We integrate information from veterinary science to discover interesting facts where mathematics, computer science, biology, and resource management converge.
Life history of moose (Alces alces)
We used the life cycles of cow and bull moose in conjunction with a projection matrix to identify the population dynamics in the Adirondacks of New York state between 2015-2019. We assumed that the life history of moose was by sex, then further subdivided into segments of individuals that share common transition probabilities during the spring and the rut. The resulting 3-stage matrices modeled calves, young adults and mature adults across the spring and rut of each calendar year. The semi-annual spring and rut matrices for each sex were then folded into a single annual matrix.
a. Average annual fertility of young cows
b. Average annual fertility of mature cows
f. Average semi-annual survival of young cows
g. Average semi-annual survival of mature cows
h. Average semi-annual survival of cow calves
b. Average annual fertility of mature bulls
d. Average spring survival of young bulls (without transition into a breeder)
f. Average spring survival of young bulls (with transition into a breeder)
g. Average spring survival of breeding bulls
h. Average rut survival of bull calves
i. Average rut survival of young bulls (without transition into a breeder)
m. Average rut survival of breeding bulls
Population dynamics of moose in New York
We integrated time series data into each annual matrix, then initiated a combinatorial optimization algorithm to estimate the survival and fertility rates of the moose population in Adirondack Park. The algorithm-predicted matrices were then used to calculate 17 asymptotic and transient demographic properties, which may be accessed by clicking the buttons below.
Explore the preliminary 2015-2019 demographic results in NY1:
Sensitivity analysis of the life cycle
Population matrix models are used to assess population growth and extinction risk, while sensitivity analyses are conducted to identify management actions that propel population responses (Morris & Doak 2002; Saltelli et al. 2004). The button below allow you to explore how alterations to vital rates will influence the population growth rate. For further information please read Hanley, Connelly, & Dennis (2019).
Conduct your own sensitivity analysis using the peer-reviewed software2:
The population scale impact of lethal parasites on moose
Necropsies of moose in New York have revealed the presence of two lethal parasites: brain worm (P. tenuis) and liver flukes (Fasciola sp.), lending questions regarding the population scale impact of associated mortalities. We compared the population dynamics of moose in the Adirondacks to those dynamics that would have ensued had mortalities from liver fluke or brain worm not occurred.
Compare the preliminary results for comparisons among the current and parasite-free dynamics in NY3:
Further details of this research
Questions can be directed to Drs. Krysten Schuler (firstname.lastname@example.org) or Jacqui Frair (email@example.com).
Funding provided by the Federal Aid in Wildlife Restoration Act and the New York State Department of Environmental Conservation. The contents of this web site, the links, the interactive apps, cited literature, and the narratives have not been reviewed nor endorsed by the NYSDEC, and the views expressed in this content do not necessarily reflect the views of the NYSDEC, its officers, directors, affiliates or agents.
This interdisciplinary research contains data contributions from the New York State Department of Environmental Conservation and academic contributions from our collaborators at the Cornell Wildlife Health Lab at Cornell University and at the State University of New York Environmental Science and Forestry. Contributions may have provided intellectual property, knowledge, data, software code, time, suggestions, comments, and extension and communication products to one or more research products. Contributors, we thank you.
Additional thanks to:
Niki Keith, who aided the project while at the Cornell Wildlife Health Lab, but has since moved on to Hamilton College of New York
Connelly, P, Hanley, B, Friar, J, Hurst, J, Stickles, J, Kramer, D, & Schuler, K. 201X. The effect of disease on Moose in New York, USA from 2015-2019. In preparation.
Hanley, B, Dennis, B, Kramer, D, & Schuler, K. Estimating parameters from adult time series data for population matrix models. In peer revision.
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
1 Connelly, P., Hanley, B., Frair, J., & Schuler, K. 2020. MoosePOPd Web Interactive: Software to investigate the demography of Moose in New York, USA from 2015-2019 [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/k033-va79
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 Connelly, P., Hanley, B., Frair, J., & Schuler, K. 2020. MooseCounterPOPd Web Interactive: Software to investigate the population scale impact of Brain Worm and Liver Fluke in Moose in New York, USA from 2015-2019 [Software]. Cornell University Library eCommons Repository. doi: https://doi.org/10.7298/kxme-kq04
Aalto, S, & Newsome, G (1980) Some methods of estimating the parameters of the Leslie Matrix using incomplete population data. Canadian Journal of Fisheries and Aquatic Sciences, 37, 1140-1148.
Abadi F, Gimenez, O, Arlettaz, R, & Schaub M (2010) An assessment of integrated population models: bias, accuracy, and violation of the assumption of independence. Ecology, 91(1): 7-14.
Alberts, S, & Altmann, J (2003) Matrix models for primate life history analysis. In - Primate life history and socioecology. University of Chicago Press. Chicago, Illinois, USA.
