Portal de Periódicos da CAPES

Elasticities: A Review of Methods and Model Limitations

2000; Wiley; Volume: 81; Issue: 3 Linguagem: Inglês

10.2307/177363

1939-9170

Hans de Kroon, Jan van Groenendael, Johan Ehrlén,

Structural Engineering and Vibration Analysis

EcologyVolume 81, Issue 3 p. 607-618 Special Feature ELASTICITIES: A REVIEW OF METHODS AND MODEL LIMITATIONS Hans de Kroon, Hans de Kroon Nature Conservation and Plant Ecology Group, Department of Environmental Sciences, Wageningen University, Bornsesteeg 69, 6708 PD Wageningen, The Netherlands E-mail: [email protected]Search for more papers by this authorJan van Groenendael, Jan van Groenendael Department of Aquatic Ecology and Environmental Biology, University of Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The NetherlandsSearch for more papers by this authorJohan Ehrlén, Johan Ehrlén Department of Ecological Botany, Uppsala University, Villavägen 14, S-752 36 Uppsala, Sweden Present address: Department of Botany, Stockholm University, S-109 91 Stockholm, Sweden.Search for more papers by this author Hans de Kroon, Hans de Kroon Nature Conservation and Plant Ecology Group, Department of Environmental Sciences, Wageningen University, Bornsesteeg 69, 6708 PD Wageningen, The Netherlands E-mail: [email protected]Search for more papers by this authorJan van Groenendael, Jan van Groenendael Department of Aquatic Ecology and Environmental Biology, University of Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The NetherlandsSearch for more papers by this authorJohan Ehrlén, Johan Ehrlén Department of Ecological Botany, Uppsala University, Villavägen 14, S-752 36 Uppsala, Sweden Present address: Department of Botany, Stockholm University, S-109 91 Stockholm, Sweden.Search for more papers by this author First published: 01 March 2000 https://doi.org/10.1890/0012-9658(2000)081[0607:EAROMA]2.0.CO;2Citations: 402 Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract Elasticity is a perturbation measure in matrix projection models that quantifies the proportional change in population growth rate as a function of a proportional change in a demographic transition (growth, survival, reproduction, etc.). Elasticities thus indicate the relative "importance" of life cycle transitions for population growth and maintenance. In this paper, we discuss the applications of elasticity analysis, and its extension, loop analysis, in life history studies and conservation. Elasticity can be interpreted as the relative contribution of a demographic parameter to population growth rate. Loop analysis reveals the underlying pathway structure of the life cycle graph. The different kinds of results of the two analyses in studies of life histories are emphasized. Because elasticities quantify the relative importance of life cycle transitions to population growth rate, it is generally inferred that management should focus on the transitions with the largest elasticities. Such predictions based on elasticities seem robust, but we do identify three situations where problems may arise. The mathematical properties and biological constraints that underlie these pitfalls are explained. Examples illustrate the additional information that needs to be taken into account for a sensible use of elasticities in population management. We conclude by indicating topics that are in need of research. Literature Cited Armitage, K. B. and J. F. Downhower . 1974. Demography of yellow-bellied marmot populations. Ecology 55: 1233–1255. 10.2307/1935452 Web of Science®Google Scholar Basilio de Matos, M. and D. M. Silva Matos . 1998. Mathematical constraints on transition matrix elasticity analysis. Journal of Ecology 86: 706–708. 10.1046/j.1365-2745.1998.00294.x Web of Science®Google Scholar Batista, W. B., W. J. Platt, and R. E. Macchiavelli . 1998. Demography of a shade-tolerant tree (Fagus grandifolia) in a hurricane-disturbed forest. Ecology 79: 38–53. 