph is problematic as it: contains a great deal of redundant information that in turn increases processing times, is constructed in a deterministic manner that precludes examination of the effects of graph structure on connectivity measures, and is known to produce results with directional bias. I present, and provide Python code for, an algorithm to produce an irregular landscape graph from a cost-surface. Tests demonstrate that comparable results to those of the traditional regular landscape graph approach can be achieved, while at the same time reducing computational expense, enabling variations in graph structure to be incorporated into an analysis, and avoiding directional bias. Therefore, this approach may allow for more robust ecological decision-making when examining matters of functional connectivity using least-cost modelling.

Monitoring and population estimation of the European badger Meles meles in Northern Ireland

The estimation of animal abundance has a central role in wildlife management and research, including the role of badgers Meles meles in bovine tuberculosis transmission to cattle. This is the first study to examine temporal change in the badger population of Northern Ireland over a medium- to long-term time frame of 14-18 years by repeating a national survey first conducted during 1990-1993. A total of 212 1-km2 squares were surveyed during 2007-2008 and the number, type and activity of setts therein recorded. Badgers were widespread with 75% of squares containing at least one sett. The mean density of active main setts, which was equivalent to badger social group density, was 0.56 (95% CI: 0.46-0.67) active main setts per km2 during 2007-2008. Social group density varied significantly among landclass groups and counties. The total number of social groups was estimated at 7,600 (95% CI: 6,200-9,000) and, not withstanding probable sources of error in estimating social group size, the total abundance of badgers was estimated to be 34,100 (95% CI: 26,200-42,000). There was no significant change in the badger population from that recorded during 1990-1993. A resource selection model provided a relative probability of sett construction at a spatial scale of 25 m. Sett locations were negatively associated with elevation and positively associated with slope, aspect, soil sand content, the presence of cover, and the area of improved grassland and arable agriculture within 300 m.

Quantifying the Direct Transfer Costs of Common Brushtail Possum Dispersal using Least-Cost Modelling: A Combined Cost-Surface and Accumulated-Cost Dispersal Kernel Approach

Dispersal costs need to be quantified from empirical data and incorporated into dispersal models to improve our understanding of the dispersal process. We are interested in quantifying how landscape features affect the immediately incurred direct costs associated with the transfer of an organism from one location to another. We propose that least-cost modelling is one method that can be used to quantify direct transfer costs. By representing the landscape as a cost-surface, which describes the costs associated with traversing different landscape features, least-cost modelling is often applied to measure connectivity between locations in accumulated-cost units that are a combination of both the distance travelled and the costs traversed. However, we take an additional step by defining an accumulated-cost dispersal kernel, which describes the probability of dispersal in accumulated-cost units. This novel combination of cost-surface and accumulated-cost dispersal kernel enables the transfer stage of dispersal to incorporate the effects of landscape features by modifying the direction of dispersal based on the cost-surface and the distance of dispersal based on the accumulated-cost dispersal kernel. We apply this approach to the common brushtail possum (Trichosurus vulpecula) within the North Island of New Zealand, demonstrating how commonly collected empirical dispersal data can be used to calibrate a cost-surface and associated accumulated-cost dispersal kernel. Our results indicate that considerable improvements could be made to the modelling of the transfer stage of possum dispersal by using a cost-surface and associated accumulated-cost dispersal kernel instead of a more traditional straight-line distance based dispersal kernel. We envisage a variety of ways in which the information from this novel combination of a cost-surface and accumulated-cost dispersal kernel could be gainfully incorporated into existing dispersal models. This would enable more realistic modelling of the direct transfer costs associated with the dispersal process, without requiring existing dispersal models to be abandoned.

