We integrate information from veterinary science and ecology to discover interesting and exciting facts where mathematics, computer science, resource management, and ornithology converge.

Life history of bald eagles

Life cycle graphs accurately reflect the biology of bald eagles and are the mathematical building blocks of their projection matrix (e.g. de Kroon, van Groenendael & Ehrlen, 2000). We assume that the life history of bald eagles is subdivided into classes of individuals that share transition probabilities across the breeding and non-breeding periods (de Kroon, van Groenendael, & Ehrlen 2000). We use a 3-stage matrix model that contains bi-annual periods, density dependence, and stage-structured migration parameters. The matrices for the breeding and non-breeding periods are folded into a single annual model matrix. For further details on the mathematical representation of the life cycle, please see Hanley, Dhondt, Dennis, & Schuler (2019).

BAEA Breeding period.jpg

BAEA breeding period

Key:

  1. Fertility of breeding eagles.
  2. Failure of an immature or non-breeding eagle to move up into the breeding category.
  3. Successful transition of an immature or non-breeding eagle into the breeding category.
  4. Survival of an iteroparous adult.
  5. The demotion of a breeding eagle into the non-breeding category.

BAEA Non-Breeding period.jpg

BAEA non-breeding period

Key:

  1. (Before fall) Seasonal immigration of non-resident immatures or non-breeders.
  2. Failure of an immature or non-breeding eagle to move up into the breeding category.
  3. Successful fledging of a hatchling into the immature category. 
  4. (Before fall) Seasonal immigration of non-resident breeders.
  5. The demotion of a breeding eagle into the non-breeding category.
  6. Survival of an iteroparous adult. 
  7. Successful transition from an immature or non-breeding adult into a breeding adult.
  8. (Before fall) Seasonal emigration of part-time resident immatures or non-breeders into an alternative system.
  9. (After fall) Dispersion of resident immatures or non-breeders into an alternative system. 
  10. (After fall) Return immigration of part-time resident immatures or non-breeders.
  11. (Before fall) Seasonal emigration of part-time resident breeders into an alternative system.
  12. (After fall) Dispersion of resident breeders into an alternative system.
  13. (After fall) Return immigration of part-time resident breeders.
Bald eagle parent feeding nestling

Population dynamics of the recovery in the Northeast (NE)

We integrated observed adult time series data and the life history skeleton of bald eagles into the combinatorial optimization algorithm to obtain values of matrix elements and migration parameters for several states in the Northeastern United States. 

Vital rates are traditionally estimated using presence-absence data obtained in field-based activities (Fujiwara & Caswell, 2002). The presence-absence data is generated by repeatedly visiting and reporting the survival of marked individuals who are interacting naturally in their habitat (Caswell, 2001). This repeated visitation is known as the capture–mark–recapture (CMR) sampling method. Survival and transition probabilities are calculated with this mark-recapture data by applying analytical techniques derived from the Cormack-Jolly-Seber (CJS) modeling framework (Gilroy, Virzi, Boulton, & Lockwood, 2012) and maximum likelihood theory (Fujiwara & Caswell, 2002). 

We did not find vital rate estimates in the traditional manner. Instead, we used a combinatorial optimization algorithm in conjunction with adult time series data to "backfill" the symbolic life history of the annual matrix model. The algorithm-predicted matrix was used to calculate the 25 demographic results that are found in the app. To see how we did this, please read Hanley, Dhondt, Dennis, & Schuler (2019).

Explore the peer-reviewed 1990-2018 demographic results in the NE1:

Current population dynamics  

Sensitivity analysis of the bald eagle life cycle

Population matrix models are used to assess population growth and extinction risk, while sensitivity analysis is used to identify which management actions may propel a desired population response (Morris & Doak 2002; Saltelli et al. 2004). 

A single change to a life history produces a complex, non-linear response in the overall population dynamics (de Kroon et al., 2000). The influence of a given management strategy on population scale dynamics is governed by the configuration of the life history. The characteristic equation describes the relationship between the life history characteristics and the long-term growth rate and is therefore the translational key to understand cause and effect. The coefficients of the characteristic equation ("superparameters" Hanley & Dennis, 2019) are key quantities to visualize the situational influence of any matrix element on the long term growth rate.

IsoPOPd reveals how and why the superparameters that are naturally embedded in a life cycle can function to differentially absorb (and neutralize) or react (deleteriously) to situational perturbations from contaminants or disease. As well, the superparameters may function to help or hinder management activities that are designed to combat population-scale threats. The app reveals the fact that the population scale impact of any disease, contaminant or management regime is situational. For further information on the app, or to follow an example scenario, please read Hanley, Connelly, & Dennis (2019).

