A Model of Contagion Through Competition

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Journal of Abnormal Child Psychology, Vol. 33, No. 3, June 2005, pp. 283292 ( C2005)

DOI: 10.1007/s10802-005-3565-5

A Model of Contagion Through Competition

in the Aggressive Behaviors of Elementary School Students

Keith Warren,1,5 Susan Schoppelrey,2 D. Paul Moberg,3 and Marilyn McDonald4

Received January 13, 2004; revision received July 15, 2004; accepted August 25, 2004

This article extends the work of Kellam, Ling, Merisca, Brown and Ialongo (1998) by applying a

mathematical model of competition between children to peer contagion in the aggressive behaviors of

elementary school students. Nonlinearity in the relationship between group aggression and individual

aggression at 2-year follow-up is present. Consistent with the findings of Kellam et al. (1998),

hierarchical linear modeling indicates that the relationship is statistically significant for those students

whose initial parental ratings of aggressive behavior were above the sample median. In the contextof competition between students, the behavior of initially aggressive students may be negatively

reinforced. Lowering aggression in the school environment may therefore be the most effective way

to lower the level of these students aggressive behavior.

KEY WORDS: aggressive behavior; ecological psychology; elementary school; students; peers; red queenmodel.

The last decade has seen an increased interest in

peer contagion as a factor in the aggressive and delin-

quent behaviors of children in elementary and middle

school (Anderson, 1999; Dishion, McCord, & Poulin,

1999; Dishion, Poulin, & Burraston, 2001; Ialongo,

Poduska, Werthamer, & Kellam, 2001; Ialongo et al.,1999; Kellam, Ling, Merisca, Brown, & Ialongo, 1998;

Patterson, Dishion, & Yoerger, 2000; Snyder, Horsch, &

Childs, 1997). Peer contagion is of both theoretical and

pragmatic interest, since a better understanding of the dy-

namics of the spread of aggressive behavior could guide

the design of programs that aim to attenuate the effects of

an aggressiveenvironment (Ialongo, Poduska, Werthamer,

& Kellam, 2001).

A persistent finding in the peer contagion literature

is that aggregation with peers who display aggressive

1

College of Social Work, The Ohio State University, Columbus, Ohio.2School of Social Work, University of Illinois at Urbana-Champaign,

Urbana, Illinois.3Department of Population Health Sciences, University of Wisconsin-

Madison, Madison, Wisconsin.4Wisconsin Center for Educational Research, University of Wisconsin-

Madison.5Address allcorrespondenceto Keith Warren, TheOhio StateUniversity,

College of Social Work, Stillman Hall 325Q, 1947 College Road,

Columbus, Ohio 43210; e-mail: [email protected].

and delinquent behavior is particularly problematic for

children who are themselves at risk for aggressive and

delinquent behavior (Dishion et al., 1999; Kellam et al.,

1999). This finding even extends to very young children.

In their study of first-grade children exposed to classroom

aggression, Kellam et al. (1999) found an interaction ef-fect in which exposure to aggressive classrooms lead to

increased aggression in middle school in the most aggres-

sive elementary school children, but had little effect on

others. Snyder et al. (1997) found that preschool children

who associated with aggressive peers at school were likely

to show increased aggression 3 months later.

Why does exposure to aggressive peers worsen the

behavior of those children who already behave aggres-

sively? One possibility lies within the model developed by

researchers at the University of Oregon, which suggests

that aggressive children aggregate into peer groups that

positively reinforce aggressive and delinquent behavior

(Dishion et al., 2001; Reid, Patterson, & Snyder, 2002).Kellam et al. (1999, p. 183) seem to take this position,sug-

gesting that, . . . the experience of the aggressive child

in aggressive first grade classrooms sets the pattern of

the childs behavioral responses . . . as well as member-

ship in poor behaving peer groups and lack of attach-

ment to school. On the other hand, Snyder et al. (1997,

p. 154) observe that, Disagreeable, coercive behavior

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284 Warren, Schoppelrey, Moberg, and McDonald

characteristic of the aggressive childs repertoire evoked a

reciprocal response from peers . . . This raises the possi-

bility that peer contagion might occur through reciprocal

negative reinforcement.

