A Voronoi diagram based population model for social species of wildlife

A population model is presented that accounts for spatial structure within habitat patches. It is designed for social species of wildlife that form social group home ranges that are much smaller than patch size. The model represents social group home ranges by Voronoi regions that tessellate a patch to form a Voronoi diagram. Neighbouring social groups are linked with habitat-confined shortest paths and form a dispersal network. The model simulates population dynamics and makes use of Voronoi diagrams and dispersal networks as a spatial component. It then produces density maps as outputs. These are maps that show predicted animal densities across the patches of a landscape. A construction procedure for the particular Voronoi diagram type used by the model is described. As a test case, the model is run for the squirrel glider (Petaurus norfolcensis), a small arboreal marsupial native to Australia. A time series of density maps are produced that show squirrel glider density changing across a landscape through time.

[1]  Kenneth Steiglitz,et al.  Operations on Images Using Quad Trees , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  M. Tanemura,et al.  Geometrical models of territory. I. Models for synchronous and asynchronous settlement of territories. , 1980, Journal of theoretical biology.

[3]  Marie-Josée Fortin,et al.  Spatial Graphs: Principles and Applications for Habitat Connectivity , 2007, Ecosystems.

[4]  Boris Aronov.  On the geodesic Voronoi diagram of point sites in a simple polygon , 1987, SCG '87.

[5]  Hanan Samet,et al.  Neighbor finding techniques for images represented by quadtrees , 1982, Comput. Graph. Image Process..

[6]  D. Sharpe,et al.  Home Range of the Australian Squirrel Glider, Petaurus norfolcensis (Diprotodontia) , 2007 .

[7]  S. Harrison,et al.  Local extinction in a metapopulation context: an empirical evaluation , 1991 .

[8]  M. Mcdonnell,et al.  Ecology of Cities and Towns: Comments and synthesis , 2009 .

[9]  L. Fahrig,et al.  Effects of Road Fencing on Population Persistence , 2004 .

[10]  Joseph S. B. Mitchell.  Shortest paths among obstacles in the plane , 1996, Int. J. Comput. Geom. Appl..

[11]  Andrew F. Bennett,et al.  Gap-crossing by gliding marsupials: thresholds for use of isolated woodland patches in an agricultural landscape , 2003 .

[12]  Joseph S. B. Mitchell,et al.  An Efficient Algorithm for Euclidean Shortest Paths Among Polygonal Obstacles in the Plane , 1997, Discret. Comput. Geom..

[13]  R. A. Jarvis,et al.  Collision-free trajectory planning using distance transforms , 1985 .

[14]  R. Loyn,et al.  The influence of time since fire and distance from fire boundary on the distribution and abundance of arboreal marsupials in Eucalyptus regnans-dominated forest in the Central Highlands of Victoria , 2002 .

[15]  Peter Kareiva,et al.  Spatial ecology : the role of space in population dynamics and interspecific interactions , 1998 .

[16]  Stephen M. Jackson,et al.  The biology of Australian possums and gliders , 2004 .

[17]  Ian Stewart,et al.  Complex Analysis , 1983 .

[18]  Peter Kareiva,et al.  Biotic interactions and global change. , 1993 .

[19]  E. Wilson.  Sociobiology: The New Synthesis , 1976 .

[20]  Hanan Samet,et al.  An Overview of Quadtrees, Octrees, and Related Hierarchical Data Structures , 1988 .

[21]  Andrew F. Bennett,et al.  Home range of the squirrel glider (Petaurus norfolcensis) in a network of remnant linear habitats , 2003 .

[22]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[23]  D. T. Lee,et al.  A New Approach for the Geodesic Voronoi Diagram of Points in a Simple Polygon and Other Restricted Polygonal Domains , 1998, Algorithmica.

[24]  Daniel Lunney,et al.  Conservation of Australia's forest fauna , 1991 .

[25]  Leon G. Higley,et al.  Forensic Entomology: An Introduction , 2009 .

[26]  R. Ree.  The population ecology of the squirrel glider (Petaurus norfolcensis) within a network of remnant linear habitats , 2002 .

[27]  Michael Drielsma,et al.  A raster-based technique for analysing habitat configuration : The cost-benefit approach , 2007 .

[28]  Naiara Pinto,et al.  Beyond the least-cost path: evaluating corridor redundancy using a graph-theoretic approach , 2009, Landscape Ecology.

[29]  Subhash Suri,et al.  An Optimal Algorithm for Euclidean Shortest Paths in the Plane , 1999, SIAM J. Comput..

[30]  Eldridge S. Adams,et al.  TERRITORY SIZE AND SHAPE IN FIRE ANTS: A MODEL BASED ON NEIGHBORHOOD INTERACTIONS , 1998 .

[31]  A. Bradley,et al.  Reproduction in the squirrel glider, Petaurus norfolcensis (Petauridae) in south-east Queensland , 2001 .

[32]  Joseph S. B. Mitchell,et al.  The weighted region problem: finding shortest paths through a weighted planar subdivision , 1991, JACM.

[33]  Lenore Fahrig,et al.  Relative Effects of Habitat Loss and Fragmentation on Population Extinction , 1997 .

[34]  Erik Matthysen,et al.  The application of 'least-cost' modelling as a functional landscape model , 2003 .

[35]  Danny Ziyi Chen,et al.  Planning Shortest Paths among 2D and 3D Weighted Regions Using Framed-Subspaces , 1998, Int. J. Robotics Res..

[36]  Thorsten Wiegand,et al.  ASSESSING THE RISK OF EXTINCTION FOR THE BROWN BEAR (URSUS ARCTOS) IN THE CORDILLERA CANTABRICA, SPAIN , 1998 .

[37]  Ulf Dieckmann,et al.  The Geometry of Ecological Interactions: Simplifying Spatial Complexity , 2000 .

[38]  D. Quin.  Population ecology of the squirrel glider (Petaurus norfolcensis) and the sugar glider (P. breviceps) (Maruspialia:Petauridae) at Limeburners Creek, on the central north coast of New South Wales , 1995 .

[39]  D. Sharpe,et al.  How do we conserve the squirrel glider in Brisbane's urban matrix? , 2004 .

[40]  Eric Renshaw.  Modelling biological populations in space and time , 1990 .

[41]  Roland H. Lamberson,et al.  Conservation planning for species occupying fragmented landscapes: the case of the northern spotted owl , 1993 .

[42]  P. Menkhorst,et al.  Distribution, habitat and conservation status of the squirrel glider Petaurus norfolcensis (Petauridae: Marsupialia) in Victoria. , 1988 .

[43]  Clifford A. Shaffer,et al.  Optimal quadtree construction algorithms , 1987, Comput. Vis. Graph. Image Process..

[44]  Michael A. McCarthy,et al.  Extinction dynamics of the helmeted honeyeater: effects of demography, stochasticity, inbreeding and spatial structure , 1996 .

[45]  Danny Ziyi Chen,et al.  A framed-quadtree approach for determining Euclidean shortest paths in a 2-D environment , 1997, IEEE Trans. Robotics Autom..

[46]  Rae A. Earnshaw,et al.  Theoretical Foundations of Computer Graphics and CAD , 1988, NATO ASI Series.