| [1] | Cushing JM, Zhou Y (1994) The net reproductive value and stability in matrix population models. Natural Resources Modeling 8: 297–333.
|
| [2] | Caswell H (2001) Matrix population models: Construction, analysis, and interpretation. Second edition. Sunderland: Sinauer Associates.
|
| [3] | Caswell H (2009) Stage, age, and individual stochasticity in demography. Oikos 118: 1763–1782.
|
| [4] | Rhodes EC (1940) Population mathematics I. Journal of the Royal Statistical Society 103: 61–89.
|
| [5] | de Camino-Beck T, Lewis MA (2007) A new method for calculating net reproductive rate from graph reduction with applications to the control of invasive species. Bulletin of Mathematical Biology 69: 1341–1354.
|
| [6] | Grafen A (1988) On the uses of data on lifetime reproductive success. In: Clutton-Brock TH, editor. Reproductive success. Chicago: University of Chicago Press. pp. 454–471.
|
| [7] | Partridge L (1989) Lifetime reproductive success and life-history evolution. In: Newton I, editor. Lifetime reproduction in birds. New York: Academic Press. pp. 421–440.
|
| [8] | Stearns SC (1992) The evolution of life histories. Oxford: Oxford University Press.
|
| [9] | Mylius SD, Diekmann O (1995) On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos 74: 218–224.
|
| [10] | Kozlowski J (1999) Adaptation: a life history perspective. Oikos 86: 185–194.
|
| [11] | Diekmann O, Heesterbeek JAP, Metz JAJ (1990) On the definition and the computation of the basic reproduction number R0 in models for infectious diseases in heterogeneous population. Journal of Mathematical Biology 28: 365–382.
|
| [12] | Heesterbeek JAP (2002) A brief history of R0 and a recipe for its calculation. Acta Biotheoretica 50: 189–204.
|
| [13] | van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 180: 29–48.
|
| [14] | Clutton-Brock TH (1988) Reproductive success. Chicago: University of Chicago Press.
|
| [15] | Newton I (1989) Lifetime reproduction in birds. New York: Academic Press.
|
| [16] | Carey JR (2003) Longevity: The biology and demography of life span. Princeton: Princeton University Press.
|
| [17] | Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WE (2005) Superspreading and the effect of individual variation on disease emergence. Nature 438: 355–359.
|
| [18] | Engen S, Lande R, Saether B-E (2005) Effective size of a fluctuating age-structured population. Genetics 170: 941–954.
|
| [19] | Rockwell RF, Barrowclough GF (1995) Effective population size and lifetime reproductive success. Conservation Biology 9: 1225–1233.
|
| [20] | Clutton-Brock TH (1998) Reproductive skew, concessions, and limited control. Trends in Ecology and Evolution 13: 288–292.
|
| [21] | Haydock J, Koenig WD (2002) Reproductive skew in the polygynandrous acorn woodpecker. Proceedings of the National Academy of Sciences 99: 7178–7183.
|
| [22] | Crow JF (1958) Some possibilities for measuring selection intensities in man. Human Biology 30: 1–13.
|
| [23] | Tuljapurkar S, Steiner UK, Orzack SH (2009) Dynamic heterogeneity in life histories. Ecology Letters 12: 93–106.
|
| [24] | Steiner UK, Tuljapurkar S, Orzack SH (2010) Dynamic heterogeneity and life history variability in the kittiwake. Journal of Animal Ecology 79: 436–444.
|
| [25] | Barrowclough GF, Rockwell RF (1993) Variance of lifetime reproductive success: estimation based on demographic data. American Naturalist 141: 281–295.
|
| [26] | Caswell H (2006) Applications of Markov chains in demography. In: Langville AN, Stewart WJ, editors. MAM2006: Markov Anniversary Meeting. Raleigh: Boson Books. pp. 319–334.
