applications
applications
1 Department of Biology and Center for Conservation Biology, University of California, Riverside, California and 2USGS Forest and Range Ecosystem Science Center, Snake River Field Station, Boise, Idaho
Introduction
Ecological “niche modeling” combines species occurrence data and Geographic Information Systems (GIS) environmental variables into a powerful tool for identifying and mapping suitable habitat for species over large spatial extents. We are currently developing and testing ecological niche models for use in conservation planning. We presented our partitioned Mahalanobis D 2 modeling technique at the National Gap Conference in Reno in December 2005. This approach was originally developed by James Dunn, John Rotenberry, Steven Knick, and Lynette Duncan (Knick and Rotenberry 1998; Dunn and Duncan 2000; Duncan and Dunn 2001; Rotenberry et al. 2002). A detailed description of the model and corresponding SAS code will soon be available for use by researchers (Rotenberry et al. In Press).
The University of California, Riverside’s Center for Conservation Biology (CCB) is using this modeling approach to assist with conservation planning in southern California (Allen et al. 2005). In this article, we briefly describe the Mahalanobis D 2 modeling approach and basic steps involved in constructing our niche models. We discuss potential uses of niche models for conservation planning and for adaptive management and monitoring activities, using our current research as an example.
Conceptual Basis of the Partitioned Mahalanobis D 2 Modeling Approach
The partitioned Mahalanobis D 2 model is a multivariate statistical modeling approach that identifies a minimum (rather than an optimum) set of basic habitat requirements for a species. It is based on the assumption that it is the constant environmental relationships in a species’ distribution ( i.e., variables that maintain a consistent value where the species occurs) that are most likely to be associated with limiting factors. Environmental variables taking on a wide range of values over locations where a species occurs are less informative since they are not restrictive of a species’ distribution. Mahalanobis D 2 is an index of habitat suitability that represents the standardized difference between values of a set of environmental variables for any point and the mean values for those same variables calculated from all points where a species occurs. Smaller differences indicate a point lying closer to the overall mean, and implies more similar habitat to that generally occupied by the species. Dunn showed that Mahalanobis D 2 could be partitioned into a set of independent, additive distances. This partitioning is achieved through principal components analysis of the set of variables measured at all points where the species occurs. Each component (linear combination of variables) describes a hyperplane; the eigenvalue of a component describes the variance in the distance of all the points from that hyperplane. Thus, the component (“partition”) with the smallest eigenvalue represents the linear combination of variables for whom the variance of points at which the species occurs is at a minimum, and thus most likely represents the limiting factors we are looking for. In contrast, increasingly higher components with greater eigenvalues are linear combinations of variables around which points have higher variances, and hence they are less likely to represent limits to distribution. For any point the distances associated with each component are additive (principal components are independent) and over all components sum to the original Mahalanobis D 2. Recognizing that more than one set of combinations could be limiting, we also examine the components with the second smallest eigenvalue, third smallest, etc., until variances become substantially larger.
A benefit of this technique is that inclusions of environmental variables unassociated with limits to a species distribution (and hence with high variances) have less impact on the model results. Likewise, by focusing on those components with minimal variance, we should be able to identify similar habitat outside of the spatial range sampled in the original study area and apply the model to new areas or to changing environments. By examining eigenvector values, we are able to identify which specific environmental variables seem important in determining a species distribution.
The Basic Components of Niche Modeling
In constructing our models, we create two related datasets. First, we compile a “species location” dataset that includes geographic coordinates for each location where a species was detected. In contrast to presence-absence habitat modeling techniques there is no need to determine where a species is absent. To determine that a species is absent requires specific data collection methodologies and extensive survey effort often involving repeated sampling. With presence-only modeling approaches, we can include data that comes from a variety of sources and that has been collected with differing methodologies and levels of effort. Presence-only datasets can include species location information from museums, herbaria, government natural diversity databases, and experts in the field, as well as from more formal survey efforts. Second, we develop a “map points” dataset consisting of geographical coordinates of a grid of points overlaying the entire study area. In our own work we use a grid spacing of ~ 250m between points, reflecting tradeoffs between the biology of the species being modeled, map precision, area to be covered, and computational convenience. Using GIS we calculate the value of selected environmental variables for each map point in the study area and for each species location. In our own work we summarize environmental variables at both local- (within 125 meters of the point) and landscape-scales (within a kilometer of the point). Some of the GIS layers we use to derive our environmental variables include temperature, precipitation, digital elevation models, vegetation type, land use, soils, and hydrology.
Once environmental variables are calculated for each species point and for all map points, we are ready to construct our niche model. For each model, we include environmental variables we hypothesize a priori to be important to that species distribution. As a general rule, we use 10 observations per environmental variable in the model. We run the principal components analysis to create the partitions (this is, in essence, the model), and examine the distribution of eigenvalues to determine whether our final model should consist of the last component, the last two components, etc. We also examine eigenvector values to see which environmental variables are most closely associated with selected components. We then use the selected model to calculate Habitat Similarity Index (HSI) values for every grid point on the map. The HSI values represent on a scale of 0 to 1 how similar each point in the landscape is to the hyperplane that describes the limiting combination of variables where the species was originally detected.