This article will replicate the work of Kellam et al.

(1998), using a hierarchical model to test the hypothe-

sis that the level of aggressive behaviors in classroom-grouped children will predict the childrens individual ag-

gressive behaviors outside the classroom at a 2-year time

lag. Itwillalso extend thatworkby describing a model that

suggests that peer contagion through competition leads to

increases in the aggressive behavior of elementary school

students.

A Competitive Model of Peer Contagion

Studies of the aggressive behaviors of elementary

school and preschool children suggest that aggressive

behavior is functional when a child is confronted with

aggressive peers. A number of studies have found that

children as young as preschoolers reciprocate aggressive

behavior, even when they are not themselves initially

aggressive (Hall & Cairns, 1984; Patterson, Littman, &

Bricker, 1967; Reid et al., 2002; Snyder & Brown, 1983).

Reciprocation of aggression is likely to terminate an

aggressive event (Patterson et al., 1967; Reid et al., 2002;

Snyder & Brown, 1983). This termination then acts as

a negative reinforcement for aggressive behavior (Reid

et al., 2002). For instance, Patterson et al. (1967) found

that preschool children who were frequently victimized

became more aggressive over time if their aggression was

successful in warding off bullies. Coie, Dodge, Terry,and Wright (1991) suggest that, because aggressive boys

are less likely to submit to bullying than those who are

not aggressive, they may make less-attractive targets for

bullies.

Children in inner-city neighborhoods are especially

likely to be exposed to aggressive peers. Anderson (1994,

1999) has given a vivid account of reciprocal aggression

in these neighborhoods. He argues that the residents of

inner-city neighborhoods sometimes develop a code of

the street, which emphasizes willingness to resort to ag-

gressive behavior as a means of gaining respect. Respect

is valuable, since aggressors are unlikely to victimize a

respected individual (Anderson, 1999).Consonant with the findings of developmental psy-

chologists, Anderson notes that willingness to resort to

aggressive behavior begins among young children. He

reports, Even small children test one another, pushing

and shoving, and are ready to hit other children over

circumstances not to their liking. In turn, they are read-

ily hit by other children, and the child who is toughest

prevails . . . Thechild in effect is initiatedinto a systemthat

is really a way of campaigning for respect (Anderson,

1994, p. 86). Such competition occurs in schools as well

as outside of them (Anderson, 1999).

Ones ability to defend oneself can only be judged

in context, against likely aggressors. Respect is therefore

fragile, and dependent on comparison to ones peers. An-derson writes that, In this often violent give-and-take,

raising oneself up largely depends on putting someone

else down (1994, p. 75). If peers gain respect by being

tougher or more aggressive, a child has to become tougher

or more aggressive him or herself in order to maintain

respect.

In such a competitive situation, children are not so

much seeking each others approval as seeking to meet

each others threats. The relationship between exposure

to aggressive peers in the classroom and aggressive be-

havior in other settings is expected to be nonlinear. In

less-aggressive classrooms, a loss of respect is less likely

to result in victimization. When classroom aggressionreaches the point where the relationship between loss of

respect and increased victimization is clear to the stu-

dents, competition will increase sharply. At this point, the

ability to ward off others will become a powerful nega-

tive reinforcement that would be expected to strengthen

childrens willingness to engage in aggressive behavior

(Bandura, 1977, 1983; Reid et al. 2002).

Most competitive models in social science assume

two or three competitors (Boulding, 1962). Such mod-

els are not appropriate for a situation in which multiple

children are competing against each other in the same

classroom. On the other hand, evolutionary models as-sume competition between multiple individuals, species

or groups (Vermeij, 1994). This article will apply a model

of competition between multiple agents drawn from evo-

lutionary biology, known as the Red Queen Model. First

proposed by van Valen (1973), the Red Queen posits an

evolutionary competition in which each species contin-

ually adapts to changes in the fitness of all others. The

parallel with Andersons account of inner-city children is

straightforward; each child must continually adapt to all

others in order to maintain respect.

