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  • Articles  (6)
  • Sensitivity analysis  (4)
  • Population growth rate  (2)
  • 1
    Publication Date: 2022-05-25
    Description: Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Theoretical Population Biology 82 (2012): 329-339, doi:10.1016/j.tpb.2012.03.008.
    Description: Periodic matrix models are frequently used to describe cyclic temporal variation (seasonal or interannual) and to account for the operation of multiple processes (e.g., demography and dispersal) within a single projection interval. In either case, the models take the form of peri- odic matrix products. The perturbation analysis of periodic models must trace the e ects of parameter changes, at each phase of the cycle, on output variables that are calculated over the entire cycle. Here, we apply matrix calculus to obtain the sensitivity and elasticity of scalar-, vector-, or matrix-valued output variables. We apply the method to linear models for periodic environments (including seasonal harvest models), to vec-permutation models in which individ- uals are classi ed by multiple criteria, and to nonlinear models including both immediate and delayed density dependence. The results can be used to evaluate management strategies and to study selection gradients in periodic environments.
    Description: This research was supported by NSF Grant DEB-0816514, by a Research Award from the Alexander von Humboldt Foundation, and by WHOI Academic Programs Funds.
    Keywords: Periodic environments ; Seasonal models ; Nonlinear models ; Sensitivity analysis ; Elasticity analysis ; Matrix calculus
    Repository Name: Woods Hole Open Access Server
    Type: Preprint
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  • 2
    Publication Date: 2022-05-25
    Description: Author Posting. © University of Chicago Press, 2004. This article is posted here by permission of University of Chicago Press for personal use, not for redistribution. The definitive version was published in American Naturalist 164 (2004): E46-E61.
    Description: We present a Markov chain model of succession in a rocky subtidal community based on a long-term (1986–1994) study of subtidal invertebrates (14 species) at Ammen Rock Pinnacle in the Gulf of Maine. The model describes successional processes (disturbance, colonization, species persistence, and replacement), the equilibrium (stationary) community, and the rate of convergence. We described successional dynamics by species turnover rates, recurrence times, and the entropy of the transition matrix. We used perturbation analysis to quantify the response of diversity to successional rates and species removals. The equilibrium community was dominated by an encrusting sponge (Hymedesmia) and a bryozoan (Crisia eburnea). The equilibrium structure explained 98% of the variance in observed species frequencies. Dominant species have low probabilities of disturbance and high rates of colonization and persistence. On average, species turn over every 3.4 years. Recurrence times varied among species (7–268 years); rare species had the longest recurrence times. The community converged to equilibrium quickly (9.5 years), as measured by Dobrushin’s coefficient of ergodicity. The largest changes in evenness would result from removal of the dominant sponge Hymedesmia. Subdominant species appear to increase evenness by slowing the dominance of Hymedesmia. Comparison of the subtidal community with intertidal and coral reef communities revealed that disturbance rates are an order of magnitude higher in coral reef than in rocky intertidal and subtidal communities. Colonization rates and turnover times, however, are lowest and longest in coral reefs, highest and shortest in intertidal communities, and intermediate in subtidal communities.
    Description: This research was supported by National Science Foundation grants DEB-9527400, OCE-981267, OCE-9302238, and OCE-0083976 and by the National Oceanic and Atmospheric Administration’s National Undersea Research Program, University of Connecticut—Avery Point.
    Keywords: Markov chain ; Sensitivity analysis ; Transition matrix ; Species diversity ; Entropy ; Dobrushin’s coefficient
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 3
    Publication Date: 2022-05-25
    Description: Author Posting. © Springer, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Bulletin of Mathematical Biology 70 (2008): 1634-1659, doi:10.1007/s11538-008-9312-7.
    Description: Ecological systems with asymptotically stable equilibria may exhibit significant transient dynamics following perturbations. In some cases, these transient dynamics include the possibility of excursions away from the equilibrium before the eventual return; systems that exhibit such amplification of perturbations are called reactive. Reactivity is a common property of ecological systems, and the amplification can be large and long-lasting. The transient response of a reactive ecosystem depends on the parameters of the underlying model. To investigate this dependence, we develop sensitivity analyses for indices of transient dynamics (reactivity, the amplification envelope, and the optimal perturbation) in both continuous- and discrete-time models written in matrix form. The sensitivity calculations require expressions, some of them new, for the derivatives of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix calculus. Sensitivity analysis provides a quantitative framework for investigating the mechanisms leading to transient growth. We apply the methodology to a predator-prey model and a size-structured food web model. The results suggest predator-driven and prey-driven mechanisms for transient amplification resulting from multispecies interactions.
    Description: Financial support provided by NSF grant DEB-0343820, NOAA grant NA03-NMF4720491, the Ocean Life Institute of the Woods Hole Oceanographic Institution, and the Academic Programs Office of the MIT-WHOI Joint Program in Oceanography.
