Scaling integral projection models for analyzing size demography. (English) Zbl 1331.91145

Summary: Historically, matrix projection models (MPMs) have been employed to study population dynamics with regard to size, age or structure. To work with continuous traits, in the past decade, integral projection models (IPMs) have been proposed. Following the path for MPMs, currently, IPMs are handled first with a fitting stage, then with a projection stage. Model fitting has, so far, been done only with individual-level transition data. These data are used in the fitting stage to estimate the demographic functions (survival, growth, fecundity) that comprise the kernel of the IPM specification. The estimated kernel is then iterated from an initial trait distribution to obtain what is interpreted as steady state population behavior. Such projection results in inference that does not align with observed temporal distributions. This might be expected; a model for population level projection should be fitted with population level transitions. S. Ghosh et al. [J. Agric. Biol. Environ. Stat. 17, No. 4, 693–699 (2012; Zbl 1302.62256)] offer a remedy by viewing the observed size distribution at a given time as a point pattern over a bounded interval, driven by an operating intensity. They propose a three-stage hierarchical model. At the deepest level, demography is driven by an unknown deterministic IPM. The operating intensities are allowed to vary around this deterministic specification. Further uncertainty arises in the realization of the point pattern given the operating intensities. Such dynamic modeling, optimized by fitting data observed over time, is better suited to projection. Here, we address scaling of population IPM modeling, with the objective of moving from projection at plot level to projection at the scale of the eastern U.S. Such scaling is needed to capture climate effects, which operate at a broader geographic scale, and therefore anticipated demographic response to climate change at larger scales. We work with the Forest Inventory Analysis (FIA) data set, the only data set currently available to enable us to attempt such scaling. Unfortunately, this data set has more than 80% missingness; less than 20% of the 43,396 plots are inventoried each year. We provide a hierarchical modeling approach which still enables us to implement the desired scaling at annual resolution. We illustrate our methodology with a simulation as well as with an analysis for two tree species, one generalist, one specialist.


91D20 Mathematical geography and demography
62P12 Applications of statistics to environmental and related topics
62M30 Inference from spatial processes
62D05 Sampling theory, sample surveys


Zbl 1302.62256
Full Text: DOI arXiv Euclid


[1] Bechtold, W. A. and Patterson, P. L. (2005). The enhanced forest inventory and analysis program: National sampling design and estimation procedures. General Technical Report SRS-80 edn. USDA Forest Service, Southern Research Station, Asheville, NC.
[2] Canham, C. D. and Thomas, R. Q. (2010). Frequency, not relative abundance, of temperate tree species varies along climate gradients in eastern North America. Ecology 91 3433-3440.
[3] Caswell, H. (2001). Matrix Population Models : Construction , Analysis and Interpretation , 2nd ed. Sinauer, Sunderland, MA.
[4] Caswell, H. (2008). Perturbation analysis of nonlinear matrix population models. Demographic Research 18 59-116.
[5] Clark, J. S., Bell, D., Dietze, M. et al. (2010). Models for demography of plant populations. In The Oxford Handbook of Applied Bayesian Analysis (T. O’Hagan and M. West, eds.) 431-481. Oxford Univ. Press, Oxford.
[6] Daly, C., Halbleib, M., Smith, J. I., Gibson, W. P., Doggett, M. K., Taylor, G. H., Curtis, J. and Pasteris, P. P. (2008). Physiographically sensitive mapping of climatological temperature and precipitation across the conterminous United States. International Journal of Climatology 28 2031-2064.
[7] Dennis, B., Desharnais, R. A., Cushing, J. M. and Costantino, R. F. (1995). Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments. Ecological Monographs 65 261-281.
[8] Dennis, B., Desharnais, R. A., Cushing, J. M. and Costantino, R. F. (1997). Transitions in population dynamics: Equilibria to periodic cycles to aperiodic cycles. Journal of Animal Ecology 66 704-729.
[9] Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns , 2nd ed. Arnold, London. · Zbl 1021.62076
[10] Easterling, M. R., Ellner, S. P. and Dixon, P. M. (2000). Size-specific sensitivity: Applying a new structured population model. Ecology 81 694-708.
[11] Ellner, S. P. and Rees, M. (2006). Integral projection models for species with complex demography. Am. Nat. 167 410-428.
[12] Ellner, S. P. and Rees, M. (2007). Stochastic stable population growth in integral projection models: Theory and application. J. Math. Biol. 54 227-256. · Zbl 1116.92050
[13] Ghosh, S., Gelfand, A. E. and Clark, J. S. (2012). Inference for size demography from point pattern data using integral projection models (with discussion). J. Agric. Biol. Environ. Stat. 17 641-699. · Zbl 1302.62255
[14] Guisan, A. and Rahbeck, C. (2011). SESAM-A new framework integrating macroecological and species distribution models for predicting spatio-temporal patterns of species assemblages. Journal of Biogeography 38 1433-1444.
[15] Keyfitz, N. and Caswell, H. (2005). Applied Mathematical Demography , 3rd ed. Springer, New York. · Zbl 1104.91063
[16] Møller, J. and Waagepetersen, R. P. (2004). Statistical Inference and Simulation for Spatial Point Processes . Chapman & Hall/CRC, Boca Raton. · Zbl 1044.62101
[17] Rees, M. and Ellner, S. P. (2009). Integral projection models for populations in temporally varying environments. Ecological Monographs 79 575-594.
[18] Smith, W. B., Miles, P. D., Perry, C. H. and Pugh, S. A. (2009). Forest resources of the United States, 2007. General Technical Report WO-78 edn. USDA Forest Service, Washington Office, Washington, DC.
[19] Tuljapurkar, S. and Caswell, H. (1997). Structured-Population Models in Marine , Terrestrial , and Freshwater Systems . Chapman & Hall, New York.
[20] Wakefield, J. (2009). Multi-level modelling, the ecologic fallacy, and hybrid study designs. Int. J. Epidemiol. 38 330-336.
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