Maynard Smith (1976) has published a closer look

at the mathematics of the model and pointed out that it

does not necessarily imply ruthless competition. Rather, itcan yield either high or low competition, with a nonlinear

tipping point between the two regimes. The relationship

between the average level of aggression in the classroom

and aggression outside the classroom will be flat in the

low-aggression classrooms, with a slope approximating

zero, and positive in the high-aggression classrooms. This

nonlinearity should be apparent in a statistical analysis.


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Contagion Through Competition 285

A more complete discussion of themathematics of the Red

Queen Model can be found in the appendix to this article.

Bandura (1977) has argued that association, the

opportunity for practice, and motivation all facilitate

learning and generalizing a behavior. All of these require-

ments for learning and generalizing aggressive behavior

are present in the high-competition regime. As thegroup level of aggressive behavior increases, children by

definition associate with more highly aggressive children;

it then becomes increasingly important to practice some

levelof aggressive behavior so that one will not be targeted

and the negative reinforcement for aggressive behavior

avoiding victimizationbecomes a more powerful

motivator. Thus, it seems likely that the high-competition

regime, characterized by increased aggression on the

group level, will lead to the generalization of aggressive

behavior outside the classroom. In Andersons phrase, the

school becomes a staging area for the streets (Anderson,

1999). It was therefore hypothesized that there would

be a positive relationship between group aggression asmeasured in the classroom and individual aggression as

measured outside the classroom, but that such a relation-

ship would exist only at higher levels of aggression.

METHODS

The data for this study were collected as part of an

evaluation of the Families and Schools Together (FAST)

program. FASTis a programfor thefamiliesof elementary

school children, aimed at improving family communica-

tion and social support, in which 812 families meet in a

group setting weekly over an 8-week period, and once a

month over the next 2 years, a follow-up period known as

FASTWORKS (McDonald et al., 1997).

Design

The evaluation took place in 10 inner-city elementary

schools in Milwaukee, Wisconsin (Moberg, McDonald,

Burke, & Brown, 2002). The children in each school

were drawn from the surrounding neighborhood, and the

assignment of children to classrooms followed standard

procedures in each school. The researchers had no influ-

ence over the assignment of the children. Second- andthird-grade classrooms within each school were then cho-

sen and randomly assigned to either FAST or a control

condition in which written materials on parenting were

mailed to families. Investigators entitled the control con-

dition Family Education (FAME). Once a classroom had

been assigned to a condition, families were recruited to

participate in the evaluation. Recruitment was universal,

but participation was not; the number of families in any

given classroom who participated varied from 116. If

an insufficient number of families volunteered after the

initial assignment, further classrooms were drawn and

randomly assigned. Thus, the final sample included first-

through fourth-grade classrooms. Results of the compari-

son between the two interventions have been discussed inprevious and forthcoming articles and presentations and

will not be detailed in this article (Moberg et al., 2002;

Moberg, McDonald, Posner, Burke, & Brown, 2004;

Warren, Moberg, & McDonald, 2004).

Participants and Context

For the current study, all classroom groups in which

fewer than four families participated were removed from

the data set regardless of random assignment to FAST or

FAME, leaving a total of 59 groups. The 10 schools in the

study served low-income populations; in seven of themover 90% of the students qualified for free or reduced

lunch prices, and in all of them over 60% qualified. The

overall mobility of students in each school, as measured by

the percentage of students who left the school during the

year, varied from 15 to 47%. Sixty-seven percent of the

participating families reported incomes below $20,000,

and 84% reported incomes below $30,000. Fifty-three

percent of the parents reported that they were unmar-

ried. Forty-five percent of the students in the study were

African-American, 38% were Latino/Latina; with the re-

mainder predominantly European-American. Forty-four

percent of the students were male and 56% were female.

Twenty-one percent of the students were in first grade atthe beginning of the study, 33% in second grade, 40% in

third grade, and 5% in fourth grade.