10.1890/0012-9658(1998)079[0038:DOASTT]2.0.CO;2 Google Scholar Benton, T. G. and A. Grant . 1996. How to keep fit in the real world: elasticity analyses and selection pressures on life histories in a variable environment. American Naturalist 147: 115–139. 10.1086/285843 Web of Science®Google Scholar Boyce, M. S. . 1977. Population growth with stochastic fluctuations in the life table. Theoretical Population Biology 12: 366–373. 10.1016/0040-5809(77)90050-8 CASPubMedWeb of Science®Google Scholar Brault, S. and H. Caswell . 1993. Pod-specific demography of killer whales (Orcinus orca). Ecology 74: 1444–1454. 10.2307/1940073 Web of Science®Google Scholar Caswell, H. . 1978. A general formula for the sensitivity of population growth rate to changes in life history parameters. Theoretical Population Biology 14: 215–230. 10.1016/0040-5809(78)90025-4 CASPubMedWeb of Science®Google Scholar Caswell, H. . 1982. Optimal life histories and the maximization of reproductive value: a general theorem for complex life cycles. Ecology 63: 1218–1222. 10.2307/1938846 Web of Science®Google Scholar Caswell, H. . 1985. The evolutionary demography of clonal reproduction. Pages 187–224 in J. B. C. Jackson, L. W. Buss, and R. E. Cook, editors. Population biology and evolution of clonal organisms. Yale University Press, New Haven, Connecticut, USA. Google Scholar Caswell, H. . 1986. Life cycle models for plants. Lectures on mathematics in the life sciences 18: 171–233. Google Scholar Caswell, H. . 1989a. Analysis of life table response experiments. I. Decomposition of effects on population growth rate. Ecological Modeling 46: 221–237. 10.1016/0304-3800(89)90019-7 CASWeb of Science®Google Scholar Caswell, H. . 1989b. Matrix population models. Construction, analysis and interpretation. Sinauer, Sunderland, Massachusetts, USA. Google Scholar Caswell, H. . 1996a. Analysis of life table response experiments. II. Alternative parameterizations for size- and stage-structured models. Ecological Modeling 88: 73–82. 10.1016/0304-3800(95)00070-4 Web of Science®Google Scholar Caswell, H. . 1996b. Second derivatives of population growth rate: calculation and applications. Ecology 77: 870–879. 10.2307/2265507 Web of Science®Google Scholar Caswell, H. . 1997. Matrix methods for population analysis. Pages 19–58 in S. Tuljapurkar and H. Caswell, editors. Structured population models in marine, terrestrial and freshwater systems. Chapman and Hall, New York, New York, USA. Google Scholar Caswell, H. . 2000. Prospective and retrospective perturbation analyses: their roles in conservation biology. Ecology 81: 619–627. 10.1890/0012-9658(2000)081[0619:PARPAT]2.0.CO;2 Web of Science®Google Scholar Caswell, H. and A. M. John . 1992. From the individual to the population in demographic models. Pages 36–61 in D. L. DeAngelis and L. J. Gross, editors. Individual-based models and approaches in ecology. Chapman and Hall, New York, New York, USA. Google Scholar Caswell, H., R. J. Naiman, and R. Morin . 1984. Evaluating the consequences of reproduction in complex salmonid life cycles. Aquaculture 43: 123–134. 10.1016/0044-8486(84)90016-4 Web of Science®Google Scholar Charlesworth, B. . 1994. Evolution in age-structured populations. Cambridge University Press, Cambridge, UK. Google Scholar Crouse, D. T., L. B. Crowder, and H. Caswell . 1987. A stage-based population model for loggerhead sea turtles and implications for conservation. Ecology 68: 1412–1423. 10.2307/1939225 Web of Science®Google Scholar Crowder, L. B., D. T. Crouse, S. S. Heppell, and T. H. Martin . 1994. Predicting the impact of turtle excluder devices on loggerhead sea turtle populations. Ecological Applications 4: 437–445. 10.2307/1941948 Web of Science®Google Scholar Cunnington, D. C. and R. J. Brooks . 1996. Bet-hedging theory and eigenelasticity: a comparison of the life histories of loggerhead sea turtles (Caretta caretta) and snapping turtles (Chelydra serpentina). Canadian Journal of Zoology 74: 291–296. 