Stat 534
Fall 2013
References: Population Models
Books:
Clark, J.S. 2007. Models for Ecological Data. Princeton Univ. Press, Princeton NJ.
Intermediate-level text, emphasizing plants and hierarchical Bayesian methods.
Cousens, R. and Mortimer, M. 1995. Dynamics of Weed Populations. Cambridge Univ. Press
Application of these ideas to weeds. Chap 5 describes population models.
Daley, D.J. and Gani, J. 1999. Epidemic Modelling. Cambridge Univ. Press.
Application of these ideas to diseases. More mathematical than the other books in this
section.
Haddon, M. 2011. Modelling and Quantitative Methods in Fisheries, 2nd ed. Chapman and
Hall/CRC, Boca Raton
Introduction to models in fisheries, many include density dependence (stock-recruitment)
Hilborn, R. and Walters, C. 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. Chapman and Hall, New York.
Older, but a very readable review of models. pre-MCMC Bayesian methods.
Morris, W.F. and Doak, D.F. 2002. Quantitative Conservation Biology Sinauer, Sunderland
MA.
All about Population Viability Analysis, i.e. incorporating various forms of stochasticity
into population models.
Nisbet, R. M. and Gurney, W. S. C. 1982. Modelling Fluctuating Populations Wiley, Chichester.
Comprehensive summary of continuous time models. Old, but still extremely useful.
Mathematical details and lots of insight.
Nowak, M.A. and May, R.M. 2000. Virus Dynamics. Oxford Univ. Press
Application to virus populations. Currently, very active area of research. Quite readable.
Royama, T. 1992. Analytical Population Dynamics. Chapman and Hall, London.
Theory and examples, mostly involving differential equations for continuous time.
Williams, B.K., Nichols, J.D. and Conroy, M.J. 2002. Analysis and Management of Animal
Populations. Academic Press, San Diego.
Huge compendium of all sorts of quantitative techniques. Source of two of the readings
for this section of material.
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Structured Populations:
Caswell, H. 2001, Matrix Population Models: Construction, Analysis, and Interpretation,
2nd. ed. Sinauer, Sunderland MA.
Comprehensive treatise on all aspects of matrix models for structured populations. My
lectures draw heavily from this book.
Horvitz, C.C. and Schemske, D.W. 1995. Spatiotemporal variation in demographic transitions
of a tropical understory herb - projection matrix analysis. Ecol Monogr 65:155-192.
One example (the first?) of the megamatrix approach to spatial and temporal variability.
Tuljapurkar, S. and Caswell, H. (eds). Structured-Population Models in Marine, Terrestrial,
and Freshwater Systems. Chapman and Hall, New York.
Edited volume that provides overview of all approaches (matrix, stochastic matrix, delaydifferential equation, partial differential equation) for modeling structured populations.
Stochastic models:
Dennis, B. and Costantino, R. F. 1988. Analysis of steady-state populations with the Gamma
abundance model: application to Tribolium. Ecology 69:1200-1213.
Develops a stochastic differential equation version of the logistic model. The stationary
distribution of population size is a Gamma distribution.
Haridas, C.V., Keeler, K.H., and Tenhumberg, B. 2015. Variation in the local population
dynamics of the short-lived Opuntia macrorhiza (Cactaceae). Ecology 96:800-807.
Results from stochastic matrix models for five individual populations are substantially
different from results of a deterministic model that lumps the populations.
Kaye, T.N. and Pyke, D.A. 2003. The effect of stochastic technique on estimates of population
viability from transition matrix models. Ecology 84: 1464-1476
Estimates stochastic log lambda from different stochastic models (variants of random
element, random matrix) for 5 different species. Estimate of mean depends on the model,
but ranking does not.
Nakaoka, M. 1996. Dynamics of age- and size-structured populations in fluctuating environemnts: applications of stochastic matrix models to natural populations. Researches in
Population Ecology 38:141-152.