Anderson, D, Burnham, K, White, G (1994) AIC model selection in overdispersed capture-recapture data. Ecology, 75, 1780–1793.
Arnold, T (2010) Uninformative parameters and model selection using Akaike’s Information Criterion. Journal of Wildlife Management, 74, 1175–1178.
Arthur, W (1982) The ergodic theorems of demography; a simple proof. Demography, 19:4, 439-445.
Bartlett, M (1990) Chance or chaos? (with discussion) Journal of the Royal Statistical Society, A52, 321–347.
Basu, A, H Shioya, and C Park. 2011. Statistical Inference: The Minimum Distance Approach. Chapman & Hall (CRC Press)
Bernardelli, H (1941) Population waves. Journal of Burma Research Society, 31, 1-18.
Beyer, W (ed.) 1978. Algebra. – In: CRC handbook of mathematical sciences. CRC Press, 69-72. Boca Raton, Florida, USA.
Bolen, E, & Robinson, W (1999) - In: Wildlife Ecology and Management. 5th Ed. Pearson, London, United Kingdom.
Box, G (1979), "Robustness in the strategy of scientific model building", in Launer, R. L.; Wilkinson, G. N, Robustness in Statistics, Academic Press, pp. 201–236.
Box, G and Tiao, G (1973) Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, Mass.
Bowyer R, Van Ballenberghe, V, & Kie, J (2003) Moose (Alces alces).
Bozdogan, H (1987) Model selection and Akaike's information criterion (AIC): the general theory and its analytical extensions. Psychometrika 52, 345-370.
Burgman M, Ferson S, & Akcakaya H (1993) Risk assessment in conservation biology. Chapman and Hall. London, United Kingdom.
Burnham K, Anderson D (2002) Model Selection & Multimodel Inference: A Practical Information-Theoretic Approach, 2nd Edn. Springer, New York
Cade, B (2015) Model averaging and muddled multimodel inferences. Ecology, 96, 2370‑2382.
Case, T (2000) – In: An illustrated guide to theoretical ecology. Oxford University Press, New York, New York, USA.
Caswell, H, Brault, S, Read, A, & Smith, T (1998) Harbor porpoise and fisheries: an uncertainty analysis of incidental mortality. Ecological Applications, 8:4, 1226-1238.
Caswell, H (2001) Matrix population models: Construction, analysis, and interpretation. 2nd edition. Sunderland: Sinauer Associates.
Caswell, H, & Neubert, M (2007) Reactivity and transient dynamics of discrete-time ecological systems. Journal of Difference Equations and Applications, 2, pgs. 295-310.
Caswell, H (2007) Sensitivity analysis of transient population dynamics. Ecology Letters, 10:1, 1-15.
Caswell, H (ed.) 2009. -In: Advances in Ecological Research. Vol. 41. Elsevier. Academic Press. Amsterdam, Netherlands.
Charlesworth, B (2009) Effective population size and patterns of molecular evolution and variation. Genetics, 10, pgs. 195-205.
Chatfield, C (1995) Model Uncertainty, Data Mining and statistical Inference. Journal of the Royal Statistical Society: Series A (Statistics in Society) 158:419-466.
Claeskens, G & Hjort, N (2008) Model Selection and Model Averaging. Cambridge University Press, Cambridge.Edwards, A. W. F. 1972. Likelihood. Cambridge University Press, Cambridge.
Costantino, R, & Desharnais, R (1981) Gamma distributions of adult numbers for Tribolium populations in the region of their steady states. Journal of Animal Ecology, 50, 667–681.
Coulson, T, Catchpole, E, Albon, S, Morgan, B, Pemberton, J, Clutton-Brock, T. et al (2001) Age, sex, density, winter weather, and population crashes in Soay sheep. Science, 292, 1528–1531.
Crone E, Ellis M, Morris W, Stanley A, Bell T, Bierzychudek P, Ehrlen J, Kaye T, Knight T, Lesica P, Oostermeijer G, Quintana-Ascencio P, Ticktin T, Valverde T, Williams J, Doak D, Ganesan R, McEachern K, Thorpe A, & Menges E (2012) Ability of matrix models to explain the past and predict the future of plant populations. Conservation Biology, 27(5), 968-978.
Cross, M, Oakes, L, & Kretser, H (2018) Summary report: Climate change and moose management in New York state. New York State Department of Environmental Conservation.
Cull, P, & Vogt, A (1973) Mathematical analysis of the asymptotic behavior of the Leslie population matrix model. Bulletin of Mathematical Biology, 35, 645-661.
Dalal, S and Hall, W. (1983) ”Approximating Priors by Mixtures of Natural Conjugate Priors” J. R. Statist. Soc, B, 45, 278-286.
de Kroon, H, van Groenendael, J, & Ehrlen, J (2000) Elasticities: a review of methods and model limitations. Ecology, 81, 607-618.
Deevey, E (1947) Life tables for natural populations of animals. Quarterly Review of Biology, 22, 283-314.