Conduct your own sensitivity analysis using the peer-reviewed software2:

Explore the nature of the growth rate

The population scale impact of lead toxicosis on eagles

The population scale impact of lead (Pb) toxicosis in eagles is an important topic in wildlife management. We compared the population dynamics of recovery of bald eagles in the Northeast to those dynamics that would have ensued had mortalities from acute and chronic lead toxicosis not occurred. 

Compare the preliminary results for the Pb and non-Pb dynamics in the NE3:

Female dynamics      Male dynamics

The impact of Pb in hypothetically closed systems

What if the birds didn't emigrate or immigrate? Then how would Pb toxicosis impact the population dynamics of the recovery? Although federal banding data shows that the NE experienced losses and gains through dispersal4, we removed the effects of dispersal to assess this question. 

Compare the preliminary Pb and non-Pb dynamics in the absence of dispersal5:

Female dynamics      Male dynamics

The impact of Pb on density dependence

The processes that drive changes in population size may differ in the same species when population size varies. If, for example, reproductive rate is density dependent it will be larger at low density but smaller at higher densities. Thus dynamics will vary between populations of different size. The recovery in the NE, USA began with very few eagles and grew to a moderate amount of eagles over time. We isolated the early years of recovery (when abundances were low; 1990-2006) and compared them to the recent years of recovery (when abundances were much higher; 2002-2018). The slight temporal overlap is due to a mathematical technicality. Although abundances of eagles in the NE are still increasing, we are seeing signatures of density dependence in their population dynamics.

Explore the preliminary results in the early and recent windows of recovery in the NE6,7:

In a system open to dispersal6:

Female dynamics     Male dynamics

In a system closed to dispersal7:

Female dynamics     Male dynamics

In a system open to dispersal6:

Female dynamics     Male dynamics

In a system closed to dispersal7:

Female dynamics     Male dynamics

The impact of Pb on life history plasticity

The life cycles of long-lived species contain naturally embedded plasticity; that is, they contain some assortment of strategies that may be used to circumvent environmental obstacles. For example, individuals may breed earlier or later than normal in response to altered environmental conditions. Life history plasticity is not infinite; ongoing stressors can deplete the amount with which the species can adapt to additional environmental obstacles. Populations may grow in the presence of veterinary diseases, but that growth comes at a cost in remaining adaptive potential. 

Explore the preliminary results of remaining plasticity in the NE8:

Using this parameterization of the life history, we can assess the population-scale impacts of veterinary maladies on bald eagles in the Northeast United States. 

 

Juvenile bald eagle

Watch a short video on the project

The influence of lead on bald eagle dynamics in the northeast United States

Presentation at the 2020 Annual Conference for the Ecological Society of America

Further details of this research

Questions can be directed to Drs. Krysten Schuler (ks833@cornell.edu) or Brenda Hanley (bjh262@cornell.edu). 

Financial support was provided in part by the Morris Animal Foundation under grant # D18ZO-103. The contents of this web site, the links, the interactive apps, cited literature, and the narratives have not been reviewed nor endorsed by the Foundation, and the views expressed in this content do not necessarily reflect the views of the Foundation, its officers, directors, affiliates or agents. 

 

This research contains diverse and interdisciplinary contributions from professionals all over the region. Contributions may include intellectual property, knowledge, data, software code, time, ideas, suggestions, comments, reviews, a professional network, and communication materials. Contributions from each participant may have been made to one or more of our research products or software. Thank you!

 

Contributors (alphabetical order):

André A. Dhondt, Lab of Ornithology, Cornell University, Ithaca, New York, USA

Barb Bodenstein, United States Geological Survey, National Wildlife Health Center, Madison, Wisconsin, USA

Brenda Hanley, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Brian Hess, Connecticut Department of Energy and Environmental Protection, Hartford, Connecticut, USA

Chris Martin, New Hampshire Audubon, Concord, New Hampshire, USA

David Needle, New Hampshire Veterinary Diagnostic Laboratory, University of New Hampshire, Durham, New Hampshire, USA

David O. Brown, Ithaca, New York, USA

David W. Kramer, New York Department of Environmental Conservation, Albany, New York, USA

Diane Winn, Avian Haven Wild Bird Rehabilitation Center, Freedom, Maine, USA

Dieter Heylen, Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, USA, Interuniversity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium

Elizabeth M. Bunting, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Ernesto Dominguez-Villegas, The Wildlife Center of Virginia, Waynesboro, Virginia, USA

Florina Tseng, Wildlife Clinic & Center for Conservation Medicine, Cummings School of Veterinary Medicine Tufts University, North Grafton, Massachusetts, USA 

Jennifer Peaslee, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Justin D. Brown, Department of Veterinary and Biomedical Sciences, Pennsylvania State University, University Park, Pennsylvania, USA

Karyn L. Bischoff, Cornell University College of Veterinary Medicine, Animal Health Diagnostic Center, Ithaca, New York, USA

