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Population Modeling to Estimate Norway 

Rat Infestations in Urban Areas

Alex Francisco, Michele Buonanduci, and Carolyn Meyer

ARCADIS U.S., Inc.

Exposure Modeling Public Meeting

United States Environmental Protection Agency

Washington, DC

October 28, 2014
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Overview

• Why population models?

• Population modeling case-study

• Results

• Conclusions
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• Workshop publication forthcoming, 

recommends models should:

− Provide quantitative risk estimates

− Incorporate realistic variability in 

environmental and demographic factors 

− Integrate complex patterns of exposure 

and effects 

− Use baseline conditions that include 

present factors that have caused the 

species to be listed (e.g., habitat loss, 

invasive species) or have resulted in 

positive management action

• Rodenticide model is an example of such 

a model.

Forum evaluating population 

models for pesticide effects on 

Endangered Species
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Why Population Models?

Greater emphasis on moving from risk quotient methods 

toward higher-tier probabilistic and population-level risk 

assessments

Risk Quotient Methods Population Models

• Scaled to the individual

• Do not represent a doseresponse relationship to 

evaluate effects

• Have minimal predictive 

ability for responses in 

population dynamics

• Focus on endpoints important to 

populations (e.g., extinction risk, 

population size, growth rates)

• Include dose response relationships to 

establish magnitude of effects

• Can be developed to evaluate threatened 

and endangered species without using 

subjective uncertainty factors
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• Specifically evaluate endpoints 

important to population dynamics (e.g., 

population size and recovery time) 

• Explicitly address toxicity doseresponse relationships

• Include density-dependent 

relationships that may change 

population dynamics responses to 

toxicity

• Include metapopulation dynamics that 

occur across geography and/or habitat

Population Modeling 

Advantages
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Rodenticide Efficacy as Case-Study

• Warfarin efficacy expected to be lower than bromethalin

• Norway rats develop warfarin resistance

• Reduced efficacy could lead to commensal rat infestation 

increases

• Could increase human-health risks and economic costs.

* Bromethalin efficacy assumed due to limited data in literature. Actual efficacy may be less than 100%.

Active Ingredient Reduction in Rats After Two Weeks 

(Standard Bait Presentation)

Reduction in Rats After Two Weeks 

(Tamper Resistant Station)

Bromethalin* 100% 100%

Warfarin (non-resistant) 90% 60%

Warfarin (resistant) 50% 20%
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• Estimate infestation rate changes over 

six weeks for commensal populations 

based on efficacy differences 

• Incorporate two rodenticide use 

scenarios:

• Incorporate warfarin resistance: 20% and 

75% population resistance across U.S.

− Estimates based on range of resistance 

observed in U.S. populations of mice and 

rats (Kohn 2014)

Modeling 

Objectives

Scenario Bromethalin Warfarin

1 75% 25%

2 25% 75%
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Model Basis

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0 0 0

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• Leslie Matrix Metapopulation 

Viability Analysis Model

− Age structured

− Birth flow

− Bi-weekly time steps

− Included density dependence and 

demographic stochasticity

• Commensal population in a city 

block of 20 housing units

− Assumed 33% dispersal between 

units

• Constructed in RAMAS 

Metapop v5.0
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Vital Rates

• Estimated average vital 

rates from literature for 

near stable populations 

• 1:1 sex ratio assumed

• Selected carrying capacity 

of each housing unit as 6 

rats (i.e., 3 females)

• Bi-weekly per capita 

geometric growth rate 

maximum (max) equal to 

1.15

Age at Sexual

Maturity (Weeks)

12

Litters Per 

Two Weeks

0.196

12-20 

Weeks

21-40 

Weeks

41-73 

Weeks

74+ 

Weeks

Proportion Females Pregnant

0.235 0.299 0.325 0.636

Litter Size

8.9 11.1 11.4 10.4

Fecundity (Bi-weekly)

0.205 0.325 0.362 0.649

Bi-weekly Survival

Juvenile

0.896

Adult

0.856
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Birth Flow Leslie Matrix

• Birth-flow Leslie matrix values 

calculated from estimated vital 

rates

• Fecundity adjusted for density 

dependence and for a  of 1.00 

are shown:

Fecundity

0-9 Weeks 0.000

10-11 Weeks 0.108

12-17 Weeks 0.235

18-19 Weeks 0.298

20-37 Weeks 0.372

38-39 Weeks 0.392

40-71 Weeks 0.414

72-73 Weeks 0.566

74+ Weeks 0.743

Survival

0-1 Weeks 0.896

2-3 Weeks 0.877

4-74+ Weeks 0.856
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Density-Dependence affects Fecundity 

and Population Growth Rate ()
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Model Calibration

• Calibrated model to observed trajectory in 

literature

• Revised efficacy application to a group of 

housing units rather than single units

• Staggered rodenticide applications among first 

three time steps

• Adjusted max from 1.15 to 1.17

• Added outside immigration source of 0.5 female 

rats per bi-weekly time step
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Model Calibration (continued)

• Observed trajectories generally fell within 

+/- 1 standard deviation of the average 

results in calibrated models.
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Results
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Modeling Endpoints

• Change in infestation days per household

− Infestation days = number of rats * days of infestation 

in six weeks

• Extrapolated total change in U.S. infestation days 

− Estimated number of housing units with rat infestations 

from American Housing Survey (2011)

− Estimated percent of housing units applying 

rodenticides (IRI 2012)

− Multiplied per-unit infestation days by number of 

housing units with rat infestations that apply rodenticide
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Other Possible Model Outputs

• Total population size, recovery time, re-application 

frequency
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Model Results – Per Housing Unit

• Switching from 75% using bromethalin to 75% using warfarin 

increased infestation days by approximately 47 to 70 days 

(an approximate doubling, regardless of resistance).

• Increased resistance alone also increased infestation days by 

approximately 20 to 30%. 
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Model Results – Total U.S.

• Switching from 75% bromethalin to 75% warfarin increased 

U.S. infestation days by 17 to 25 million days.

• Increased resistance alone increased infestation days by 

approximately 4 to 12 million days.
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Conclusions

• Human-health toxicity tradeoffs may affect consumer use 

(i.e., bromethalin as a neurotoxin).

• Warfarin’s expected lower efficacy could significantly 

affect rat population dynamics. 

• Population modeling indicated that if consumers choose 

warfarin over bromethalin, rat infestation days could 

double.

• Quantitative models of important population dynamics 

endpoints (e.g., population size and recovery time) 

provide useful tools to evaluate population-level.

• Population models can be used to evaluate both target 

species and non-target species effects.
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Acknowledgements

Dr. Alan Buckle, Consulting Ltd., Guildford UK

Dr. Michael Kohn, Rice University, Houston TX

Tim Negley, ARCADIS, Syracuse NY