Participant Attrition

The longitudinal design of the study and the high

mobility of the sample meant that a large number of

participants eventually dropped out; of the 444 students

who participated at the time of the pretest, only 334,

or 75.2%, were still participating at the 2-year follow-

up. Exploratory analysis with the aim of finding predic-

tors of attrition revealed only one statistically significantpredictor, ethnicity ( 2 = 22.86, p < .0001); African-

American families were more likely to leave the study

than other families. Because the parents of several stu-

dents refused to answer demographic questions such as

ethnicity or marital status, the final number of participants

available for the current study was 331, or 74.5% of those

who participated in the pretest.


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Measures and Covariates

Teachers and parents reported data on the childrens

behavior. Parents rated their children on aggressive be-

haviors using the Achenbach Child Behavior Checklist

(CBCL) (Achenbach & McConaughy, 1997) in research

interviews at pretest, 8 weeks later at posttest, and at 1-and 2-year follow-up. Teachers completed paper and pen-

cil ratings of participating childrens aggressive behaviors

using the Teachers Report Form (TRF) of the CBCL at

pretest, posttest, and 2-year follow-up. Group aggression

was calculated by taking the average of the teacher rated

aggressive behavior raw scores of all the children in each

group at the time of the posttest. It was assumed that this

mean reflected aggressive behavior in the classroom envi-

ronment. Teachers posttest scores were used to construct

the group-level aggression variable because parent and

teacher pretest scores were gathered over the same time

period, with parent scores sometimes being gathered later

than teacher scores. Since our hypothesis was that group-level aggressive behavior would predict parental ratings

of individual aggressive behavior, using the group average

teacher rating and the parent rating at pretest would have

amounted to including an earlier version of the dependent

variable as a covariate for some children, leading to an

endogeneity problem (Greene, 2000). On the other hand,

it was known that the parents pretest scores of childrens

aggressive behavior predated the teachers posttest scores.

The initial parent ratings could therefore not have been in-

fluenced by the later group-level ratings. The mean level

of raw score group aggression was 6.4 on the TRF (SD =

4.21, range = 19.8).The dependent variable was the parental rating of

the individual childs level of aggression at 2-year follow-

up. This variable was positively skewed and kurtotic

(skew = 1.43, SE= .13; kurtosis = 1.81, SE= .27), and

thus statistical analysis using a hierarchical linear model

could lead to a biased estimate. The variable was therefore

dichotomized at the median (Kellam et al., 1998).

Since participation in the study was voluntary, ran-

domization of classrooms would not necessarily control

for selection bias that could, in turn, lead to a spurious

group-level aggression effect (Manski, 2000). The analy-

sis, therefore, controlled for five individual-level variables

that might reflect selection bias. Three of thesegender,ethnicity and parent rating of aggression at pretestmight

reflect selection bias if children volunteered with their

friends and chose their friends along these lines. As men-

tioned, parent rating of aggression at pretest, rather than

at posttest, was used since it predated group ratings at

posttest and therefore could not have been influenced by

them. Initial parent rating of aggression was dichotomized

at the median. Collinearity precluded separate dummy

variables for Latino/Latinas and African-Americans, so

ethnicity was treated as a dummy variable in which the

numberone indicated African-American families and zero

indicated European-American or Latino/Latina families.

The analysis also controlled for the grade level of chil-

dren at pretest. Finally, the analysis controlled for maritalstatus of parents, on the grounds that this might influence

the propensity of parents to volunteer for the study.

On the group level, the analysis controlled for the

percentage of children in each school on free and reduced

cost lunches as a proxy variable for the poverty level

of the school, along with the mobility of children in the

school, both variables that could affect the individual level

of aggressive behavior and therefore mimic the effects

of peer contagion (Kellam et al., 1998; Manski, 2000).

Descriptive statistics for the continuous variables before

transformation are given in Table I.

