Adaptation of an ecological territorial model to street gang spatial patterns in Los Angeles

Laura M. Smith; Andrea L. Bertozzi; P. Jeffrey Brantingham; George E. Tita; Matthew Valasik

doi:10.3934/dcds.2012.32.3223

Article Contents

2012, Volume 32, Issue 9: 3223-3244. Doi: 10.3934/dcds.2012.32.3223 open access

This issue Previous Article Lessons in uncertainty quantification for turbulent dynamical systems Next Article Symbolic dynamics for the $N$-centre problem at negative energies

Adaptation of an ecological territorial model to street gang spatial patterns in Los Angeles

1.
University of California Los Angeles, Department of Mathematics, 520 Portola Plaza Box 951555, Los Angeles, CA 90095-1555
2.
University of California Los Angeles, Department of Anthropology, 375 Portola Plaza, 341 Haines Hall, Box 951553, Los Angeles, CA 90095-1553
3.
University of California Irvine, Department of Criminology, Law and Society, 2340 Social Ecology II, Irvine, CA 92697-7080

Received: December 2011

Revised: March 2012

Published: September 2012

Abstract / Introduction Related Papers Cited by

Abstract

Territorial behavior is often found in nature. Coyotes and wolves organize themselves around a den site and mark their territory to distinguish their claimed region. Moorcroft et al. model the formation of territories and spatial distributions of coyote packs and their markings in [31]. We modify this ecological approach to simulate spatial gang dynamics in the Hollenbeck policing division of eastern Los Angeles. We incorporate important geographical features from the region that would inhibit movement, such as rivers and freeways. From the gang and marking densities created by this method, we create a rivalry network from overlapping territories and compare the graph to both the observed network and those constructed through other methods. Data on the locations of where gang members have been observed is then used to analyze the densities created by the model.

Keywords:

Mathematics Subject Classification: Primary: 35Q80, 91D25; Secondary: 91D10, 91D30, 92F05.

Citation:

Related Papers

Cited by

References

[1]	A. S. Ackleh, B. G. Fitzpatrick, R. Scribner, N. Simonsen and J. J. Thibodeaux, Ecosystem modeling of college drinking: Parameter estimation and comparing models to data, Mathematical and Computer Modelling, 50 (2009), 481-497.doi: 10.1016/j.mcm.2009.03.012.
[2]	A. Alonso, "Urban Graffiti on the City Landscape," Western Geography Graduate Conference, San Diego State University, February 14, 1998.
[3]	Elijah Anderson, "Code of the Street: Decency, Violence, and the Moral Life of the Inner City," W. W. Norton & Company, Inc., New York, 2000.
[4]	J. Austin, E. Smith, S. Srinivasan and F. Sanchez, "Social Dynamics of Gang Involvement: A Mathematical Approach," Mathematical and Theoretical Biology Institute, MTBI-08-08M, 2011.
[5]	A. Barbaro, L. Chayes and M. R. D'Orsogna, Territorial development based on graffiti: A statistical mechanics approach, 2011. Available from: ftp://ftp.math.ucla.edu/pub/camreport/cam11-70.pdf.
[6]	Jordi Bascompte and Ricard V. Sole, On wolf territoriality and deer survival, in "Modeling Spatiotemporal Dynamics in Ecology," Springer-Verlag, New York, (1998), 105-126.
[7]	L. M. A. Bettencourt, A. Cintròn-Arias, D. I. Kaiser and C. Castillo-Chàvez, The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models, Physica A: Statistical Mechanics and its Applications, 364 (2006), 513-536.
[8]	P. J. Brantingham, G. Tita, M. B. Short and S. Reid, The ecology of gang territorial boundaries, Criminology, in press.
[9]	B. Briscoe, M. Lewis and S. Parrish, Home range formation in wolves due to scent marking, Bulletin of Mathematical Biology, 64 (2002), 261-284.doi: 10.1006/bulm.2001.0273.
[10]	W. K. Brown, Graffiti, identity and the delinquent gang, Internal Journal of Offender and Comparative Criminology, 22 (1978), 46-48.
[11]	S. H. Decker and B. Van Winkle, "Life in the Gang: Family, Friends, and Violence,'' Cambridge University Press, New York, New York, 1996.
[12]	Perri K. Eason, Gary A. Cobbs and Kristin G. Trinca, The use of landmarks to define territorial boundaries, Animal Behavior, 58 (1999), 85-91.
[13]	J. Eck and L. Liu, Contrasting simulated and empirical experiments in crime prevention, Journal of Experimental Criminology, 2008.
[14]	Mike Egesdal, Chris Fathauer, Kym Louie and Jeremy Neuman, Statistical modeling of gang violence in Los Angeles, SIAM Undergraduate Research Online, 3 (2010).
[15]	S. Fortune, Voronoĭ diagrams and Delaunay triangulations, in "Computing in Euclidean Geometry" (eds. D. Du and F. Hwang), Lecture Notes Ser. Comput., 1, World Scientific Publ., River Edge, NJ, (1992), 193-233.
[16]	Linton C. Freeman, Centrality in social networks conceptual clarification, Social Networks, 1 (1979), 215-239.
[17]	Celeste Fremon, "G-Dog and the Homeboys: Father Greg Boyle and the Gangs of East Los Angeles," University of New Mexico Press, Albuquerque, New Mexico, 2008.
[18]	Luca Giuggioli, Jonathan R. Potts, and Stephen Harris, Animal interactions and the emergence of territoriality, PLoS Computational Biology, 7 (2011), 1-9.doi: 10.1371/journal.pcbi.1002008.
[19]	Mirta B. Gordon, A random walk in the literature on criminality: A partial and critical view on some statistical analyses and modelling approaches, European Journal of Applied Mathematics, 21 (2010), 283-306.doi: 10.1017/S0956792510000069.
[20]	Kristen Hawkes, Kim Hill and James F. O'Connell, Why hunters gather: Optimal foraging and the Achè of eastern Paraguay, American Ethnologist, 9 (1982), 379-398.doi: 10.1525/ae.1982.9.2.02a00100.
[21]	Rachel A. Hegemann, Erik A. Lewis and Andrea L. Bertozzi, An "Estimate & Score Algorithm" for simultaneous parameter estimation and reconstruction of missing data on social networks, 2012. Available from: ftp://ftp.math.ucla.edu/pub/camreport/cam12-12.pdf.
[22]	Rachel A. Hegemann, Laura M. Smith, Alethea B. T. Barbaro, Andrea L. Bertozzi, Shannon E. Reid and George E. Tita, Geographical influences of an emerging network of gang rivalries, Physica A: Statistical Mechanics and its Applications, 390 (2011), 3894-3914.
[23]	E. E. Holmes, M. A. Lewis, J. E. Banks and R. R. Veit, Partial differential equations in ecology: Spatial interactions and population dynamics, Ecology, 75 (1994), 17-29.doi: 10.2307/1939378.
[24]	S. R. Jammalamadaka and A. SenGupta, "Topics in Circular Statistics,'' Series on Multivariate Analysis, 5, World Scientific Publishing Co., Inc., River Edge, NJ, 2001.
[25]	Jill E. Jankowski, Scott K. Robinson and Douglas J. Levey, Squeezed at the top: Interspecific aggression may constrain elevational ranges in tropical birds, Ecology, 91 (2010), 1877-1884.doi: 10.1890/09-2063.1.