10.1139/z96-036 Web of Science®Google Scholar de Kroon, H., A. Plaisier, and J. van Groenendael . 1987. Density-dependent simulation of the population dynamics of a perennial grassland species, Hypochaeris radicata. Oikos 50: 3–12. 10.2307/3565395 Web of Science®Google Scholar de Kroon, H., A. Plaisier, J. van Groenendael, and H. Caswell . 1986. Elasticity: the relative contribution of demographic parameters to population growth rate. Ecology 67: 1427–1431. 10.2307/1938700 Web of Science®Google Scholar Doak, D. F., P. Kareiva, and B. Klepetka . 1994. Modeling population viability for the desert tortoise in the western Mojave desert. Ecological Applications 4: 446–460. 10.2307/1941949 Web of Science®Google Scholar Drechsler, M. . 1998. Sensitivity analysis of complex models. Biological Conservation 86: 401–412. 10.1016/S0006-3207(98)00021-4 Web of Science®Google Scholar Easterling, M. R., S. P. Ellner, and P. Dixon . 2000. Size-specific sensitivity: a new structured population model. Ecology 81: 694–708. 10.1890/0012-9658(2000)081[0694:SSSAAN]2.0.CO;2 Web of Science®Google Scholar Ehrlén, J. . 1995. Demography of the perennial herb Lathyrus vernus: II. Herbivory and population dynamics. Journal of Ecology 83: 297–308. 10.2307/2261568 Web of Science®Google Scholar Ehrlén, J. and J. van Groenendael . 1998. Direct perturbation analysis for better conservation. Conservation Biology 12: 470–474. 10.1111/j.1523-1739.1998.96420.x Web of Science®Google Scholar Enright, N. J., M. Franco, and J. Silvertown . 1995. Comparing plant life histories using elasticity analysis: the importance of life span and the number of life-cycle stages. Oecologia 104: 79–84. 10.1007/BF00365565 CASPubMedWeb of Science®Google Scholar Eriksson, O. . 1996. Regional dynamics of plants: a review of evidence for remnant, source–sink and metapopulations. Oikos 77: 248–258. 10.2307/3546063 Web of Science®Google Scholar Gaillard, J. M., M. Festa-Bianchet, and N. Yoccoz . 1998. Population dynamics of large herbivores: variable recruitment with constant adult survival. Trends in Ecology and Evolution 13: 58–63. 10.1016/S0169-5347(97)01237-8 CASPubMedWeb of Science®Google Scholar Grant, A. and T. G. Benton . 2000. Elasticity analysis for density-dependent populations in stochastic environments. Ecology 81: 680–693. 10.1890/0012-9658(2000)081[0680:EAFDDP]2.0.CO;2 Web of Science®Google Scholar Heppell, S. S. . 1998. Application of life-history theory and population model analysis to turtle conservation. Copeia 1998: 367–375. 10.2307/1447430 Web of Science®Google Scholar Heppell, S. S., L. B. Crowder, and H. Caswell . 2000. Life histories and elasticity patterns: perturbation analysis for species with minimal demographic data. Ecology 81: 654–665. 10.1890/0012-9658(2000)081[0654:LHAEPP]2.0.CO;2 Web of Science®Google Scholar Heppell, S. S., L. B. Crowder, and D. T. Crouse . 1996a. Model to evaluate headstarting as a management tool for long-lived turtles. Ecological Applications 6: 556–565. 10.2307/2269391 Web of Science®Google Scholar Heppell, S. S., C. J. Limpus, D. T. Crouse, N. B. Frazer, and L. B. Crowder . 1996b. Population model analysis for the Loggerhead Sea Turtle, Caretta caretta, in Queensland. Wildlife Research 23: 143–159. 10.1071/WR9960143 Web of Science®Google Scholar Heppell, S. S., J. R. Walters, and L. B. Crowder . 1994. Evaluating management alternatives for red-cockaded woodpeckers: a modeling approach. Journal of Wildlife Management 58: 479–487. 10.2307/3809319 Web of Science®Google Scholar Hoffmann, W. A. . 1999. Fire frequency and population dynamics of woody plants in a Neotropical savanna: matrix model projections. Ecology 80: 1354–1369. 10.1890/0012-9658(1999)080[1354:FAPDOW]2.0.CO;2 Web of Science®Google Scholar Horvitz, C. C. and D. W. Schemske . 1995. Spatiotemporal variation in demographic transitions of a tropical understory herb: projection matrix analysis. Ecological Monographs 65: 155–192. 10.2307/2937136 Google Scholar Horvitz, C. C., D. W. Schemske, and H. Caswell . 