Dennis, B (2013) – In: The R student companion. CRC Press. Boca Raton, Florida, USA.
Dennis, B, & Costantino, R (1988) Analysis of steady-state populations with the gamma abundance model: application to Tribolium. Ecology, 69, 1200-1213.
Dennis, B, & Taper, M (1994) Density dependence in time series observations of natural populations: estimation and testing. Ecological Monographs, 64, 205-224.
Dennis, B, Desharnais, R, Cushing, J, & Costantino, R (1995) Nonlinear demographic dynamics: mathematical models, statistical methods, and biological experiments. Ecological Monographs, 65, 261–281.
Dennis, B, Desharnais, R, Cushing, J, Hensen, S, & Costantino R (2001) Estimating chaos and complex dynamics in an insect population. Ecological Monographs, 71, 277-303.
Devenish-Nelson, E, Harris, S, Soulsbury, C, Richards, S, & Stephens, P (2010) Uncertainty in population growth rates. Determining confidence intervals from point estimates of parameters. PlosOne, 5:10, e13628.
Ding, H, Trajcevski, G, Scheuermann, P, Wang, X, & Keogh, E (2008) Querying and mining of time series data: Experimental comparison of representations and distance measures. Proceedings of the VLDB Endowment, 1, 1542-1552.
Dinsmore, S, & Johnson, D (2012) In - Silvy (Ed.), The wildlife techniques manual. Johns Hopkins University Press. Baltimore, Maryland, USA.
Doak, D, Kareiva, P, & Klepetka, B (1994) Modeling population viability for the desert tortoise in the western Mojave Desert. Ecological Applications, 4, 446-460.
Dohoo, I (2014) Bias – Is it a problem, and what should we do? Preventative Veterinary Medicine, Vol 113, pgs. 331-337.
Elandt, R, & Johnson, N (1980) - In: Survival models and data analysis. John Wiley & Sons, New York, New York, USA.
Ersoy, Y, & Moscardini, A (1994) In – Mathematical modelling courses for engineering education. Springer-Verlag. Berlin, Germany.
Ezard, T, Bullock, J, Dalgleish, H, Million, A, Pelletier, F, Ozgul, A, & Koons, D (2010) Matrix models for a changeable world: the importance of transient dynamics in population management. Journal of Applied Ecology, 47, 515-523.
Forrester, S, Lankester, M (1997) Extracting protostronglyid nematode larvae from ungulate feces. Wildlife Disease Association, 33(3): 511-516.
Fox, G, & Gurevitch, J (2000) Population numbers count: tools for near-term demographic analysis. American Naturalist, 156, 242–256.
Fox, J (2016) Applied regression analysis and generalized linear models. 2nd edition. Sage Publications Inc. Los Angeles, California, USA.
Frankham, R (2005) Genetics and extinction. Biological Conservation, 126, 131-140.
Friend M, Franson J, Ciganovich E (1999) Field Manual of Wildlife Diseases. Chapter 43. U.S. Department of The Interior, U.S. Geological Survey, Washington, D.C
Friend M, Franson J, Anderson W (2009) Biological & Societal Dimensions of Lead Poisoning in Birds in the USA. In: Watson RT, Fuller M, Pokras M, Hunt WG (Eds) Ingestion of Lead from Spent Ammunition: Implications for Wildlife & Humans. The Peregrine Fund, Boise, Pp 34–60.
Friend, M (1987) Field Guide to Wildlife Diseases. United States Fish & Wildlife Service, Washington, DC, USA.
Fryxell, J, Sinclair, A, & Caughley, G (2014) In - Wildlife ecology, conservation, and management. 3rd edition. Johns Wiley & Sons. Hoboken, New Jersey, USA.
Fujiwara, M, & Caswell, H (2002) Estimating population projection matrices from multi-stage mark-recapture data. Ecology, 83, 3257-3265.
Futuyma, D (2009) Evolution. 2nd ed. Sinuaer and Associates. Sunderland, Massachusetts, USA.
Gallardo, J, Vilella, F, & Colvin, M (2019) A seasonal population matrix model of the Caribbean Red-tailed Hawk Bueo jamaicensis jamaicensis in eastern Puerto Rico. Ibis, 161, 459-466.
Gelman, A, Hill, J, & Yajima, M (2012) Why we (usually) don't have to worry about multiple comparisons. Journal of Research on Educational Effectiveness, 5, 189-211.
Gerber, B, & Kendall, W (2016) Considering transient population dynamics in the conservation of slow life-history species: An application to the sandhill crane. Biological Conservation, 200, 228.
Gerrodette, T (2011) Inference without significance: measuring support for hypotheses rather than rejecting them. Marine Ecology: An Evolutionary Perspective, 32, 404–418.
Gilroy, J, Virzi, T, Boulton, R, & Lockwood, J (2012) A new approach to the “apparent survival” problem: Estimating true survival rates from mark-recapture studies. Ecology, 93:7, 509-1516.