Mapping organism spread potential by integrating dispersal and transportation processes using graph theory and catchment areas

Geographical concepts and technologies are highly valued and have found useful applications in a wide range of geographical disciplines. Unfortunately there is a lack of communication between disciplines such as landscape ecology and transport geography. This presents a barrier to addressing geographical issues such as the spread of organisms, which in some instances require an integrated geography approach. In an attempt to encourage integrated geographical research on organism spread, that uses existing research from landscape ecology and transport geography, an integrated conceptual and technical framework is presented that could be used to produce maps that differentiate areas based on their spread potential. Conceptually, the terms patch connectivity and accessibility are recognised as being near identical in scope, and as such are suggested a useful basis for approaching the integration of movement modelling used in landscape ecology and transport geography. Technically, this integration can be achieved using modelling methodologies established in both disciplines, as the graph theory-based shortest path Dijkstras Algorithm used in transport geography is demonstrated to be equivalent to raster GIS least-cost modelling used in landscape ecology. This conceptual and technical common ground has been used to create an analytical approach based on catchment areas that can map differing levels of spread potential across a landscape. A demonstration of how these graph theory methods can also be integrated to map spread potential as a combined function of both organism dispersal and transportation is also provided. The practical challenges and assumptions in applying the methodology are also highlighted, and to facilitate understanding and further development of the approach presented, example scripts and data for producing maps of spread potential are provided for use with a variety of software.

Reducing Wildlife Damage with Cost-Effective Management Programmes.

Limiting the impact of wildlife damage in a cost effective manner requires an understanding of how control inputs change the occurrence of damage through their effect on animal density. Despite this, there are few studies linking wildlife management (control), with changes in animal abundance and prevailing levels of wildlife damage. We use the impact and management of wild pigs as a case study to demonstrate this linkage. Ground disturbance by wild pigs has become a conservation issue of global concern because of its potential effects on successional changes in vegetation structure and composition, habitat for other species, and functional soil properties. In this study, we used a 3-year pig control programme (ground hunting) undertaken in a temperate rainforest area of northern New Zealand to evaluate effects on pig abundance, and patterns and rates of ground disturbance and ground disturbance recovery and the cost effectiveness of differing control strategies. Control reduced pig densities by over a third of the estimated carrying capacity, but more than halved average prevailing ground disturbance. Rates of new ground disturbance accelerated with increasing pig density, while rates of ground disturbance recovery were not related to prevailing pig density. Stochastic simulation models based on the measured relationships between control, pig density and rate of ground disturbance and recovery indicated that control could reduce ground disturbance substantially. However, the rate at which prevailing ground disturbance was reduced diminished rapidly as more intense, and hence expensive, pig control regimes were simulated. The model produced in this study provides a framework that links conservation of indigenous ecological communities to control inputs through the reduction of wildlife damage and suggests that managers should consider carefully the marginal cost of higher investment in wildlife damage control, relative to its marginal conservation return.

Experimental simulation : using generative modeling and palaeoecological data to understand human-environment interactions.

The amount of palaeoecological information available continues to grow rapidly, providing improved descriptions of the dynamics of past ecosystems and enabling them to be seen from new perspectives. At the same time, there has been concern over whether palaeoecological enquiry needs to move beyond descriptive inference to a more hypothesis-focussed or experimental approach; however, the extent to which conventional hypothesis-driven scientific frameworks can be applied to historical contexts (i.e., the past) is the subject of ongoing debate. In other disciplines concerned with human-environment interactions, including physical geography and archaeology, there has been growing use of generative simulation models, typified by agent-based approaches. Generative modelling encourages counter-factual questioning (“what if…?”), a mode of argument that is particularly important in systems and time-periods, such as the Holocene and now the Anthropocene, where the effects of humans and other biophysical processes are deeply intertwined. However, palaeoecologically focused simulation of the dynamics of the ecosystems of the past either seems to be conducted to assess the applicability of some model to the future or treats humans simplistically as external forcing factors. In this review we consider how generative simulation-modelling approaches could contribute to our understanding of past human-environment interactions. We consider two key issues: the need for null models for understanding past dynamics and the need to be able learn more from pattern-based analysis. In this light, we argue that there is considerable scope for palaeocology to benefit from developments in generative models and their evaluation. We discuss the view that simulation is a form of experiment and, by using case studies, consider how the many patterns available to palaeoecologists can support model evaluation in a way that moves beyond simplistic pattern-matching and how such models might also inform us about the data themselves and the processes generating them. Our emphasis is on how generative simulation might complement traditional palaeoecological methods and proxies rather than on a detailed overview of the modelling methods themselves.