|
| [27] | Croxall JP, Rothery P, Pickering SPC, Prince PA (1990) Reproductive performance, recruitment, and survival of wandering albatrosses Diomedea exulans at Bird Island, South Georgia. Journal of Animal Ecology 59: 775–796.
|
| [28] | Fujiwara M, Caswell H (2002) Estimating population projection matrices from multi-stage mark-recapture data. Ecology 83: 3257–3265.
|
| [29] | Caswell H, Fujiwara M (2004) Beyond survival estimation: mark-recapture, matrix population models, and population dynamics. Annals of Biological Conservation 27: 471–488.
|
| [30] | Hunter CM, Caswell H (2005a) Selective harvest of sooty shearwater chicks: effects on population dynamics and sensitivity. Journal of Animal Ecology 74: 589–600.
|
| [31] | Lawler RL, Caswell H, Richard AF, J. Ratsirarson J, Dewar RE, et al. (2009) Population dynamics of Verreauxs sifaka in a stochastic rainfall environment. Oecologia 161: 491–504.
|
| [32] | Hunter CM, Caswell H, Runge MC, Regehr EV, Amstrup SC, et al. (2010) Climate change threatens polar bear populations: a stochastic demographic analysis. Ecology 91: 2883–2898.
|
| [33] | Jenouvrier S, Caswell H, Barbraud C, Weimerskirch H (2010) Mating behavior, population growth and the operational sex ratio: a periodic two-sex model approach. American Naturalist 175: 739–752.
|
| [34] | Steiner UK, Tuljapurkar S (2011) A neutral theory for life histories, computing variances in fitness components. Unpublished manuscript.
|
| [35] | Howard RA (1960) Dynamic programming and Markov processes. New York: Wiley.
|
| [36] | Hatori H (1966) On Markov chains with rewards. Kodai Mathematics Seminar Reports 18: 184–192.
|
| [37] | Puterman ML (1994) Markov decision processes. New York: Wiley.
|
| [38] | Frigui I, Alfa AS (1999) Analysis of a discrete time table polling system with MAP input and time-limited service discipline. Telecommunication Systems 12: 51–77.
|
| [39] | Paramonov Y, Hauka M (2010) Using the theory of Markov chains and a semi-Markov process to estimate the reliability of aircraft and airlines. pp. 104–111. Proceedings of the 10th International conference on Reliability and Statistics in Transportation and Communication, Riga, Latvia.
|
| [40] | Feichtinger G (1971) Stochastische modelle demographischer prozesse. Lecture notes in operations research and mathematical systems. Berlin: Springer-Verlag.
|
| [41] | ochran ME, Ellner S (1992) Simple methods for calculating age-based life history parameters for stage-structured populations. Ecological Monographs 62: 345–364.
|
| [42] | Benito F (1982) Calculating the variance in Markov processes with random reward. Trabajos de Estadistica y de Investigacion Operativa 33: 73–85.
|
| [43] | Munz P, Hudea I, Imad J, Smith RJ (2009) When zombies attack!: mathematical modelling of an outbreak of zombie infection. In: Tchuenche JM, Chiyaka C, editors. Infectious disease modelling research progress. Hauppauge: Nova Science Publishers. pp. 133–150.
|
| [44] | Mangel M, Clark CW (1988) Dynamic modeling in behavioral ecology. Princeton: Princeton University Press.
|
| [45] | Sladky K, van Dijk NM (2004) Total reward variance in discrete and continuous time Markov chains. pp. 319–325. Operations Research Proceedings 2004: Selected Papers of the Annual International Conference of the German Operations Research Society.
|
| [46] | van Dijk NM, Sladky K (2006) On the total reward variance for continuous-time Markov reward chains. Journal of Applied Probability 43: 1044–1052.
|
| [47] | Evan M, Hastings N, Peacock B (1993) Statistical distributions. Second edition. New York: Wiley-Interscience.
|
| [48] | Horvitz CC, Tuljapurkar S (2008) Stage dynamics, period survival, and mortality plateaus. American Naturalist 171: 203–215.