Goodman D (2004) Methods for joint inference from multiple data sources for improved estimates of population size and survival rates. Mar Mam Sci 20:401–423.
Gotelli, N (2004) - In: A Primer of ecology. Sinuaer Associates, Inc. Sunderland, Massachusetts, USA.
Graur, D, & Li, W (2000) Dynamics of genes in populations. In – Fundamentals of molecular evolution. 2nd edition. Sinuaer Associates Inc. Sunderland, Massachusetts, USA.
Grueber, C, Nakagawa, S, Laws, R, & Jamieson, I (2011) Multimodel inference in ecology and evolution: challenges and solutions. J. Evolutionary Biology, 24, 699-711.
Guthery, F, Brennan, L, Peterson, M & Lusk, J (2005) Information theory in wildlife science: critique and viewpoint. J. Wildlife Manage, 69, 457-465.
Guttorp, Peter and Lockhart, Richard A (1988) ”Finding the Location of a Signal: A Bayesian Approach”, Journal of the American Statistical Association 83, 322-330.
Hacking, I (1965) Logic of statistical inference. Cambridge University Press, Cambridge.
Hanley, B, & B. Dennis (2019) Analytical expressions for the eigenvalues, demographic quantities, and extinction criteria arising from a three-stage wildlife population matrix. Natural Resource Modeling.
Hartl, D. L, & Clark, A. G (1999) In - Principles of population genetics 4th edition. Sinauer Associates Inc. Publishers. Sunderland, Massachusetts, USA.
Hazewinkel, M (ed.) (1988) "Cardano formula" In - Encyclopedia of mathematics. Kluwer Academic Publishers, Dordrecht, Netherlands.
Hegarty, M, & Kozhevnikov, M (1999) Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 4, pgs. 684-689.
Heppell, S, Caswell, H, & Crowder, L (2000) Life histories and elasticity patterns: perturbation analysis for species with minimal demographic data. Ecology, 81, 654-665.
Hodgson, D, & Townley, S (2004) Methodological insight: Linking management changes to population dynamic responses: the transfer function of a projection matrix perturbation. Journal of Applied Ecology, 41:6, 1155-1161.
Hooten, M, Garlick, M, & Powell, J (2013) Computational efficient spatial differential equation modeling using homogenization. Journal of Agriculture, Biological, and Environmental Statistics. 18, 3, pgs. 405-428.
Hosmer D, Lemeshow S (2000) Applied Logistic Regression, 2nd Edn. Wiley, New York
Hurlbert, S, & Lombardi, C (2009) Final collapse of the Neyman-Pearson decision theoretic framework and rise of the neoFisherian. Annales Zoologici Fennici, 46, 311–349.
Jeffreys, H (1961) Theory of Probability, 3rd ed. Clarendon Press, Oxford (1st. ed , 1939)
Johnson, D (1999) The insignificance of statistical significance testing. Journal of Wildlife Management 63:763–772.
Johnson, J & Omland, K (2004) Model selection in ecology and evolution. Trends in Ecology and Evolution 19, 101-108.
Keyfitz, N & Caswell, H (2005) – In: Applied mathematical demography. 3rd Ed. Springer Science. New York, New York, USA.
Keyfitz, N (1964) The population projection as a matrix operator. Demography, 1, 56-73.
Keyfitz, N (1971) On the momentum of population growth. Demography, 8, 71-80.
Kissel, A, Palen, W, Govindarajulu, P, and Bishop, C (2014) Quantifying ecological life support: The biological efficacy of alternative supplementation strategies for imperiled amphibian populations. Conservation Letters, 7:5, 441-450.
Kliman, R, Sheehy, B, & Schultz, J (2008) Genetic drift and effective population size. Nature Education, 1:3, 3.
Klimko, L, & Nelson, P (1978) On conditional least squares estimation for stochastic processes. The Annals of Statistics, 6, 629-642.
Knight, K (2000) In - Mathematical statistics. Chapman & Hall, Boca Raton, Florida, USA.
Koons, D, Grand, J, Zinner, B, & Rockwell, R (2005) Transient population dynamics: relations to life history and initial population state. Ecological Modeling, 185, 283-297.
Koons, D, Rockwell, R, & Grand, J (2006) Population momentum: implications for wildlife management. Journal of Wildlife Management, 70, 19-26.
Koons, D, Grand, J, & Arnold, J (2006) Population momentum across vertebrate life histories. Ecological Modeling, 197, 418-430.
Koons, D, Holmes, R, & Grand, J (2007) Population inertia and its sensitivity to changes in vital rates and population structure. Ecology, 88, 2857-2867.
Koopman, B (1936) ”On distributions admitting a sufficient statistic”, Trans. Am. Math. Soc, 39, 399-409.