Analysis

Because of the nested nature of the data, a hierar-

chical linear model was used for the present analyses

(Raudenbush & Bryk, 2002). The use of a hierarchical

model controls for the effect of differing sizes of groups

and the possibility that the predictive value of group ag-

gression simply reflects the correlation of individual levels

of aggression (Raudenbusch & Bryk, 2002). Thegroups of

children were also nested into schools, but the small num-

ber of schools (n = 10) did not allow the inclusion of this

third level in the model. The model therefore included two

levels, individuals and classroom-derived groups. Giventhat the dependent variable was dichotomous, the model

utilized a logistic link function.

A simple test for the presence of nonlinearity, as

suggested by Lemeshow (2001), was run. In this test, a

Table I. Descriptive Statistics for Continuous Variables Before

Transformation

Standard

Variable Mean deviation Median Range

Group-level variables

Teacher rating of group 6.39 4.21 6 19.8

aggression (posttest)% free or reduced lunch 89.1 9.8 93 32

% students changed schools 29.6 8.7 28 32

Individual-level variables

Parent rating of 10.48 8.32 9 40

aggression (pretest)

Parent rating of aggression 7.26 7.54 5 37

(2-year follow-up)


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hierarchical logistic regression model using 01 dummy

variables delineating the second, third and fourth quar-

tiles were entered in place of the mean group aggression

variable. The log odds ratio coefficients that each quar-

tile yielded were then graphed against the midpoints of

each quartile as a test for nonlinearity. If the relationship

between initial group aggression and parent-rated aggres-sion at 2-year follow-up is nonlinear, such a graph should

indicate a tipping point (Lemeshow, 2001). Below this

point the relationship should be zero, and above it the

relationship should be positive.

The initial analysis was carried out on the entire

data set. The set was then subdivided into two parts, one

for those children whose pretest parent rating of aggres-

sion was equal to or below the median and one for those

whose pretest parent rating was above the median. This

division reflects the interaction between initially high- and

low-aggression children and aggressive peers reported by

Kellam et al. (1998).

RESULTS

Full Sample

The initial model included all children in the sample,

regardless of their initial level of aggressiveness as indi-

cated by parental ratings at pretest. The results of the test

for nonlinearity in the relationship between teacher-rated

group aggression and parent-rated individual aggression

at 2-year follow-up are illustrated in Fig. 1. As expected,

the relationship is virtually zero at low levels of groupaggression and positive at high levels. This is important

in the context of the current study; if the dummy variable

for the second or third quartile yielded a log odds ratio

that was higher than that for the fourth quartile, this would

falsify the hypothesized competitive relationship. Given

that there are limits to the level of aggressive behavior

Fig. 1. Scatterplot of group aggression quartile midpoints versus log

odds ratios: Full Sample.

Table II. Predictors of Parent Ratings of Aggression at 2-Year

Follow-Up: Full Sample

Log odds Standard

Variable ratio error t-value Probability

Group-level effects

Intercept 1.302 0.476 2.734 .009

Free lunch 0.010 0.017 0.583 .562

Student mobility 0.031 0.021 1.495 .140

Group aggressiona 0.090 0.032 2.819 .007

Individual-level effects

Initial grade level 0.165 0.152 1.087 .277

Ethnicity 1.924 0.346 5.546


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Subsample Analyses

In order to further examine the effect of a childs

initial level of aggression on the observed relationship

between group aggression and individual aggression at

follow-up, the sample was split into two subsamples.

The low-aggression subsample included those studentswhose initial parental ratings of aggression were at or

below the median and the high-aggression subsample

included children with scores above the median. The re-

sults of the test for nonlinearity in the relationship be-

tween group aggression and parental rating of individual

aggression at 2-year follow-up are given in Fig. 2. Again,

the relationship is flat at low levels of group aggression

and positive at high levels. This is true for both groups, but

the incline is steeper for children with initially high levels

of aggression. All values of group aggression below the

median were set to zero to reflect this nonlinearity, and

the model was then run separately for the higher- and

lower-aggression students.The results of the first subsample analysis, for

those students with initially lower ratings of aggression,

are presented in Table III. An immediately striking

difference is that group aggression as a predictor of

parental ratings of individual aggression now falls short

of statistical significance (t= 1.367, p = .178). This

lack of statistical significance is not entirely explained by

the erosion of statistical power that comes with dividing

a data set; although the standard error is inevitably higher

in this model, the maximum likelihood estimate of the log

odds ratio for this variable is lower for the initially less-

aggressive students than for the sample as a whole (0.06vs. 0.09). These students appear to react less strongly

