CounterPOPd Web Interactive: Software to investigate the population scale impact of lead in bald eagles in the Northeast United States from 1990-2018

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Population matrix models are used to conduct sensitivity analyses and to assess the population-scale impacts of perturbations. The CounterPOPd software app goes one step further, in that it uses a matrix model to compare the real and hypothetical dynamics in the presence and absence of perturbations that arise from veterinary diseases. In particular, this CounterPOPd app builds on two previous apps to utilize a combinatorial optimization algorithm in conjunction with adult time series data of bald eagles to compare asymptotic and transient population dynamics with and without lead toxicosis mortalities. The first building block to this CounterPOPd app, the “EaglePOPd” software, assesses the dynamics of the current eagle population only (i.e. that with lead toxicosis. EaglePOPd is located at The second building block to this CounterPOPd, the “OptiPOPd” software, is a generalized version of the algorithm that may be modified to test the use of an algorithm in backfilling a symbolic matrix model using time series data. OptiPOPd is located at In the CounterPOPd app, comparative demographic quantities among lead and non-lead conditions include the annual abundances, bi-annual abundances, migration and dispersal, growth rates (asymptotic, transient, cumulative, and stochastic), stable stage distribution, reproductive value, survival rates, sensitivities, elasticities, damping ratios, convergence times, and more. The software also provides interpretation for each demographic quantity from the mathematical modeling, biological, ecological, and resource management perspectives. The CounterPOPd app is programmed to compare population with and without lead toxicosis in bald eagles, but the software may be modified to assess the population scale impact of other maladies in bald eagles.

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This software is being shared under a MIT license. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.


This study was funded in part by the Morris Animal Foundation under Grant # D18ZO-103. This software has not been reviewed nor endorsed by the Foundation, and the views expressed in this software do not necessarily reflect the views of the Foundation, its officers, directors, affiliates or agents.

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Lefkovitch matrix; resource management; recovery; Haliaeetus leucocephalus


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Hanley, B. J., Dhondt, A. A., Forzán, M. J., Bunting, E. M., Pokras, M. A., Hynes, K. P., Dominguez-Villegas, E., and Schuler, K. L.. 2022. Environmental lead reduces the resilience of bald eagle populations. Journal of Wildlife Management 1– 18.

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2020-11-25 13:04:36
Naming modifications and package dependencies version updates.
2019-10-23 16:09:13
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