Korte, B, & Vygen J (2018) Combinatorial Optimization: Theory and Algorithms. 6th edition. New York: Springer Publishing.
Kot, M (2001) An overview of linear age structured models. In - Elements of mathematical ecology. Cambridge University Press. Cambridge, United Kingdom.
Kruschke, J and Vanpaemel, W (2015) Bayesian estimation in hierarchical models. In: J. R. Busemeyer, Z. Wang, J. T. Townsend, and A. Eidels (Eds.), The Oxford Handbook of Computational and Mathematical Psychology, pp. 279-299. Oxford, UK: Oxford University Press.
Kuehl, R (2000) In - Design of experiments: Statistical principles of research design and analysis. 2nd Edition. Brooks Cole, Belmont, California, USA.
Kullback, S & Leibler, R (1951) On information and sufficiency. Annals of Mathematical Statistics, 22, 79-86.
Lande, R (1982) A quantitative genetic theory of life history evolution. Ecology, 63:3, 607-615.
Lankester, M (2010) Understanding the impact of meningeal worm (Parelaphostrongylus tenuis) on moose populations. ALCES 46: 53-70.
Lax, P (1997) Positive matrices. - In: Linear algebra. John Wiley and Sons, Hoboken, New Jersey, USA.
Lay, D, Lay, S, & MacDonald, J (2016) – In: Linear algebra and its applications. Pearson. London, England.
Lebreton, J et al (1992) Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecol. Monogr. 62, 67-118.
Lebreton, J (2005) Age, stages, and the role of generation time in matrix models. Ecological Modelling, 188, 22-29.
Lebreton, J, Nichols, J, Barker, J, Pradel, R, & Spendelow, J (2009) Modeling individual animal histories with multistate capture-recapture models. In - Advances in Ecological Research. Vol. 41. Elsevier. Amsterdam, Netherlands.
Lee, C (2017) Elasticity of population growth with respect to the intensity of biotic or abiotic driving factors. Ecology, 98:4, 1016-1025.
Lefkovitch, L (1965) The study of population growth in organism groups by stages. Biometrics, 21, 1-18.
Leirs, H, Stenseth, N, Nichols, J, Hines, J, Verhagen, R. & Verheyen, W (1997) Stochastic seasonality and nonlinear density-dependent factors regulate population size in an African rodent. Nature, 389, 176–180.
Leslie, P (1945) On the use of matrices in certain population mathematics. Biometrika, 35, 213-245.
Lewis, E (1941) On the generation and growth of a population. Sankhya, Indian Journal of Statistics, 6, 93-96.
Lindsay, B (1995) Mixture Models: Theory, Geometry and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics, 5, I-163.
Loehle, C (1987) Hypothesis testing in ecology: psychological aspects and the importance of theory maturation. Quarterly Review of Biology, 62, 397–409.
Lomnicki, A (2011) Individual-based Models in Population Ecology. In: eLS. John Wiley & Sons, Ltd: Chichester.
Lopez, A (1961) – In: Problems in stable population theory. Princeton University Press, Princeton, New Jersey, USA.
Lotka, A (1925) Elements of Physical Biology. Williams and Wilkins, Baltimore, Maryland, USA.
Mallows, C (1972) A Note on Asymptotic Joint Normality. Annals of Mathematical Statistics, 43:2, 508-515.
Manly, B (2007) – In: Randomization, bootstrap, and Monte Carlo methods in biology. Chapman and Hall. New York, New York, USA.
Marescot, L, Forrester, T, Casady, D, & Wittmer, H (2014) Using multistate capture–mark–recapture models to quantify effects of predation on age-specific survival and population growth in black-tailed deer. Population Ecology, 57, 185-197.
Martin, W (2014) Making valid causal inferences from observational data. Preventative Veterinary Medicine, 13: 281-297.
Matsuda, H (2003) Challenges Posed by The Precautionary Principle & Accountability in Ecological Risk Assessment. Environmetrics 14: 245–254.
May, R (1974) - In: Stability and complexity in model ecosystems. 2nd edition. Princeton University Press. Princeton, New Jersey, USA.
Mayo, D, and A. Spanos (2006) Severe testing as a basic concept in a Neyman-Pearson philosophy of induction. British Journal for the Philosophy of Science 57:323-357.
McDonald J, Stott I, Townley S, & Hodgson D (2016) Transients drive the demographics of plant populations in variable environments. Journal of Ecology, 104, 306-314.
McGowan, C, Allan, N, Servoss, J, Hedwall, S, & Wooldridge, B (2017) Incorporating population viability models into species status assessment and listing decisions under the U.S. Endangered Species Act. Global Ecology and Conservation, 12, 119-130.
Mertz, D (1971) The Mathematical Demography of The California Condor Population. American Naturalist 105:437– 453.
Meyer, J, Ingersoll, C, McDonald, L, & Boyce, M, (1986) Estimating uncertainty in population growth rates: jackknife vs. bootstrap techniques. Ecology, 67, 1156-1166.