to aggressive environments than the initially more-

aggressive students. Another notable difference between

this model and the full sample model is that the mobility

of students in the school as a whole is a statistically

significant predictor of parental ratings of student aggres-

sion (t= 2.589, p = .013). The negative direction of

Fig. 2. Scatterplot of group aggression quartile midpoints versus log

odds ratios: Sample split by initial level of group aggression.

Table III. Predictors of Parent Ratings of Aggression at Follow-Up:

Students with Initial Levels of Aggression Below the Median

Log odds Standard

Variable ratio error t-value Probability

Group-level effects

Intercept 0.933 0.709 1.309 .197

Free lunch 0.007 0.026 0.289 .774

Student mobility 0.086 0.033 2.589 .013

Group aggressiona 0.064 0.046 1.367 .178

Individual-level effects

Initial grade level 0.459 0.257 1.786 .074

Ethnicity 2.231 0.523 4.239


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mobility, predicts parental ratings of aggressive behav-

ior. Among the individual-level variables, only ethnicity

(t= 3.679, p < .001) predicts parental ratings of student

aggression.

DISCUSSION

Summary of Findings

This study analyzed the relationship between teach-

ers ratings of aggressive behavior aggregated to the group

level and parents ratings of individual level of aggressive

behavior 2 years later, using a hierarchical logistic model

and a sample of 331 inner-city elementary school students.

In the sample as a whole, group aggression, independent

of individual aggression, predicted parental ratings of ag-

gressive behavior 2 years later. The relationship was flat

at low levels of group aggression and positive above the

median, consistent with the hypothesis that competitivedynamics lie behind peer contagion in this sample.

When the sample was broken down into subsets of

children whose initial parental rating of aggressive be-

havior was above and below the median, group aggres-

sion significantly predicted parental rating of aggressive

behavior 2 years later only for those children whose ini-

tial parental rating of aggressive behavior was above the

median. This interaction between the students initial lev-

els of aggressive behavior and the level of aggression in

their environment is similar to the results of Kellam et al.

(1998), and Dishion et al. (1999).

Limitations

Because participation in this study was voluntary, it

is possible that selection bias led to aggregation of ag-

gressive children, which in turn would have led to a group

mean that did not reflect the level of aggressive behavior in

the classroom. The model controlled for five individual-

level variables that might reflect selection biasinitial

grade of the students, gender, ethnicity, parents rating of

aggressive behavior at pretest, and parent marital status.

The inclusion of these variables in the model did not al-

ter the statistical significance of group-level aggression

as a predictor. As previous research has found, two ofthese variables, parents rating of aggressive behavior at

pretest and ethnicity, were statistically significant predic-

tors (Eamon & Altshuler, 2004; Loeber & Stouthamer-

Loeber, 1998). The consistency of ethnicity as a predictor

of aggressive behavior in all models may reflect the struc-

ture of the Achenbach parent and teacher scales, which

include verbal behaviors (Achenbach & McConaughy,

1997). These may vary between ethnic groups. There was

no statistically significant effect of gender; this may re-

flect either a narrowing of the gap in physical aggression

between boys and girls (Anderson, 1999), or the struc-

ture of the CBCL. The only variable related to differential

study attrition was ethnicity ( 2 = 22.86, p < .0001), for

which the present analyses control.The inclusion of two group-level variables, percent-

age of students who received free and reduced lunches

a proxy variable for the overall level of poverty in the

schoolsand student mobility did not alter the signifi-

cance of group-level aggression as a predictor variable.

This is consonant with the previous findings of Kellam

et al. (1998), who found that aggression in first-grade

classrooms predicted individual aggression into middle

school independent of the poverty level of the classroom.