Once a model is developed it is tested to determine how well it predicts suitable habitat for the target species. One method of testing the models is to randomly withhold a subset of points from the species location dataset when creating the model and to use this “validation” dataset to evaluate model performance. A second, higher standard of testing is to use an independent dataset specifically collected from areas where there is no location information for the species being modeled.
Application of Niche Models to Conservation Planning
CCB is currently revising and testing niche models for invertebrate, plant, reptile, bird, and mammal species conserved by Western Riverside County’s Multiple Species Habitat Conservation Plan (WRC MSHCP). The plan seeks to protect 146 sensitive plant and animal species in a rapidly urbanizing study area of ~490,000 ha. We are conducting fieldwork this spring to collect independent datasets to evaluate our models. Figures 1-3 show untested, preliminary models for three sensitive bird species inhabiting coastal sage scrub habitats in the plan area. These models illustrate differences in suitable habitat even among species generally thought to co-occur within the same vegetation community. To facilitate conservation planning we have used our niche models to develop “community” models. We overlay individual species niche models to create community models that predict the potential for lands to support multiple species of conservation interest. The community model is simply the sum of the individual HSI values for the s species being considered, and ranges from 0 to s . Figure 4 is a community model constructed for the three sensitive coastal sage scrub bird species illustrated in Figs. 1-3.
Once the models are tested, they will be used to identify suitable habitat for species of conservation interest and can be used to assist with the reserve assembly process. The models can be used to provide a preliminary assessment of candidate lands for acquisition and inclusion in the reserve system. They can also be used to quantify how well the reserve system has achieved species conservation goals in terms of the amount and configuration of suitable habitat conserved. An emerging use of niche models is predicting habitat suitability under changing environmental conditions resulting from global climate change, nitrogen deposition from air pollution and agriculture, and other anthropogenic processes. We can use these models to make predictions about how effectively reserve systems may be expected to conserve suitable habitat for sensitive plant and animal species in the future.
Once we have identified important relationships between environmental variables and species occurrences, we can use them to guide future research into habitat relationships and to develop adaptive management plans and prioritize management activities. Niche models of relevant species can be used to identify lands suitable for restoration of native vegetation or for the introduction of species of conservation interest. These models can also be used to identify lands vulnerable to invasion by non-native plants and animals.
Conclusion
The partitioned Mahalanobis D 2 modeling approach is a tool available to GAP projects to map suitable habitat for species and to predict community richness over large spatial areas. Niche models are powerful conservation tools, the uses of which are just in the beginning stages of development.
Literature Cited
Allen, M.F., J.T. Rotenberry, K.L.. Preston, K.J. Halama, T. Tennant, C.W. Barrows, V. Rivera del Rio, A. Celis Murrillo, X. Chen, and V.M. Rorive. 2005: Towards developing a monitoring framework for Multiple Species Habitat Conservation Plans. Part I." ( June 1, 2005). Center for Conservation Biology.http://repositories.cdlib.org/ccb/CCB2005/
Duncan, L. and J.E. Dunn. 2001. Partitioned Mahalanobis D 2 to improve GIS classification. Proceedings of the SAS User Group International Number 26, Paper 198-26. SAS Institute, Cary, North Carolina, USA.
Dunn, J.E. and L. Duncan. 2000. Partitioning Mahalanobis D 2 to sharpen GIS classification. Pages 195-204 in C.A. Brebbia and P. Pascolo, editors. Management information systems 2000: GIS and remote sensing. WIT Press, Southampton, UK.
Knick, S.T. and J.T. Rotenberry. 1998. Limitations to mapping habitat use areas in changing landscapes using the Mahalanobis distance statistic. Journal of Agricultural, Biological, and Environmental Statistics 3:311-322.
Rotenberry, J.T., S.T. Knick, and J.E. Dunn. 2002. A minimalist approach to mapping species’ habitat: Pearson’s planes of closest fit. Pages 281-289 in J.M. Scott, P.J. Heglund, M.L. Morrison, J.B. Haufler, M.G. Raphael, W.A. Wall, and F.B. Samson, editors. Predicting species occurrences: issues of accuracy and scale. Island Press, Washington, D.C. USA.
Rotenberry, J.T., K.L. Preston, and S.T. Knick. In Press. GIS-based niche modeling for mapping species’ habitat. Ecology.
Untested model. Not intended for use in policy decisionmaking.
Figure 1 “HSIs” of habitat similarity for Bell’s Sage Sparrow across the Plan Area: The higher the HSI, the greater the similarity between occupied habitat and other areas.
Untested model. Not intended for use in policy decision making.
Figure 2 “HSIs” of habitat similarity for California Gnatcatcher across the Plan Area: The higher the HSI, the greater the similarity between occupied habitat and other areas.
Untested model. Not intended for use in policy decision making.
Figure 3 “HSIs” of habitat similarity for Southern California Rufous-crowned Sparrow across the Plan Area: The higher the HSI, the greater the similarity between occupied habitat and other areas.
Untested model. Not intended for use in policy decision making.
Figure 4 Cumulative habitat similarity index (HSI) values for four covered coastal sage scrub bird species across the Plan Area. The higher the cumulative HSI, the greater the predicted habitat suitability for multiple bird species. The map is from Allen et al. (2005).