[26]	Matthew James Keeling and Pejman Rohani, "Modeling Infectious Diseases in Humans and Animals," Princeton University Press, Princeton, New Jersey, 2008.
[27]	Malcolm Klein and Cheryl Maxson, "Street Gang Patterns and Policies," Oxford University Press, Oxford, New York, 2006.
[28]	M. A. Lewis and J. D. Murray, Modelling territoriality and wolf-deer interactions, Nature, 366 (1993), 738-740.doi: 10.1038/366738a0.
[29]	M. A. Lewis, K. A. White and J. D. Murray, Analysis of a model for wolf territories, Journal of Mathematical Biology, 35 (1997), 749-774.doi: 10.1007/s002850050075.
[30]	David Ley and Roman Cybriwsky, Urban graffiti as territorial markers, Annals of the Association of American Geographers, 64 (1974), 491-505.doi: 10.1111/j.1467-8306.1974.tb00998.x.
[31]	Paul R. Moorcroft and Alex Barnett, Mechanistic home range models and resource selection analysis: A reconciliation and unification, Ecology, 89 (2008), 1112-1119.doi: 10.1890/06-1985.1.
[32]	Paul R. Moorcroft, Mark A. Lewis and Robert L. Crabtree, Home range analysis using a mechanistic home range model, Ecology, 80 (1999), 1656-1665.
[33]	Paul R. Moorcroft, Mark A. Lewis and Robert L. Crabtree, Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone, Proceedings: Biological Sciences, The Royal Society, 273 (2006), 1651-1659.doi: 10.1098/rspb.2005.3439.
[34]	Joan Moore, "Homeboys: Gangs, Drugs, and Prison in the Barrios of Los Angeles," Temple University Press, Philadelphia, 1978.
[35]	Joan Moore, "Going Down to the Barrio: Homeboys and Homegirls in Change," Temple University Press, Philadelphia, 1991.
[36]	Joan Moore, Diego Vigil and Robert Garcia, Residence and Territoriality in Chicano Gangs, Social Problems, 31 (1983), 182-194.doi: 10.1525/sp.1983.31.2.03a00070.
[37]	Roger P. Peters and L. David Mech, Scent-marking in wolves: Radio-tracking of wolf packs has provided definite evidence that olfactory sign is used for territory maintenance and may serve for other forms of communication within the pack as well, American Scientist, 63 (1975), 628-637.
[38]	S. Radil, C. Flint and G. Tita, Spatializing social networks: Using social network analysis to investigate geographies of gang rivalry, territoriality, and violence in Los Angeles, Annals of the Association of American Geographers, 100 (2010), 307-326.doi: 10.1080/00045600903550428.
[39]	D. M. Romero, C. M. Kribs-Zaleta, A. Mubayi and C. Orbe, An epidemiological approach to the spread of political third parties, Social Sciences Research Network, 2009. Available from: http://dx.doi.org/10.2139/ssrn.1503124.
[40]	Pamela Effrein Sandstrom, An optimal foraging approach to information seeking and use, The Library Quarterly, 64 (1994), 414-449.doi: 10.1086/602724.
[41]	M. Short, G. Mohler, P. J. Brantingham and G. Tita, Gang rivalry dynamics via coupled point process networks, 2011. Available from: http://math.scu.edu/~gmohler/gangnetwork.pdf.
[42]	A. Stomakhin, M. B. Short and A. L. Bertozzi, Reconstruction of missing data in social networks based on temporal patterns of interactions, Inverse Problems, 27 (2011), 115013, 15 pp.
[43]	Travis A. Taniguchi, Jerry H. Ratcliffe and Ralph B. Taylor, Gang set space, drug markets, and crime around drug corners in Camden, Journal of Research in Crime and Delinquency, 48 (2011), 327-363.doi: 10.1177/0022427810393016.
[44]	F. M. Thrasher, "The Gang: A Study of 1313 Gangs in Chicago,'' University of Chicago Press, Chicago, 1927.doi: 10.1525/sp.2005.52.2.272.
[45]	G. Tita, J. Cohen and J. Engberg, An ecological study of the location of gang "set space'', Social Problems, 52 (2005), 272-299.
[46]	G. Tita, K. Riley, G. Ridgeway, C. Grammich, A. Abrahamse and P. Greenwood, "Reducing Gun Violence: Results from an Intervention in East Los Angeles," RAND Corporation, Santa Monica, California, 2003.
[47]	James Vigil, "Barrio Gangs: Street Life and Identity in Southern California," University of Texas Press, Austin, Texas, 1988.
[48]	Stanley Wasserman and Katherine Faust, "Social Network Analysis: Methods and Applications," Cambridge University Press, New York, 2009.
[49]	David P. Watts and John C. Mitani, Boundary patrols and intergroup encounters in wild chimpanzees, Behaviour, 138 (2001), 299-327.doi: 10.1163/15685390152032488.
[50]	K. A. White, M. A. Lewis and J. D. Murray, A model for wolf-pack territory formation and maintenance, Journal of Theoretical Biology, 178 (1996), 29-43.doi: 10.1006/jtbi.1996.0004.