Using network connectivity to prioritise sites for the control of invasive species

Summary 1.Habitat connectivity is a crucial determinant of population dynamics in fragmented landscapes. The corollary of the emphasis on maintaining connectivity to enhance the movement of organisms is that disrupting connectivity should minimise it. Here we evaluate the efficiency of an invasive species control strategy that targets the most connected habitats in a landscape. 2.A network (spatial graph) provides an intuitive representation of a landscape, and the topology of this network can be used to identify the most connected patches. We implemented a simulation model of the spread of an invasive species on a network and used it to evaluate whether targeting the better-connected components of the landscape enhances control effectiveness. 3.Control strategies based on network topology consistently outperformed both a null strategy of random habitat selection and one based on separation distance alone. The advantages of the connectivity-based strategy were strongest in the early phases of the invasion process, when a small number of habitats are occupied at low population density. However, if long distance dispersal events were common the advantages of the connectivity approach weakened. 4.The performance of the connectivity-based strategy is robust to habitat-level demographic stochasticity. In fact, connectivity-based targeting outperforms a strategy focussing on source habitats, with the additional benefit that it requires less information to be implemented. 5.Synthesis and applications. Our simulation model outcomes demonstrate that deliberately targeting the best-connected components of a landscape is an efficient control strategy for invasive species when long-distance dispersal is infrequent, and it is likely to be cheaper than other alternatives such as targeting population sources. Network scientists have developed a range of methods designed to identify the minimal set of nodes on a graph that will disrupt the network as a whole; these tools have potential to aid in the design of more effective control strategies. This article is protected by copyright. All rights reserved.

Visualising continuous intra-landscape isolation with uncertainty using least-cost modelling based catchment areas: common brushtail possums in the Auckland isthmus

Invasive species have become a major stressor in many ecosystems. Therefore, public-policy decision-makers desire ecologically informed risk assessments that characterise the likelihood and severity of potential adverse effects from invasive species. These risk assessments often take the form of maps, but risk maps have generally ignored uncertainty and avoided incorporating processes such as the risk of spread. One method that has been proposed to map risk of spread is a least-cost modelling based catchment area approach. In summary, using a raster cost-surface that represents the difficulty associated with traversing different parts of a landscape, least-cost catchments are calculated for all cells in a landscape, and the catchments’ areas are then visualised as a map of intra-landscape isolation. However, there are challenges with parameterising least-cost modelling in an ecological context which means it is particularly important that any estimates of isolation are coupled with associated estimates of uncertainty. Using an example of the common brushtail possum (Trichosurus vulpecula) on the Auckland isthmus (New Zealand), we provide a demonstration of how the least-cost modelling based catchment area approach to mapping isolation can be applied to estimate isolation with uncertainty. We use a Python geoprocessing and geovisualisation framework to quantify isolation for four least-cost modelling based possum dispersal scenarios in order to produce a bivariate colour-by-alpha map that simultaneously visualises predicted isolation with associated uncertainty. The bivariate colour-by-alpha map clearly reinforces the need to consider uncertainty when producing catchment area isolation maps. While the overall pattern in isolation was a relatively simple function of the different isolation maps, the associated uncertainty had a complex spatial structure that would be difficult to understand without representing it explicitly. Providing policy decision-makers with bivariate maps that simultaneously include isolation and uncertainty will help support more robust invasive species risk assessments.