Spatial point pattern analysis of available and exploited resources

A patchy spatial distribution of resources underpins many models of population regulation and species coexistence, so ecologists require methods to analyse spatially-explicit data of resource distribution and use. We describe a method for analysing maps of resources and testing hypotheses about species' distributions and selectivity. The method uses point pattern analysis based on the L-function, the linearised form of Ripley's K-function. Monte Carlo permutations are used for statistical tests. We estimate the difference between observed and expected values of L(t), an approach with several advantages: 1) The results are easy to interpret ecologically. 2) It obviates the need for edge correction, which has largely precluded the use of L-functions where plot boundaries are “real”. Including edge corrections may lead to erroneous conclusions if the underlying assumptions are invalid. 3) The null expectation can take many forms, we illustrate two models: complete spatial randomness (to describe the spatial pattern of resources in the landscape) and the underlying pattern of resource patches in the landscape (akin to a neutral landscape approach). The second null is particularly useful to test whether spatial patterns of exploited resource points simply reflect the spatial patterns of all resource points. We tested this method using over 100 simulated point patterns encompassing a range of patterns that might occur in ecological systems, and some very extreme patterns. The approach is generally robust, but Type II decision errors might arise where spatial patterns are weak and when trying to detect a clumped pattern of exploited points against a clumped pattern of all points. An empirical example of an intertidal lichen growing on barnacle shells illustrates how this technique might be used to test hypotheses about dispersal mechanisms. This approach can increase the value of survey data, by permitting quantification of natural resource patch distribution in the landscape as well as patterns of resource use by species.

[1]  Brian D. Ripley,et al.  Spatial Statistics: Ripley/Spatial Statistics , 2005 .

[2]  Peter J. Diggle,et al.  Simple Monte Carlo Tests for Spatial Pattern , 1977 .

[3]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[4]  A. Møller,et al.  The importance of host spatial distribution for parasite specialization and speciation: a comparative study of bird fleas (Siphonaptera: Ceratophyllidae) , 2002 .

[5]  B. Shorrocks,et al.  Aggregation of Larval Diptera Over Discrete and Ephemeral Breeding Sites: The Implications for Coexistence , 1984, The American Naturalist.

[6]  R. Cole,et al.  Using spatial pattern analysis to distinguish causes of mortality: an example from kelp in north‐eastern New Zealand , 1999 .

[7]  P. Doak.  HABITAT PATCHINESS AND THE DISTRIBUTION, ABUNDANCE, AND POPULATION DYNAMICS OF AN INSECT HERBIVORE , 2000 .

[8]  B. Downes,et al.  The distribution of aquatic invertebrate egg masses in relation to physical characteristics of oviposition sites at two Victorian upland streams , 2003 .

[9]  S. Hawkins,et al.  Patchiness and fluctuations on moderately exposed rocky shores , 1985 .

[10]  George R. Parker,et al.  Long-term spatial dynamics in an old-growth deciduous forest , 1996 .

[11]  J. Wiens,et al.  A novel use of the lacunarity index to discern landscape function , 2000, Landscape Ecology.

[12]  M. Palmer,et al.  Streambed landscapes: evidence that stream invertebrates respond to the type and spatial arrangement of patches , 2000, Landscape Ecology.

[13]  Anthony W. King,et al.  The Use and Misuse of Neutral Landscape Models in Ecology , 1997 .

[14]  J. Warren.  Isolation by distance in the crustose lichens Candelariella vitellina and Placynthium nigrum colonising gravestones in northeast Scotland , 2003, Biodiversity & Conservation.

[15]  T. O. Crist,et al.  Critical Thresholds in Species' Responses to Landscape Structure , 1995 .

[16]  Krijger,et al.  Higher species diversity explained by stronger spatial aggregation across six neotropical Drosophila communities , 2001 .

[17]  R. Bailey.  Ecological aspects of dispersal and establishment in lichens , 1976 .

[18]  Peter Haase,et al.  Can isotropy vs. anisotropy in the spatial association of plant species reveal physical vs. biotic facilitation , 2001 .

[19]  B. Peckarsky,et al.  Hydrologic and behavioral constraints on oviposition of stream insects: implications for adult dispersal , 2000, Oecologia.

[20]  Mark Rees,et al.  Identifying aggregation and association in fully mapped spatial data , 1999 .

[21]  Lenore Fahrig,et al.  Effect of Spatial Arrangement of Habitat Patches on Local Population Size , 1988 .

[22]  A. Baddeley,et al.  Estimating the J function without edge correction , 1999, math/9910011.

[23]  S. Hartley,et al.  A general framework for the aggregation model of coexistence , 2002 .

[24]  J. Lancaster,et al.  Linking landscape patterns of resource distribution with models of aggregation in ovipositing stream insects , 2003 .

[25]  S. Heard.  Resource patch density and larval aggregation in mushroom-breeding flies , 1998 .

[26]  A. Ives.  Aggregation and Coexistence in a Carrion Fly Community , 1991 .

[27]  Hills Jm,et al.  A multi-scale analysis of settlement density and pattern dynamics of the barnacle Semibalanus balanoides , 1996 .

[28]  S. Heard,et al.  Local Movement and Edge Effects on Competition and Coexistence in Ephemeral‐Patch Models , 1998, The American Naturalist.

[29]  M. Keller,et al.  The Effect of Resource Aggregation at Different Scales: Optimal Foraging Behavior of Cotesia rubecula , 2001, The American Naturalist.

[30]  Bernard W. Silverman,et al.  Methods for Analysing Spatial Processes of Several Types of Points , 1982 .

[31]  M. Palmer,et al.  The arrangement of resources in patchy landscapes: effects on distribution, survival, and resource acquisition of chironomids , 2000, Oecologia.

[32]  B. Ripley.  The Second-Order Analysis of Stationary Point Processes , 1976 .

[33]  Zengo Furukawa,et al.  A General Framework for , 1991 .

[34]  Raphaël Pélissier,et al.  On explicit formulas of edge effect correction for Ripley's K‐function , 1999 .

[35]  P. Chesson.  Mechanisms of Maintenance of Species Diversity , 2000 .

[36]  Jeffery.  Settlement in different-sized patches by the gregarious intertidal barnacle Chamaesipho tasmanica Foster and Anderson in New South Wales. , 2000, Journal of experimental marine biology and ecology.

[37]  Jeffrey S. Ward,et al.  New derivation reduces bias and increases power of Ripley’s L index , 1999 .

[38]  D. Hawksworth,et al.  Lichenology: Progress and Problems , 1976 .

[39]  Scott N. Martens,et al.  Scales of aboveground and below‐ground competition in a semi‐arid woodland detected from spatial pattern , 1997 .

[40]  Dietrich Stoyan,et al.  Marked Point Processes in Forest Statistics , 1992, Forest Science.

[41]  P. Haase.  Spatial pattern analysis in ecology based on Ripley's K-function: Introduction and methods of edge correction , 1995 .

[42]  C. Duby,et al.  Comparing the Performances of Diggle's Tests of Spatial Randomness for Small Samples with and without Edge‐Effect Correction: Application to Ecological Data , 1999, Biometrics.

[43]  M. Andersen,et al.  Spatial analysis of two-species interactions , 1992, Oecologia.

[44]  Peter J. Diggle,et al.  SPLANCS: spatial point pattern analysis code in S-Plus , 1993 .