Katherine McComas, Cornell University, Ithaca, New York, USA

Kevin P. Hynes, New York Department of Environmental Conservation, New York, USA

Krysten L. Schuler, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

María J. Forzán, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Mark A. Pokras, Wildlife Clinic & Center for Conservation Medicine, Cummings School of Veterinary Medicine Tufts University, North Grafton, Massachusetts, USA 

Mark Ruder, University of Georgia, Athens, Georgia, USA

Mary Garrison, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Nick Hollingshead, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Nicole I. Keith, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Pamela Mills, Department of Lands and Forestry, Wildlife Division, Government of Nova Scotia, Nova Scotia, CA

Patrick Connelly, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Patrick P. Martin,  New York State Department of Environmental Conservation (retired), Middleburgh, New York, USA

Rachel Abbott, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Samantha Gibbs, Wildlife Health Office, National Wildlife Refuge System, U.S. Fish and Wildlife Service, Chiefland, Florida, USA

Sandra Houghton, New Hampshire Fish and Game Department, Concord, New Hampshire, USA

Sarah Ireley, Cornell University College of Veterinary Medicine, Cornell Wildlife Health Lab, Animal Health Diagnostic Center, Ithaca, New York, USA

Tom French, Division of Fisheries and Wildlife, Westborough, Massachusetts, USA

And 17 additional anonymous professionals or academic reviewers. 

Peer-reviewed research:

Hanley, B, Dhondt, A, Forzán, M, Bunting, E, Pokras, M, Hynes, K,  Domínguez-Villegas, E, & Schuler, K. 202X. Environmental Lead Reduces The Resilience Of Bald Eagle Populations (Haliaeetus Leucocephalus). In peer review. 

Hanley, B, Dhondt, A, Dennis, B, & Schuler, K. 2019. Using time series data to assess recent population dynamics of Bald Eagles in the northeast United States. Ecosphere. doi: https://doi.org/10.1002/ecs2.2963

Hanley B, Connelly P, & Dennis B. 2019. Another look at the eigenvalues of a population matrix model. PeerJ 7:e8018. doi: https://doi.org/10.7717/peerj.8018

Interactive software:

1 Hanley, B, Dhondt, A, Dennis, B, & Schuler, K. 2019. EaglePOPd Web Interactive: Software to investigate the demography of Bald Eagles in the Northeast, USA from 1990- 2018 [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/q4m1-se95.

2 Hanley, B, Connelly, P, & Dennis, B. 2019. IsoPOPd: Interactive software to understand how elements in a population matrix model influence the asymptotic population growth rate [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/bcmg-7w08.

3 Hanley, B, Dhondt, A, Bunting, E, Pokras, M, Hynes, K, Forzán, M, & Schuler, K. 2019. CounterPOPd Web Interactive: Software to investigate the population scale impact of lead in bald eagles in the Northeast United States from 1990-2018 [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/0v1k-wq39.

Hanley, B., Dhondt, A., & Schuler, K. 2020. BandingPOPd: Software to investigate the USGS bald eagle banding and encounter data in the Northeast United States. [Dataset]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/1n7f-xs53.

5 Hanley, B, Dhondt, A, Bunting, E, Pokras, M, Hynes, K, Forzán, M, & Schuler, K. 2019. ClosedCounterPOPd Web Interactive: Software to investigate the population scale impacts of lead in hypothetically closed bald eagle populations [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/q4t7-1y54.

6 Hanley, B., Dhondt, A, Bunting, E, Pokras, M, Hynes, K, Forzán, M, & Schuler, K. 2019. DensiPOPd Web Interactive: Software to investigate the impacts to density dependence by lead in bald eagles in the Northeast United States [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/6yb8-5c25.

7 Hanley, B., Dhondt, A, Bunting, E, Pokras, M, Hynes, K, Forzán, M, & Schuler, K. 2019. ClosedDensiPOPd Web Interactive: Software to investigate the impacts to density dependence by lead in bald eagles in hypothetically closed systems [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/n2x8-6p10. 

8 Hanley, B, Dhondt, A, Bunting, E, Pokras, M, Hynes, K, Forzán, M, & Schuler, K. 2019. PlastiPOPd Web Interactive: Software to investigate the life history plasticity in bald eagles in the Northeast United States [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/7rxf-ee77.​

Data package:

Hanley, B, Dhondt, A, Bunting, E, Pokras, M, Hynes, K, Forzán, M, Domínguez-Villegas, E, & Schuler, K. 2020. ​Regional Northeast, USA Study of Lead in Bald Eagles Data Package. Cornell University Library eCommons Repository. doi: https://doi.dx/10.7298/3p9p-j249​.

Dashboard:

Hanley, B., Dhondt, A.,Forzán, M., Bunting, E., Pokras, M., Hynes, K., Domínguez-Villegas, E., & Schuler, K. 2020. EagleDashboard: Assessing the population scale impacts of a disease, toxin, or contaminant in Bald Eagles [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/0dm3-tf51.

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