This finding strongly suggests that the significance of

group-level aggression as a predictor of later aggression at

the individual leveldoes not simply represent an artifact of

a shared social environment of the children in the sample.Rather, it can be attributed to the classroom environment

(Manski, 2000).

Implications

The results of this study replicate the findings of

Kellam et al. (1998) and are evocative of recent studies of

delinquent behavior in middle school students (Dishion

et al., 1999, 2001). The current study extends earlier find-

ings in important ways. The use of a hierarchical model,

which Kellam et al. (1998) did not use, makes it clear that

the relationship between group aggressive behavior andparental ratings of individual aggressive behavior is not

simply a statistical artifact (Abelson, 1995; Raudenbush

& Bryk, 2002).

The use of parental ratings of aggressive behavior at

2-year follow-up, rather than teacher ratings, shows that

aggressive behavior learned in group settings spills over

into very different settings. Perry, Perry, and Rasmussen

(1986) found that aggressive children believe that aggres-

sion will reduce the amount of aversive treatment that they

receive from others; in other words, they overestimate the

functionality of their aggressive behavior. Such an effect

may explain the relationship found in these data.

The most important way in which this study extendsearlier work is through the model of competition between

the students. The model implies not only a relationship

between group and individual aggressive behavior, but a

particular form that the relationship will take. It therefore

allows a more detailed view of the relationship.

An examination of Fig. 2 shows that, although the

relationship between group and individual aggressive


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behavior is only statistically significant for those chil-

dren who were initially above the median in aggressive

behavior, the form of both relationships is identicala

slight decline between the first and the second quartile fol-

lowed by a rise between the second and fourth quartiles.

The tipping point for both groups is fairly low, lending

further empirical support to researchers who claim thatrelatively low levels of aggression in school settings are

cause for concern (Boxer et al., 2003). The difference in

the graph parallels the difference in statistical significance

between the initially more- and less-aggressive children,

represented by a difference in the slope of the increase

in parental ratings of individual aggression between the

second and the fourth quartiles of group aggression. That

slope is .148 for the initially more-aggressive children

and .064 for the initially less-aggressive children. This

suggests that initially more- and less-aggressive children

are not reacting in fundamentally different ways to ag-

gressive environments. Rather, they are reacting with dif-

ferent intensities. The initially more-aggressive childrenreact more strongly. This may be the result of the increased

sensitivity to threats of aggression that aggressive children

possess (Coie et al., 1991).

The similarity of the two graphs throws a differ-

ent light on the behaviors of highly aggressive children.

The literature on aggressive behavior in children typically

sees such behavior as dysfunctional and in need of re-

mediation (Reid, Patterson, & Snyder, 2002). Of course,

from the point of view of parents, teachers, the childrens

peers, and the childrens own long-run well-being, that

view is entirely correct. Seen from a different viewpoint,

however, that behavior may appear to be functional. Thenonlinearity that occurs in this data is consistent with an

increase in aggressive behavior arising from competition.

The initially more-aggressive children are more likely to

learn aggressive behavior in response to aggressive peers.

Placed in a broader social context, this is problematic.

But placed in the context of their immediate peer envi-

ronment, they are the quick learners. They are winning

the competition. Coie et al. (1991) have surmised that ag-

gressive children demonstrate cognitive biases that favor

aggressive behavior as the result of earlier life experience.

This line of reasoning raises the possibility that these ex-

periences may have involved interaction with aggressive

classroom peers.This analysis suggests that before assuming that ag-

gressive behavior in inner-city elementary school children

is a clinical problem amenable to clinical solutions, we

should seriously consider the overall level of aggressive

behavior in their school environment. Competition will

produce large numbers of children whose behavior, al-

though well adapted to that of their peers, may be quite

aggressive by the standards of other peer groups. It is

likely to be prohibitively expensive to treat these children

one at a time.