1997. The relative "importance" of life-history stages to population growth: prospective and retrospective analyses. Pages 247–271 in S. Tuljapurkar and H. Caswell, editors. Structured population models in marine, terrestrial and freshwater systems. Chapman and Hall, New York, New York, USA. Google Scholar Hubbell, S. P. and P. A. Werner . 1979. On measuring the intrinsic rate of increase of populations with heterogeneous life histories. American Naturalist 113: 277–293. 10.1086/283385 Web of Science®Google Scholar Lande, R. . 1982. A quantitative genetic theory of life history evolution. Ecology 63: 607–615. 10.2307/1936778 Web of Science®Google Scholar Levin, L., H. Caswell, T. Bridges, C. Dibacco, D. Cabrera, and G. Plaia . 1996. Demographic responses of estuarine polychaetes to pollutants: life table response experiments. Ecological Applications 6: 1295–1313. 10.2307/2269608 Web of Science®Google Scholar Lewis, E. R. . 1976. Applications of discrete and continuous network theory to linear population models. Ecology 57: 33–47. 10.2307/1936396 Web of Science®Google Scholar Lewontin, R. C. . 1965. Selection for colonizing ability. Pages 77–91 in H. G. Baker and G. L. Stebbins, editors. The genetics of colonizing species. Academic Press, New York, New York, USA. Google Scholar Ludwig, D. . 1999. Is it meaningful to estimate a probability of extinction? Ecology 80: 298–310. 10.1890/0012-9658(1999)080[0298:IIMTEA]2.0.CO;2 Web of Science®Google Scholar McGraw, J. B. and H. Caswell . 1996. Estimation of individual fitness from life-history data. American Naturalist 147: 47–64. 10.1086/285839 Web of Science®Google Scholar Mendoza, G. A. and A. Setyarso . 1986. A transition matrix forest growth model for evaluating alternative harvesting schemes in Indonesia. Forest Ecology and Management 15: 219–228. 10.1016/0378-1127(86)90068-X Web of Science®Google Scholar Menges, E. . 1990. Population viability analysis for an endangered plant. Conservation Biology 4: 52–62. 10.1111/j.1523-1739.1990.tb00267.x Web of Science®Google Scholar Messerton-Gibbons, M. . 1993. Why demographic elasticities sum to one: a postscript to de Kroon et al. Ecology 74: 2467–2468. 10.2307/1939599 Web of Science®Google Scholar Mills, L. S., D. F. Doak, and M. J. Wisdom . 1999. The reliability of conservation actions based on elasticity analysis of matrix models. Conservation Biology 13: 815–829. 10.1046/j.1523-1739.1999.98232.x PubMedWeb of Science®Google Scholar Moloney, K. A. . 1988. Fine-scale spatial and temporal variation in the demography of a perennial bunchgrass. Ecology 69: 1588–1598. 10.2307/1941656 Web of Science®Google Scholar Nakaoka, M. . 1997. Demography of the marine bivalve Yoldia notabilis in fluctuating environments: an analysis using a stochastic matrix model. Oikos 79: 59–68. 10.2307/3546090 Web of Science®Google Scholar Olmsted, I. and E. R. Alvarez-Buylla . 1995. Sustainable harvesting of tropical trees: demography and matrix models of two palm species in Mexico. Ecological Applications 5: 484–500. 10.2307/1942038 Web of Science®Google Scholar Oostermeijer, J. G B., M. L. Brugman, E. R. de Boer, and H. C M. den Nijs . 1996. Temporal and spatial variation in the demography of Gentiana pneumonanthe, a rare perennial herb. Journal of Ecology 84: 153–166. 10.2307/2261351 Web of Science®Google Scholar Pfister, C. A. . 1998. Patterns of variance in stage-structured populations: evolutionary predictions and ecological implications. Proceedings of the National Academy of Sciences of the USA 95: 213–218. 10.1073/pnas.95.1.213 CASPubMedWeb of Science®Google Scholar Roff, D. A. . 1992. The evolution of life histories: theory and analysis. Chapman and Hall, New York, New York, USA. Google Scholar Sæther, B-E. and Ø Bakke . 2000. Avian life history variation and contribution of demographic traits to the population growth rate. Ecology 81: 642–653. 10.1890/0012-9658(2000)081[0642:ALHVAC]2.0.CO;2 Web of Science®Google Scholar Sæther, B. E., T. H. Ringsby, and E. Røskaft . 