Summarizes and compares published applications of stochastic matrix models. Many are
random sequence of environments models, some are random matrix models.
Tuljapurkar, S. 1990. Population Dynamics in Variable Environments. Lecture Notes in
Biomathematics, #85, Springer-Verlag, New York.
Source for much of the theory of random sequence of environments models.
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Computing:
Bolker, B.M. 2008. Ecological Models and Data in R Princeton Univ. Press.
Covers use of R for standard statistical methods and basic theory (likelihood, simulation).
Kennedy, W. J., Jr. and Gentle, J. E. 1980. Statistical Computing. Marcel Dekker, Inc. New
York
Chapter 6 is a pretty comprehensive list of ways to generate discrete and continuous
random numbers.
Estimating parameters: (Caswell’s book has an extensive section on this too).
Raftery, A. E., Givens, G. H., and Judith, E. Z. 1995. Inference from a deterministic population dynamcis model for Bowhead Whales (with discussion). Journal of the American
Statistical Association 90:402-430.
Uses Bayesian methods to combine data from different sources. The population model is
quite complex, so I find the paper hard to follow.
Vandermeer, J. 1978, Choosing category size in a stage projection matrix. Oecologia 32:79-84.
Bias vs. variance tradeoff in converting a continous size measure into discrete stages.
Wood, S. N. 1994. Obtaining birth and mortality patterns from structured population trajectories. Ecological Monographs 64:23-44.
Describes an inverse method of estimating stage-specific parameters from non-marked
individuals.
Elasticity:
Enright, N. J., Franco, M. and Silvertown, J. 1995. Comparing plant life histories using
elasticity analysis: the importance of life span and the number of life-cycle stages. Oecologia
104:79-84.
Empirical evaluation of how model structure influences elasticity coefficients. Has references to the early 1990’s debate on evolutionary interpretations of elasticity.
deKroon, H., van Groenendael, J. and Ehrlén, J. 2000. Elasticities: a review of methods and
model limitations. Ecology 81:607-618.
Overview article that starts a collection of articles on elasticity.
Caswell, H. 2007. Sensitivity analysis of transient population dynamics. Ecology Letters.
10:1-15.
Evaluates derivatives of nt and change in nt to matrix parameters, where nt is the population size at time t, before convergence to asymptotic growth rate. Can be done without
evaluating eigenvalues or eigenvectors, but requies matrix calculus.
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Density dependence in matrix models:
Caswell, H. 2009. Sensitivity and elasticity of density-dependent population models. Journal
of Difference Equations and Applications. 15:349-369.
Derives the derivatives of equilbrium density with respect to matrix parameters for nonlinear (i.e. density dependent) matrix models
Caswell, H. 2008. Perturbation analysis of nonlinear matrix population models. Demographic
Research 18:59-115.
Longer, more leisurely coverage of nonlinear matrix models. Also considers the twosex problem, which is also non-linear. If you ever wanted a short introduction to matrix
differential calculus, this is a good paper to read.
Bayesian approaches:
Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. 2003 Bayesian Data Analysis, 2nd.
ed. Chapman and Hall, London.
My favorite text on Bayesian methods.
Gelman, A. and Hill, J. 2007. Data Analysis using Regression and Multilevel/Hierarchical
Models. Cambridge Univ. Press, Cambridge.
Very readable introductory treatment of hierarchical linear models, but covers a lot of
ground. Includes R code. This is first place I look for practical Bayesian advice.
King, R., Morgan, B., Gimenez, O., and Brooks, S. 2009. Bayesian Analysis for Population
Ecology. CRC Press, Boca Raton FL.
Intermediate level book with many useful ideas
Link, W.A. and Barker, R.J. 2010. Bayesian Inference with ecological applications. Academic
Press, Amsterdam.
Intro to Bayes text with good ecological examples. My favorite intro Bayes book.
Ludwig, D. 1996. Uncertainty and the assessment of extinction probabilities. Ecological
Applications 6:1067-1076.