Moreover, if individual aggressive behavior is a re-

sponse to a competitive and aggressive peer environ-

ment, clinical intervention with an aggressive elemen-

tary school child is likely to produce only short-termchange. To produce lasting change, it is necessary to cre-

ate a peer environment in which competition does not

lead to the negative reinforcement of aggressive behav-

ior. There are a number of different programs that aim

to change the peer environment in schools, and there

is increasing evidence of the effectiveness of such pro-

grams (Erickson, Mattaini, & McGuire, 2004). The cur-

rent study suggests that the theory behind such programs is

sound.

CONCLUSION

The current study would benefit from replication us-

ing data from entire classrooms. Although this study has

identified a nonlinear effect that is consistent with pre-

vious work and with a model of peer contagion through

competition, it did not directly measure the mechanisms of

such competition. Further observation of peer interactions

among elementary school students, with an eye toward

identifying mechanisms related to the negative reinforce-

ment of aggressive behaviors, would be of value in con-

firming this model. This is the first empirical application

of a model of evolutionary competition to the aggressive

behaviors of inner-city elementary school students. Evo-

lutionary theory offers a possible way of connecting socialscience with other sciences (Wilson, 1998), but many evo-

lutionary theorists have taken a narrow and static view of

evolutionary theory, seeing it as a way of establishing the

innate limitations on human rationality and social behav-

ior (Scher & Rauscher,2003). Evolutionary models are far

richer than this; ultimately, they are dynamic models of

conflict, competition and even cooperation which promise

to shed light on many social situations (Vermeij, 1994;

Wilson, 2002).

APPENDIX: THE RED QUEEN MODEL AND

AGGRESSIVE BEHAVIOR AMONG CHILDREN

Maynard Smiths (1976) equation for the Red Queen

Model is as follows:

Li =

ijgL gLi (1)

In the left-hand term of this equation, is simply the

change in a value of Li , which is the lag in fitness


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between a species and its competitors, or between a

child and his or her classmates. Fitness is relative to

the fitness of possible competitors, as it is in Andersons

(1994, 1999) account (see also Vermeij, 1994). For the

child, it is clear from Andersons account that fitness is

measured in respect. When Li is growingi.e., when

Li is positivethe lag between the childs ability togarner respect and that of his classmates is growing.

The child is then at increasing risk of being bullied or

assaulted.

There are two factors affecting the increase or de-

crease of Li ; these are the two terms on the right-hand

side of the equation. The first term,

ijgLi , isthe more

complex of the two. The term is the sum of the effect of

increases in fitness that individual classmates have vis-a-

vis a child, as measured by the respect that they can garner.

In this term, ij determines how much a unit change in

the respect that another child j has gained affects the lag

in respect between child i and other children. It is a mea-

sure of the competitiveness of the childs environment, inthis case his or her classroom. If ij is greater than one,

any increase in the comparative respect that his or her

classmates possess more than proportionately increases

the lag in respect between the child and those classmates.

If ij is less than one, any increase in classmates com-

parative respect brings about less than a proportional de-

crease in the lag in respect between the child and those

classmates.

The second term, gLi , is a measure of any increase

in the childs ability to maintain respect. Any increase

in respect that classmates have for a child decreases

the lag in respect between him/herself and classmates.Thus, the term is subtracted from the first right-hand

term.

Thus, ij will divide classrooms into two categories,

the highly competitive and the less competitive. Children

in the highly competitive classrooms will be forced to

compete themselves or forfeit respect in a competitive

environment, where they need it the most. What deter-

mines ij? Andersons account suggests that the level of

aggression in the classroom will be the determining factor.

That is,

ij = f(classroom aggression) (2)

A loss of respect is far more likely to lead to victimizationin highly aggressive classrooms than in less-aggressive

classrooms. Since victimization will cause the children to

lose more respect, the lag between children and their peers

will increase more rapidly in highly aggressive class-

rooms. In highly aggressive classrooms, children should

therefore be more likely to respond with aggressive be-

havior in kind.

ACKNOWLEDGMENTS

This research was partially supported by the National

Institute on Drug Abuse grant #R01-DA-10067. The au-

thors would like to thank Dawn Anderson-Butcher of The

Ohio State University College of Social Work and two

anonymous reviewers for helpful comments.

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A Model of Contagion Through Competition