Butterflies, Bees & BurglarsButterflies, Bees & BurglarsThe foraging behavior of contemporary criminal The foraging behavior of contemporary criminal

offendersoffenders

P. Jeffrey BrantinghamP. Jeffrey Brantingham11

MariaMaria--Rita DRita D’’OrsognaOrsogna22

Jon AzoseJon Azose33

George TitaGeorge Tita44

Andrea BertozziAndrea Bertozzi22

Lincoln ChayesLincoln Chayes22

1 1 UCLA Anthropology, UCLA Anthropology, 22 UCLA Mathematics, UCLA Mathematics, 33 Harvey Harvey MuddMudd College, College, 44 UC Irvine Criminology, Law and SocietyUC Irvine Criminology, Law and Society

Supported by the NSF Human Social Dynamics & the Long Beach Police Department

experiments in insect foragingexperiments in insect foragingenvironment:environment: arrangement of arrangement of patchespatchesmanipulation:manipulation: alter spacing alter spacing and/or quality of patchesand/or quality of patchesquestions:questions: search for patches search for patches of different quality; residence of different quality; residence time in patch; travel time time in patch; travel time between hostsbetween hostsobservations:observations: insects are able insects are able to quickly adjust foraging to quickly adjust foraging strategies to changed patch strategies to changed patch conditionsconditions

crime opportunities & motivated offenders crime opportunities & motivated offenders unevenly distributedunevenly distributedforaging strategies are what bring motivated foraging strategies are what bring motivated offenders together with criminal opportunitiesoffenders together with criminal opportunities

Residential burglary hotspots in Long Beach, CA in two sequential three monthperiods December 2001- February 2002 and March – June 2002.

two lowtwo low--level questionslevel questions

given a serial burglargiven a serial burglar……how far away in space or time is a second how far away in space or time is a second burglary (or second series of burglaries) likely burglary (or second series of burglaries) likely to be from a first burglary (or series)?to be from a first burglary (or series)?

how long do we have to wait between repeat how long do we have to wait between repeat burglaries at the same residential location?burglaries at the same residential location?

1.1. crime as a foraging problemcrime as a foraging problem

2.2. Long Beach, CA residential burglary data Long Beach, CA residential burglary data

3.3. models of patch residence and return timesmodels of patch residence and return times

4.4. implications and future directionsimplications and future directions

road map for this talkroad map for this talk

optimal foraging theory and crimeoptimal foraging theory and crime

obligate resource acquisitionobligate resource acquisitioncrime is a crime is a ““boundedlyboundedly rationalrational”” behaviorbehavior

behavioral optionsbehavioral optionsstrategies to find targets, victimize, and avoid strategies to find targets, victimize, and avoid detectiondetection

selectionselectionbiased social or trialbiased social or trial--andand--error learning leads error learning leads offenders to arrive at an optimal foraging patternoffenders to arrive at an optimal foraging pattern

Long Beach residential burglaryLong Beach residential burglaryCPC 459R & GCPC 459R & G

unlawful entry into a residence with the intent to unlawful entry into a residence with the intent to commit larceny or any felonycommit larceny or any felony12,690 burglaries between Jan 2000 12,690 burglaries between Jan 2000 –– Dec 2005Dec 2005geocodedgeocoded address locations and reporting dateaddress locations and reporting date3,951 repeat burglaries at the same addresses3,951 repeat burglaries at the same addresses

0

400

800

1200

0 500 1000 1500

number of repeats

waiting time to repeat burglary (days)

num

ber o

f rep

eats

most repeats very quick

Repeat VictimizationRepeat Victimization

Long Beach residential burglaries 2000-2005

patch foraging modelspatch foraging modelscurrencycurrency

assume offender wants to maximize return or payoff assume offender wants to maximize return or payoff per unit time spent in a patch OR minimize the travel per unit time spent in a patch OR minimize the travel times between patchestimes between patches

decision variablesdecision variableshow long to remain in a patchhow long to remain in a patchhow much time to dedicate to travel between patcheshow much time to dedicate to travel between patches

constraintsconstraintssize and/or quality of patchessize and/or quality of patchesspatial distribution of patchesspatial distribution of patchesquality of information about the environmentquality of information about the environment

g'(t)

marginal value theorem (MVT)marginal value theorem (MVT)

travel time trt* residence time

g(t)

net gain

ttt

g'(t)

optimal travel timeoptimal travel time

travel time trt

g(trt)

net gain

ttt* residence time

general burglary predictionsgeneral burglary predictions

trt

net gain

trtttt*ttt* residence time

larger takes from burglaries inone patch may translate intoa greater temporal (and/or spatial)lag to the next set of burglaries

anecdotal evidenceanecdotal evidence

most burglaries produce only most burglaries produce only small economic gains/losses, but small economic gains/losses, but happen very oftenhappen very often

major gains/losses are very rare major gains/losses are very rare eventsevents

burglars that travel further burglars that travel further (between patches) tend to net (between patches) tend to net greater returnsgreater returns

