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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 Wa shington, DC October 28, 2014© 2014 ARCADIS

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# Overview

• Why population models? • Population modeling case - study • Results • Conclusions© 2014 ARCADIS

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## • Wo rkshop publication forthcoming,

recommends models should:

− Provide quantitative risk estimates

− Incorporate realistic variability in environmental and demographic factors

− Integrate complex patterns of exposure and ef fects

− 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 ef

fects on Endangered Species© 2014 ARCADIS

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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 dose response relationship to evaluate ef

fects • 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 ef fects • Can be developed to evaluate threatened and endangered species without using subjective uncertainty factors© 2014 ARCADIS

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## • Specifically evaluate endpoints

important to population dynamics (e.g., population size and recovery time) • Explicitly address toxicity dose response 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© 2014 ARCADIS

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# Rodenticide Ef

ficacy as Case - Study
• Wa rfarin ef

ficacy expected to be lower than bromethalin • Norway rats develop warfarin resistance • Reduced ef

ficacy 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%. **Ac tive Ingredient**  **Reduction in Rats**  **Af ter**  **Tw o**  **We eks**  **(Standard Bait Presentation)**  **Reduction in Rats**  **Af ter**  **Tw o**  **We eks**  **(T amper Resistant**  **Station )**  Bromethalin* 100% 100% Wa rfarin (non - resistant) 90% 60% Wa rfarin (resistant) 50% 20%© 2014 ARCADIS

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### • Estimate infestation rate changes over six weeks for commensal populations based on ef

ficacy dif ferences • 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**  **Wa rfarin**  1 75% 25% 2 25% 75%© 2014 ARCADIS

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# Model Basis

           

            
                 ) ( ) ( ) ( ) ( 0 0 0 0 0 0 0 0 0 ) 1 ( ) 1 ( ) 1 ( ) 1 (
3 2 1 0
2 1 0 3

2 1 0
3 2 1 0 t N t N t N t N S S S F F F F t N t N t N t N 

## • Leslie Matrix Metapopulation Vi ability 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© 2014 ARCADIS

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# Vi tal 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 **Ag e**  **at Sexual Maturity (W** **eeks)**

12 **Litters Per**

**Tw o**  **We eks**  0.196 **12 -** **20 We**  **eks 21**  **- 40** 

**We eks**  **41 -** **73**

**We eks**  **74+**

**We eks**  Proportion Females Pregnant 0.235 0.299 0.325 0.636 Litter Size 8.9 11 .1 11 .4 10.4 Fecundity (Bi -we ekly) 0.205 0.325 0.362 0.649 **Bi -** **we ekly Surv**  **iv al**  Juvenile 0.896 Adult 0.856© 2014 ARCADIS

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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 **Surv iv** **al** 0 - 1 Weeks 0.896 2 - 3 Weeks 0.877 4 - 74+ Weeks 0.856© 2014 ARCADIS

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# Density- Dependence af fects Fecundity and Population Growth Rate (  )© 2014 ARCADIS

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# Model Calibration

• Calibrated model to observed trajectory in literature • Revised ef

ficacy 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© 2014 ARCADIS

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# Model Calibration (continued)

• Observed trajectories generally fell within +/- 1 standard deviation of the average results in calibrated models.© 2014 ARCADIS

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# Results© 2014 ARCADIS

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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 (201 1)

− 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© 2014 ARCADIS

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# Other Possible Model Outputs • Total population size, recovery time, re - application frequency© 2014 ARCADIS

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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%.© 2014 ARCADIS

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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.© 2014 ARCADIS

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# Conclusions
• Human - health toxicity tradeof fs may af

fect consumer use (i.e., bromethalin as a neurotoxin). • Wa rfarin’ s expected lower ef ficacy could significantly af fect 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 ef fects.© 2014 ARCADIS

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# Acknowledgements Dr. Alan Buckle, Consulting Ltd ., Guildford UK Dr. Michael Kohn, Rice University, Houston TX Ti m Negley, ARCADIS, Syracuse NY