Meyer, K, & Houle, D (2013) Sampling based approximation of confidence intervals for functions of genetic covariance matrices. 20th Conference of the Association for the Advancement of Animal Breeding and Genetics. Napier, New Zealand.
Mills, L, & Lindberg, M (2002) Sensitivity analysis to evaluate the consequences of conservation actions. In: S.R. Beissinger, D.R. McCullough (Eds.), Population viability analysis. University of Chicago Press. Chicago, Illinois, USA.
Monte, L (2012) Characterization of a nonlinear Leslie matrix model for predicting the dynamics of biological population in polluted environments: Applications to radioecology. Ecological Modelling, 248, 174-183.
Morris, W & Doak, D (2002) Demographic PVAs: Using projection matrices to assess population growth and viability. – In: Quantitative conservation biology: theory and practice of population viability analysis. Sinauer Associates Inc, Sunderland, Massachusetts, USA.
Murtaugh, P (2009) Performance of several variable-selection methods applied to real ecological data. Ecology Letters, 12, 1061-1068.
Murtaugh, P (2014) In defense of P-values. Ecology, 95, 611-617.
Nishii, R 1988. Maximum-likelihood principle and model selection when the true model is unspecified. Journal of Multivariate Analysis 27, 392-403.
O’Connor, A and Sargeant, J (2014) Meta-analysis including data from observational studies. Preventative Veterinary Medicine. Vol. 113, pgs. 313-322.
Oehlert, G (1992) A note on the delta method. The American Statistician. 46,1, pgs. 2729.
Ott, R (2010) In: An introduction to statistical methods and data analysis. 6th Ed. Brooks and Cole Publishing. Belmont, California, USA.
Pawitan, Y (2001) In all likelihood: statistical modelling and inference using likelihood. Oxford University Press, Oxford, UK.
Picard, N, Chagneau, P, Mortier, F, & Bar-Hen, A (2009) Finding confidence limits on population growth rates: Bootstrap and analytic methods. Mathematical Biosciences, 219, 23-31.
Pickett, S, & White, P (1985) In- The ecology of natural disturbance and patch dynamics. Academic Press. Orlando, Florida, USA.
Pike, D, Pizzatto, L, Pike, B, & Shine, R (2008) Estimating survival rates of uncatchable animals: the myth of high juvenile mortality in reptiles. Ecology, 89:3, 607-611.
Pinero, D, Martínez-Ramos, M, & Sarukhan, J (1984) A Population model of Astrocaryum mexicanum and a sensitivity analysis of its finite rate of increase. Journal of Ecology, 72, 3, pgs. 977-991.
Pruvot, M, Lejeune, M, Kutz, S, Hutchins, W, Musiani, M, Massolo, A, & Orsel, K (2016) Better alone or in ill company? The effect of migration and inter-species comingling on Fascioloides magna infection in elk. PlosOne 11(7).
Quinn, J & Dunham, A 1983. On hypothesis testing in ecology and evolution. Am. Nat. 122, 602-617.
R Core Team (2019) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. R version 3.5.3 (2019-03-11)
R Shiny. (2018) Shiny. Web Application Framework for R.
Regehr, E, Hunter, C, Caswell, H, Amstrup, S & Stirling, I (2010) Survival and breeding of polar bears in the southern Beauford Sea in relation to sea ice. Journal of Animal Ecology, 79, 117-127.
Rencher, A (2002) -In: Methods of multivariate analysis. John Wiley and Sons Inc. New York, New York, USA.
Renshaw, E (1994) Chaos in biometry. IMA Journal of Mathematics Applied in Medicine & Biology, 1, 17-44.
Rice, J (2007) Mathematical Statistics and Data Analysis, Third Edition. Brooks/Cole, Belmont, California.
Richards, S (2005) Testing ecological theory using the information-theoretic approach: examples and cautionary results. Ecology, 86, 2805–2814.
Rogers, A (1966) The multiregional matrix growth operator and the stable interregional age structure. Demography, 3, 537-544.
Royall, R (2000) On the probability of observing misleading statistical evidence, with commentary. Journal of the American Statistical Association, 95, 760-780.
Royall, R (1997) Statistical Evidence: A Likelihood Paradigm. Chapman and Hall, London.
Royama, T (1992) In - Analytical Population Dynamics. Chapman, Hall, London, United Kingdom.
RStudio Team (2015) RStudio: Integrated Development for R. RStudio, Inc, Boston, MA
Samaniego, F (2014) Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists. CRC Press, Boca Raton, Florida.
Samuelson, P (1941) Conditions that the roots of a polynomial be less than unity in absolute value. Annals of Mathematical Statistics, 12, 360-364.
Schaub M & Fletcher D (2015) Estimating immigration using a Bayesian integrated population model: choice of parametrization and priors. Environ Ecol Stat, 22: 535-549.