    Keywords: Ecological models ; Transient dynamics ; Reactivity ; Sensitivity analysis ; Consumer-resource interactions ; Matrix population models
    Repository Name: Woods Hole Open Access Server
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  • 4
    Publication Date: 2022-05-25
    Description: Author Posting. © University of Chicago, 2010. This article is posted here by permission of University of Chicago for personal use, not for redistribution. The definitive version was published in American Naturalist 175 (2010): 739-752, doi:10.1086/652436.
    Description: We present a new approach to modeling two‐sex populations, using periodic, nonlinear two‐sex matrix models. The models project the population growth rate, the population structure, and any ratio of interest (e.g., operational sex ratio). The periodic formulation permits inclusion of highly seasonal behavioral events. A periodic product of the seasonal matrices describes annual population dynamics. The model is nonlinear because mating probability depends on the structure of the population. To study how the vital rates influence population growth rate, population structure, and operational sex ratio, we used sensitivity analysis of frequency‐dependent nonlinear models. In nonlinear two‐sex models the vital rates affect growth rate directly and also indirectly through effects on the population structure. The indirect effects can sometimes overwhelm the direct effects and are revealed only by nonlinear analysis. We find that the sensitivity of the population growth rate to female survival is negative for the emperor penguin, a species with highly seasonal breeding behavior. This result could not occur in linear models because changes in population structure have no effect on per capita reproduction. Our approach is applicable to ecological and evolutionary studies of any species in which males and females interact in a seasonal environment.
    Description: H.C. acknowledges support from the National Science Foundation (DEB-0343820 and DEB-0816514) and the Ocean Life Institute and the hospitality of the Max Planck Institute for Demographic Research.
    Keywords: Two‐sex periodic matrix model ; Population structure ; Population growth rate ; Mating systems ; Sex ratio ; Emperor penguin
    Repository Name: Woods Hole Open Access Server
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  • 5
    Publication Date: 2022-05-25
    Description: © The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Journal of Ecology 103 (2015): 202–218, doi:10.1111/1365-2745.12334.
    Description: Schedules of survival, growth and reproduction are key life-history traits. Data on how these traits vary among species and populations are fundamental to our understanding of the ecological conditions that have shaped plant evolution. Because these demographic schedules determine population growth or decline, such data help us understand how different biomes shape plant ecology, how plant populations and communities respond to global change and how to develop successful management tools for endangered or invasive species. Matrix population models summarize the life cycle components of survival, growth and reproduction, while explicitly acknowledging heterogeneity among classes of individuals in the population. Matrix models have comparable structures, and their emergent measures of population dynamics, such as population growth rate or mean life expectancy, have direct biological interpretations, facilitating comparisons among populations and species. Thousands of plant matrix population models have been parameterized from empirical data, but they are largely dispersed through peer-reviewed and grey literature, and thus remain inaccessible for synthetic analysis. Here, we introduce the compadre Plant Matrix Database version 3.0, an open-source online repository containing 468 studies from 598 species world-wide (672 species hits, when accounting for species studied in more than one source), with a total of 5621 matrices. compadre also contains relevant ancillary information (e.g. ecoregion, growth form, taxonomy, phylogeny) that facilitates interpretation of the numerous demographic metrics that can be derived from the matrices. Large collections of data allow broad questions to be addressed at the global scale, for example, in genetics (genbank), functional plant ecology (try, bien, d3) and grassland community ecology (nutnet). Here, we present compadre, a similarly data-rich and ecologically relevant resource for plant demography. Open access to this information, its frequent updates and its integration with other online resources will allow researchers to address timely and important ecological and evolutionary questions.
    Keywords: Big data ; Comparative approach ; Elasticity ; Matrix population model ; Open access ; Plant population and community dynamics ; Population growth rate ; Sensitivity ; Transient dynamics
    Repository Name: Woods Hole Open Access Server
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  • 6
    Publication Date: 2022-05-26
    Description: © The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Methods in Ecology and Evolution 5 (2014): 473–482, doi:10.1111/2041-210X.12179.
    Description: Second derivatives of the population growth rate measure the curvature of its response to demographic, physiological or environmental parameters. The second derivatives quantify the response of sensitivity results to perturbations, provide a classification of types of selection and provide one way to calculate sensitivities of the stochastic growth rate. Using matrix calculus, we derive the second derivatives of three population growth rate measures: the discrete-time growth rate λ, the continuous-time growth rate r = log λ and the net reproductive rate R0, which measures per-generation growth. We present a suite of formulae for the second derivatives of each growth rate and show how to compute these derivatives with respect to projection matrix entries and to lower-level parameters affecting those matrix entries. We also illustrate several ecological and evolutionary applications for these second derivative calculations with a case study for the tropical herb Calathea ovandensis.
    Description: This work was supported by a National Science Foundation Graduate Research Fellowship under Grant 1122374, by NSF Grants DEB-1145017 and DEB1257545, and by Advanced Grant 322989 from the European Research Council.
    Keywords: Eigenvalues ; Hessian matrix ; Invasion exponent ; Matrix population models ; Net reproductive rate ; Sensitivity analysis
    Repository Name: Woods Hole Open Access Server
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