Uses Bayesian methods to incorporate effects of uncertainty into simple population dynamics models.
McCarthy, M.A. 2007. Bayesian Methods for Ecology Cambridge Univ. Press.
Introductory text covering Bayesian versions of intro methods followed by 3 case studies
on mark-recapture and population modeling. Has a tutorial on running WinBUGS
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Meyer, R. and Millar, R.B. 1999. BUGS in Bayesian stock assessments. Can. J. Fish. Aquat.
Sci. 56: 1078-1086
Describes a state-space model and parameter estimating for it using bugs. Renate and
Russ have coauthored a variety of other papers applying hierarchical Bayes methods to fisheries models.
Parent, E. and Rivot, E. 2013. Introduction to Hierarchical Bayesian Modeling for Ecological
Data. CRC Press, Boca Raton FL.
Lots of population ecology examples.
Ver Hoef, J. M. 1996. Parametric empirical Bayes methods for ecological applications. Ecological Applications 6: 1047-1055.
Introductory illustration of a Bayesian approach to a combining trend information and
single estimates in a population monitoring problem. Part of a special feature on applications
of Bayesian methods in ecology. First paper in that feature (by Ellison) is an introductory
exposition of Bayesian methods, written for biologists.
Applications (a few of a very large number):
Crowder, L. B., Crouse, D. T., Heppell, S. S., and Martin, T. H. 1994. Predicting the impact
of turtle excluder devices on loggerhead sea turtle populations. Ecological Applications 4:437445.
The paper underlying my loggerhead turtle story in class. Uses elasticity to evaluate
different conservation options. Apparently responsible for major policy change: reducing
mortality of older individuals (TED’s) instead of increasing nesting success.
Davis, A. S., Dixon, P.M., and Liebman, M. 2004. Using matrix models to determine cropping
system effects on annual weed demography. Ecological Applications. 14: 655-668.
One of three papers applying matrix models to weed demography in different crop rotations (corn/soybean, corn/soybean/triticale, ...). This paper compares prospective (sensitivity and elasticity) to retrospective (Life Table Response Experiment) approaches. Other two
papers appeared in Weed Science.
Doak, D., Karieva, P., and Klepetka, B. 1994. Modeling population viability for the desert
tortoise in the western Mojave Desert. Ecological Applications 4:446-460.
Uses a random-matrix-elements stochastic model to evaluate consequences of environmental variability and compare management options.
Dixon, P., Friday, N., Ang, P., Heppell, S., and Kshatriya, M. 1997. Sensitivity analysis of
structured-population models for management and conservation. pp 471-514 in Tuljapurkar,
S. and Caswell, H. (eds). Structured-Population Models in Marine, Terrestrial, and Freshwater Systems. Chapman and Hall, New York.
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Three examples of using sensitivity analysis to evaluate management strategies. Third
example presents Tuljarpurkar’s method in an abbreviated but readable form and compares
deterministic and stochastic estimates of elasticity.
Flockhart, D.T.T., Pichancourt, J-B, Norris, D.R., and Martin, T.G. 2015. Unravelling the
annual cycle in a migratory animal: breeding-season habitat loss drives population declines
of monarch butterflies. J. Animal Ecology 84:155-165.
Spatially-structured, density-dependent, stochastic matrix model for monarch butterflies.
Uses periodic matrix model ideas to express annual changes as products of seasonal-specific
transition probabilities.
Hunter, C., et al. 2010. Climate change threatens polar bear populations: a stochastic
demographic analysis. Ecology 91:2883-2897.
Uses deterministic and stochastic (random environment) matrix models to evaluate population growth rates of polar bears as a function of sea ice extent. Uses Life Table Response
Experiment analyses to compare years with high and low sea ice. Last two sentences of the
abstract: ”The resulting stochastic population projections showed drastic declines in the polar bear population by the end of the 21st century. These projections were instrumental in
the decision to list the polar bear as a threatened species under the U.S. Endangered Species
Act.”’