Schaub M, Abadi F (2011) Integrated population models: a novel analysis framework for deeper insights into population dynamics. Journal of Ornithology, 152: S2:27-S2:37.
Scheaffer, R, Mendenhall II, W, & Ott, R (2006) In - Elementary survey sampling. 6th Ed. Thomson, Brooks & Cole. Belmont, California, USA.
Seber, G (1984) - In: Multivariate observations. John Wiley & Sons. New York, New York, USA.
Severini,T (2000) Likelihood Methods in Statistics. Oxford University Press, Oxford, UK.
Shea, K, & Kelly, D (1998) Estimating biocontrol agent impact with matrix models: Catrduuts nutans in New Zealand. Ecological Applications, 8, 824-832.
Shyu, E, & Caswell, H (2014) Calculating second derivatives of population growth rates for ecology and evolution. Methods in Ecology and Evolution, 5, 473-482.
Sibly, R, Hansen, F & Forbes, V (2000) Confidence intervals for population growth rate of organisms with two-stage life histories. Oikos, 88, 335-340.
Silvertown, J, Franco, M, & Menges, E (1996) Interpretation of elasticity matrices as an aid to the management of plant populations for conservation. Conservation Biology, 10, 591-597.
Skalski, J, Millspaugh, J, Dillingham, P & Buchanan, R (2007) Calculating the variance of the finite rate of population change from a matrix model in Mathematica. Environmental Modelling and Software, 22, 359-364.
Slomke, A, Lankester, M, & Peterson, W (1995) Infrapopulation dynamics of Parelaphostrongylus tenuis in white-tailed deer. Journal of Wildlife Diseases, 32(2): 125-135.
Smith, G, Murillo-Garcia, O, Hostetler, J, Mearns, R, Rollie, C, Newton, I, McGrady, M, & Oli, M (2015) Demography of population recovery: survival and fidelity of peregrine falcons at various stages of population recovery. Oecologia, 178, 391-401.
Spanos, A (2010) Akaike-type criteria and the reliability of inference: Model selection versus statistical model specification. Journal of Econometrics 158:204-220.
Spanos, A (2014) Recurring controversies about P-values and confidence intervals revisited. Ecology, 95, 645-651.
Stahl, J, & Oli, M (2006) Relative importance of avian life-history variables to population growth rate. Ecological Modelling, 198, 22–39,
Starfield, A (1997) A pragmatic approach to modeling for wildlife management. Journal of Wildlife Management, 61:2, 261-270.
Stenseth, N, Viljugrein, H, Saitoh, T, Hansen, T, Kittilsen, M, Bølviken, E. et al (2003) Seasonality, density dependence, and population cycles in Hokkaido voles. Proceedings of the National Academy of Sciences, 100, 11478–11483.
Stephens, P, Buskirk, S, Hayward, G, & Martinez del Rio, C (2005) Information theory and hypothesis testing: a call for pluralism. J. Applied Ecol, 42, 4-12.
Stott I (2016) Perturbation analysis of transient population dynamics using matrix projection models. Methods in Ecology and Evolution, 7, 666-678.
Stott I, Hodgson D, & Townley S (2012) Popdemo: an R package for population demography using projection matrix analysis. Methods in Ecology and Evolution, 3, 797-802.
Stott, I, Franco, M, Carslake, D, Townley, S, & Hodgson, D (2010) Boom or bust? A comparative analysis of transient population dynamics in plants. Journal of Ecology, 98:2, 302-311.
Stott, I, Hodgson, D, & Townley, S (2012) Popdemo: An R package for population demography using projection matrix analysis. Methods in Ecology and Evolution, 3, 797-802.
Stott, I, Townley, S, & Hodgson, D (2011) A framework for studying transient dynamics of population projection matrix models. Ecology Letters, 14, 959-970.
Strong, D (1980) Null hypotheses in ecology. Synthese, 43, 271–285.
Strong, D, A Whipple, A. L. Child, L, & Dennis, B (1999) Model selection for a subterranean trophic cascade: root-feeding caterpillars and entomopathogenic nematodes. Ecology, 80, 2750-2761.
Stuart, A, & Ord, K (1998) In - Kendall’s Advanced Theory of Statistics. 6th Edition, Volume 1, Wiley. London, United Kingdom.
Sturtz S, Ligges U, Gelman A (2005) R2winbugs: A Package for Running Winbugs From R. J Stat Software 12:1–16
Symonds, M & Moussalli, A (2011) A brief guide to model selection, multimodel inference and model averaging in behavioural ecology using Akaike's information criterion. Behav Ecol Sociobiol, 65, 13–21.
Takeuchi, K. 1976. Distribution of informational statistics and a criterion for model fitting. Suri-Kagaku (Mathematical Sciences) 153:12-18 (In Japanese)
Taper, M & S Lele eds (2004) The nature of scientific evidence: statistical, philosophical and empirical considerations. The University of Chicago Press, Chicago.