33% fewer burglaries, but median take 1.8 times larger

33--303012.812.8ResidentialResidential22--30.330.38.78.7CommercialCommercial

InterInter--quartile rangequartile rangeMedianMedianburglaries per monthburglaries per month

1,4671,467--13,04413,0443,5863,586ResidentialResidential3,2613,261--13,04413,0446,5226,522CommercialCommercial

InterInter--quartile rangequartile rangeMedianMedianburglary income per month (USD)burglary income per month (USD)

Stevenson, R. J., and L. M. V. Forsythe. 1998. The Stolen Goods Market in New South Wales. Sydney: NSW Bureau of Crime Statistics and Research.

individual house as a patchindividual house as a patch

quantitative expectations?quantitative expectations?

waiting time to a burglary at an individual house = the sum of all the time spent traveling between other patches (houses) and time spent burglarizing those other patches.

rnm

2D lattice model 2D lattice model –– sites sites rrnmnm

pm

simple random walksimple random walk

pn

qm

qn

pn = qn = pm = qm = .25

random walker will eventually visit every site in a 2D lattice an infinite number of times

br = 1

burglary probabilities burglary probabilities bbrr

waiting time between burglaries12 steps

probability distribution of first passageprobability distribution of first passage

21

1( , )ln

F r tA t t

=

0

0.25

0.5

0.75

1

0 10 20 30 40

return time (steps)

prob

abili

ty

a very high baseline probability that that site will be re-victimized within a short period of time

0

400

800

1200

0 500 1000 1500

number of repeats

waiting time to repeat burglary (days)

num

ber o

f rep

eats

n = 3951mean time = 297 days

stdev = 360 daysmax = 2073 days

Long Beach 459R&G 2000Long Beach 459R&G 2000--20052005

how does the model do?how does the model do?

50

100

0

150

0 10 20 30 40 50 60 70waiting/return time (days)

num

ber o

f re

turn

s theory

observed

point

bn+1bn-1 bn+2bn-2 bn

2/32/31/31/3

ρ = 1Neighborhood Risk Levels ρ

dn-2 dn-1 dn dn+1 dn+2

biased random walk based onbiased random walk based onattractive & repulsive forcesattractive & repulsive forces

0

0.01

0.02

0.03

0.04

0.05

0 100 200 300 400 500

time (steps)

prob

abili

ty

1attractive forcetT

r rb e b−

= +

0

0.01

0.02

0.03

0.04

0.05

0 100 200 300 400 500

time (steps)

prob

abili

ty

2repulsive forcetT

r rd e d−

= +

0.00

0.01

0.02

0.03

0.04

0.05

0 100 200 300 400 500

time (steps)

prob

abili

ty

1 2burglary probabilityt tT T

r r r rb e d e b d− −

= − + −

emergent crime patternsemergent crime patterns

0

0.025

0.05

0.075

0 20 40 60 80 100

time (steps)

prop

ortio

n of

ret

urns

analytical model F(r,t)

simulation

deterrent effect has to be fairly large relative to the attractive effect immediate following a burglary

random walk model & the MVTrandom walk model & the MVT

net gain

g(t)

travel time t1*t3* t2*

all travel times between patchesare equally optimal!

residence time

return from crime is fixed & burglar is obliged to leave

biased walk model & the MVTbiased walk model & the MVT

net gain

burglary probability

travel time residence timet1*

crime prevention implicationscrime prevention implications

close attention to the spatial and temporal close attention to the spatial and temporal nature of repeat burglaries has been used nature of repeat burglaries has been used successfully to apprehend serial burglarssuccessfully to apprehend serial burglarsthe same ideas are also central to the operation the same ideas are also central to the operation of hotspot policingof hotspot policing——targeting areas previously targeting areas previously victimized for steppedvictimized for stepped--up police activity is up police activity is premised on the fact that offenders will likely premised on the fact that offenders will likely repeat (in the same places) what has worked for repeat (in the same places) what has worked for them in the pastthem in the past

the causes of repeat victimization may be many, the causes of repeat victimization may be many, but foraging theory suggests thatbut foraging theory suggests that

small gains or returns from burglaries or other small gains or returns from burglaries or other crimes will tend to lead to repeat offenses that occur crimes will tend to lead to repeat offenses that occur close in space and timeclose in space and time

the the ““decaydecay--likelike”” character of the distribution of character of the distribution of burglary waiting times may reflect simple constraints burglary waiting times may reflect simple constraints on movement around in a 2D world with some on movement around in a 2D world with some contributions from deterrent & attractive effectscontributions from deterrent & attractive effects