1996. Life history variation, population processes and priorities in species conservation: towards a reunion of research paradigms. Oikos 77: 217–226. 10.2307/3546060 Web of Science®Google Scholar Schemske, D. W., B. C. Husband, M. H. Ruckelshaus, C. Goodwillie, I. M. Parker, and J. D. Bishop . 1994. Evaluating approaches to the conservation of rare and endangered plants. Ecology 75: 584–606. 10.2307/1941718 Web of Science®Google Scholar Shea, K. and D. Kelly . 1998. Estimating biocontrol agent impact with matrix models: Carduus nutans in New Zealand. Ecological Applications 8: 824–832. 10.1890/1051-0761(1998)008[0824:EBAIWM]2.0.CO;2 Web of Science®Google Scholar Shea, K., M. Rees, and S. N. Wood . 1994. Trade-offs, elasticities and the comparative method. Journal of Ecology 82: 951–957. 10.2307/2261457 Web of Science®Google Scholar Silvertown, J., M. Franco, and K. McConway . 1992. A demographic interpretation of Grime's triangle. Functional Ecology 6: 130–136. 10.2307/2389746 Web of Science®Google Scholar Silvertown, J., M. Franco, and E. Menges . 1996. Interpretation of elasticity matrices as an aid to the management of plant populations for conservation. Conservation Biology 10: 591–597. 10.1046/j.1523-1739.1996.10020591.x Web of Science®Google Scholar Silvertown, J., M. Franco, I. Pisanty, and A. Mendoza . 1993. Comparative plant demography—relative importance of life-cycle components to the finite rate of increase in woody and herbaceous perennials. Journal of Ecology 81: 465–476. 10.2307/2261525 Google Scholar Stearns, S. C. . 1992. The evolution of life histories. Oxford University Press, Oxford, UK. Google Scholar Valverde, T. and J. Silvertown . 1998. Variation in the demography of a woodland understorey herb (Primula vulgaris) along the forest regeneration cycle: projection matrix analysis. Journal of Ecology 86: 545–562. 10.1046/j.1365-2745.1998.00280.x Web of Science®Google Scholar van Groenendael, J., H. de Kroon, and H. Caswell . 1988. Projection matrices in population biology. Trends in Ecology and Evolution 3: 264–269. 10.1016/0169-5347(88)90060-2 PubMedWeb of Science®Google Scholar van Groenendael, J., H. de Kroon, S. Kalisz, and S. Tuljapurkar . 1994. Loop analysis: evaluating life history pathways in population projection matrices. Ecology 75: 2410–2415. 10.2307/1940894 Web of Science®Google Scholar van Tienderen, P. H. . 1995. Life cycle trade-offs in matrix population models. Ecology 76: 2482–2489. 10.2307/2265822 Web of Science®Google Scholar van Tienderen, P. H. . 2000. Elasticities and the link between demographic and evolutionary dynamics. Ecology 81: 666–679. 10.1890/0012-9658(2000)081[0666:EATLBD]2.0.CO;2 Web of Science®Google Scholar Vandermeer, J. . 1978. Choosing category size in a stage projection matrix. Oecologia 32: 79–84. 10.1007/BF00344691 PubMedWeb of Science®Google Scholar Wardle, G. M. . 1998. A graph theory approach to demographic loop analysis. Ecology 79: 2539–2549. 10.1890/0012-9658(1998)079[2539:AGTATD]2.0.CO;2 Web of Science®Google Scholar Werner, P. A. and H. Caswell . 1977. Population growth rates and age vs. stage-distribution models for teasel (Dipsacus sylvestris huds). Ecology 58: 1103–1111. 10.2307/1936930 Web of Science®Google Scholar Wisdom, M. J. and L. S. Mills . 1997. Sensitivity analysis to guide population recovery: prairie-chickens as an example. Journal of Wildlife Management 61: 302–312. 10.2307/3802585 Web of Science®Google Scholar Wisdom, M. J., L. S. Mills, and D. F. Doak . 2000. Life stage simulation analysis: estimating vital-rate effects on population growth for conservation. Ecology 81: 628–641. 10.1890/0012-9658(2000)081[0628:LSSAEV]2.0.CO;2 Web of Science®Google Scholar Zagt, R. J. . 1997. Tree demography in the tropical rain forest of Guyana. Dissertation. University of Utrecht, Utrecht, The Netherlands. Google Scholar Citing Literature Volume81, Issue3March 2000Pages 607-618 ReferencesRelatedInformation