Pardini, E. et al. 2009. Complex population dynamics and control of the invasive biennial,
Alliaria petiolata (garlic mustard). Ecological Applications 19:387-397.
Uses density-dependent stage-structured model to assess potential impact of management
strategies on an invasive plant, using demographic data collected at the invasion front.
Wooten, M.B., Wikle, C.K, Dorazio, R.M. and Royle, J.A. 2007. Hierarchical spatiotemporal
matrix models for characterizing invasions. Biometrics 63:558-567.
A hierarchical model for population growth and spread, illustrated by data on the Eurasian
Collared-Dove.
Concerns:
Bierzychudek, P. 1999. Looking backwards: assessing the projections of a transition matrix
model. Ecological Applications 9:1278-1287.
Uses long term data to assess whether population projection matrices constructed in 1978
predicted future fates of two populations. One model did; the other did not. Problems
include inadequate data and lambda not representing short-term dynamics.
Lubben, J., Tenhumberg, B., Tyre, A. and Rebarber, R. 2007. Management recommendations based on matrix population models: the importance of considering biological limits.
Biological Conservation 141:517-523.
Example that cautions to not ignore biology. A transition matrix that ignores senescence
gives misleading recommendations.
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Mills, L.S., Doak, D.F, and Wisdom, M.J. 1999. Reliability of conservation actions based on
elasticity analysis of matrix models. Conservation Biology 13:815-829.
Argues for caution in translating elasticity/sensitivity into management decisions. Elasticities depend on all the elements in a matrix, so changes in one poorly estimated number
can change the ranking of elasticities.
Prasad, S., Krishnadas, M., McConkey, K.R. 2014. FORUM: The tangled causes of population decline in two harvested plant especies: a comment on Ticktin et al. (2012). J. Applied
Ecology 51:642-647.
Argues a previous analysis using matrix population models was misleading because of an
unbalanced design and substitution of missing data for key parameters.
Wooten, J.T., and Bell, D.A. 2014. Assessing predictions of population viability analysis:
peregrine falcon populations in California. Ecological Applications 24:1251-1257.
Compared previously published projections from stage-structured population models to
population trajectories. Observed population counts were within the uncertainty of stochastic
simulations, both for models with and models without density dependence.
Integral Projection Models
Easterling, M. R., Ellner, S. P., and Dixon, P. 2000, Size-specific sensitivity: applying a new
structured population model. Ecology 81:694-708.
The original integral projection model paper.
Ellner, S.P. and Rees, M. 2006. Integral Projection Models for species with complex demography. American Naturalist 167:410-428.
The paper that really got people interested in IPM’s. Provides “... a unified development
that makes IPMs a practical alternative to deterministic matrix models for structured populations with continuous trait variation”. Gives all the math and derives a stability criterion
for a model with density dependence.
Mandle, L., Ticktin, T, and Zuidema, P.A. 2015. Resilience of palm populations to disturbance is determined by interactive effects of fire, herbivory and harvest. J. Ecology 103:
1032-1043.
Construct IPM’s that include the influences of three environmental effects for 14 mountain
date palm populations. The interactions between environmental effects are important to the
dynamics.
Metcalf, C.J.E., Horvitz, C.C., Tuljapurkar, S., and Clark, D.A. 2009. A time to grow and
a time to die: a new way to analyze the dynamics of size, light, age, and death of tropical
trees. Ecology 90:2766-2778
Uses IPM’s and age-from-stage analysis to understand the relationship between size, age,
and life expectancy in a dynamic environment.
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Vindenes, Y., Engen, S., and Saether, B-E. 2011. Integral projection models for finite populations in a stochastic environment. Ecology 92:1146-1156.
Develops a stochastic version of the IPM.
Vindenes Y., Saether, B.E., and Engen, S. 2012. Effects of demographic structure on key
properties of stochastic density-independent population dynamics. Theoretical Population
Biology 82:253-263
Develops many properties of stochastic IPMs and compares them to stochastic matrix
models.
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