|
| [49] | Cushing JM, Ackleh AS (2011) A net reproductive number for periodic matrix models. Journal of Biological Dynamics. DOI:10.1080/17513758.2010.544410.
|
| [50] | Hunter CM, Caswell H (2005b) The use of the vec-permutation matrix in spatial matrix population models. Ecological Modelling 188: 15–21.
|
| [51] | Henderson HV, Searle SR (1981) The vec-permutation matrix, the vec operator and Kronecker products: a review. Linear and Multilinear Algebra 9: 271–288.
|
| [52] | Gems D (2002) Ageing. In: Lee DL, editor. The biology of nematodes. New York: Taylor and Francis. pp. 413–455.
|
| [53] | Kenyon C (2005) The plasticity of aging: insights from long-lived mutants. Cell 120: 449–460.
|
| [54] | Chen J, Senturk D, Wang JL, Muller HG, Carey JR, et al. (2007) A demographic analysis of the fitness cost of extended longevity in Caenorhabditis elegans. Journal of Gerontology: Biological Sciences 62A: 126–135.
|
| [55] | Levin LA, Caswell H, Bridges T, DiBacco C, Cabrera D, et al. (1996) Demographic response of estuarine polychaetes to pollutants: Life table response experiments. Ecological Applications 6: 1295–1313.
|
| [56] | Bridges TS, Levin LA, Cabrera D, Plaia G (1994) Effects of sediment amended with sewage, algae, or hydrocarbons on growth and reproduction in two opportunistic polychaetes. Journal of Experimental Marine Biology and Ecology 177: 99–119.
|
| [57] | Human Mortality DatabaseUniversity of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de. Data downloaded July 2010.
|
| [58] | Human Fertility DatabaseMax Planck Institute for Demographic Research (Germany) and the Vienna Institute of Demography (Austria). Available at www.humanfertility.org. Data downloaded July 2010.
|
| [59] | Knight TM (2004) The effects of herbivory and pollen limitation on a declining population of Trillium grandiflorum. Ecological Applications 14: 915–928.
|
| [60] | Knight TM, Caswell H, Kalisz S (2009) Population growth rate of a common understory herb decreases non-linearly across a gradient of deer herbivory. Forest Ecology and Management 257: 1095–1103.
|
| [61] | Picó XF, de Kroon H, Retana J (2002) An extended flowering and fruiting season has few demographic effects in a Mediterranean perennial herb. Ecology 83: 1991–2004.
|
| [62] | Pendergrass KL, Miller PM, Kauffman JB, Kaye TN (1999) The role of prescribed burning in maintenance of an endangered plant species, Lomatium bradshawii. Ecological Applications 9: 1420–1329.
|
| [63] | Caswell H, Kaye TN (2001) Stochastic demography and conservation of an endangered perennial plant (Lomatium bradshawii) in a dynamic fire regime. Advances in Ecological Research 32: 1–51.
|
| [64] | Kaye TN, Pendergrass K, Findley K, Kauffman JB (2001) The effect of fire on the population viability of an endangered prairie plant. Ecological Applications 11: 1366–1380.
|
| [65] | Kaye TN, Pyke DA (2003) The effect of stochastic technique on estimates of population viability from transition matrix models. Ecology 1464–1476.
|
| [66] | Metz JAJ, Diekmann O (1986) The dynamics of physiologically structured populations. Berlin: Springer-Verlag.
|
| [67] | Clutton-Brock T, Sheldon BC (2010) Individuals and populations: the role of long-term, individual-based studies of animals in ecology and evolutionary biology. Trends in Ecology and Evolution 25: 562–573.
|
| [68] | Kendall MG, Stuart A (1963) The advanced theory of statistics. Volume 1, Second edition. London: Charles Griffin.
|
| [69] | Iosifescu M (1980) Finite Markov processes and their applications. New York: Wiley.
|