Taper, M and J Ponciano. 2016. Evidential statistics as a statistical modern synthesis to support 21st century science. Population Ecology 58:9-29.
Tong, H (1990) -In: Nonlinear time series: a dynamical systems approach. Oxford University Press, London, United Kingdom.
Townley, S, & Hodgson, D (2008) Erratum et addendum: transient amplification and attenuation in stage-structured population dynamics. Journal of Applied Ecology, 45:6, 1836-1839.
Tuljapurkar, S (1989) An uncertain life: demography in random environments. Theoretical Population Biology, 35, 227-294.
Tuljapurkar, S (1990) Population dynamics in variable environments. Lecture notes in Biomathematics Vol. 85. Springer, New York, New York, USA.
Tuljapurkar, S (1994) Stochastic demography and life histories. In - Frontiers in Mathematical Biology, S.A. Levin (ed.), Springer Verlag, 254-262.
Tuljapurkar, S (1997) Demographic uncertainty and the stable equivalent population. Mathematical Computational Modeling, 26, 39-56.
Tuljapurkar, S (2002) Population Biology. In - Encyclopedia of Population, Paul Demeny and Geoff McNicol (Eds.), Macmillan, New York, New York, USA.
Tuljapurkar, S (2003) The Emergence of Modern Human Mortality Patterns. In: The Evolution of Population Biology - Modern Synthesis. Editors: Rama Singh, Marcy Uyenoyama, and Subodh Jain. Cambridge University Press.
Tuljapurkar, S (2008) Stable population theory. In - The New Palgrave Dictionary of Economics. 2nd Edition (eds) Steven N. Durlauf and Lawrence E. Blume. Palgrave Macmillan, London, United Kingdom.
Turchin, P (1995) Population regulation: old arguments and a new synthesis. In: Population Dynamics: new approaches and synthesis (eds Cappucino, N. & Price, P.W.) Academic Press San Diego, California, USA.
Ueta, M, & V Masterov (2000) Estimation by A Computer Simulation of Population Trend of Steller’s Sea Eagles. Pages 111–116 In M. Ueta & M. J. Mcgrady (Eds.) First Symposium on Steller’s & White-Tailed Sea Eagles in East Asia. Wild Bird Society of Japan, Tokyo, Japan.
van Groenendael, J, de Kroon, H, & Caswell, H (1988) Projection matrices in population biology. Trends in Ecology and Evolution, 3, 264-269.
Van Sickle, J, Attwell, C, & Craig, G (1987) Estimating population growth rate from an age distribution of natural deaths. Journal of Wildlife Management, 51, 941-948.
Vaughan, D, & Saila, S (1976) A method for determining mortality rates using the Leslie matrix. Transactions of the American Fisheries Society, 105, 380-383.
Walker, G (2007) Public Participation as Participatory Communication in Environmental Policy Decision-Making: From Concepts to Structured Conversations. Environmental Communication 1:99–110.
Ward, E (2008) A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools. Ecological Modelling, 211, 1-10.
Whittingham, M, P. Stephens, R. Bradbury, & R. Freckleton (2006) Why do we still use stepwise modelling in ecology and behavior? Journal of Animal Ecology 75, 1182-1189.
Wiedenmann J, Fujiwara M, & Mangel M (2009) Transient population dynamics and viable stage or age distributions for effective conservation and recovery. Biological Conservation, 142, 2990-2996.
Wilks, S (1938) The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Statist. 9, 60-62.
Woiwod, I, & Hanski, I (1992) Patterns of density dependence in moths and aphids. Journal of Animal Ecology, 61, 619–629.
Wood, P (1992) Habitat use, movements, migration patterns, and survival rates of subadult Bald Eagles in north Florida. Ph.D. dissertation, Univ. of Florida, Gainesville, FL U.S.A.
Wootton, J, & Bell, D (1992) A metapopulation model of the peregrine falcon in California: viability and management strategies. Ecological Applications, 2, 307–321
Wyllie, I & Newton, I (1991) Demography of an increasing population of sparrowhawks. Journal of Animal Ecology, 60, 749-766.
Xu, C, & Gertner, G (2009) Uncertainty analysis of transient population dynamics. Ecological Modelling, 220, 283-293.
Yaw, T, Neumann, K, Bernard, L, Cancilla, J, Evans, T, Martin-Schwarze, A, & Zaffarano, B (2017) Lead poisoning in bald eagles admitted to wildlife rehabilitation facilities in Iowa, 2004-2014. Journal of Fish and Wildlife Management 8(2): 465-473.
Yearsley, J (2004) Transient population dynamics and short-term sensitivity analysis of matrix population models. Ecological Modelling, 177, 245-258.
Yoccoz, N (1991) Use, overuse, and misuse of significance tests in evolutionary biology and ecology. Bulletin of the Ecological Society of America, 72, 106–111.