# Life Table Response Experiment year effect for multiple places

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The Life Table Response Experiments Year Effect for Multiple Places workflow provides an environment to analyse two or more matrices (e.g., two or more matrices of different years from one place) at two or more different locations. The objective of this workflow is to determine the effects of the research years (2 or more) on λ. This workflow performs a fixed LTRE, one way design (Caswell 2001).

LTRE is a retrospective analysis (Caswell 1989), beginning with data on the vital rates and on λ under two or more sets of environmental conditions (in this case 2 or more years from different places) (Horvitz, Schemske and Caswell 1997). The goal of the analysis is to quantify the contribution of each of the vital rates to the variability in λ. (Caswell 1989, 1996, 2001 in Horvitz, Schemske and Caswell 1997).

Fixed Treatments: Decomposing Years Treatment Effects for multiple places

A fixed-effect analysis treats the matrices as representative of particular conditions, either experimental or natural (high vs. low nutrients in a one-way model, for example, or year and spatial location in a two-way model). The goal is to determine how much a treatment level (in this case year) on λ is contributed by each of the vital rates. The analysis uses a linear approximation in which the sensitivities appear as slopes. The effect of a treatment on λ depends on its effect on each matrix entry and on the sensitivity of λ to that entry. (Horvitz, Schemske and Caswell 1997).

For more details of the analysis see: Retrospective Analyses: Fixed Treatments (page 262 in Horvitz, Schemske and Caswell 1997) and Chapter 10 Life Table Response Experiments (page 258 in Caswell 2001).

This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359.

This workflow was created using and based on Package ‘popbio’ in R. (Stubben & Milligan 2007; Stubben, Milligan & Nantel 2011).

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Literature

Caswell, H. 1989. The analysis of life table response experiments. I. Decomposition of treatment effects on population growth rate. Ecological Modelling 46: 221-237.

Caswell, H. 1996. Demography meets ecotoxicology: Untangling the population level effects of toxic substances. Pp. 255-292 in M. C. Newman and C. H. Jagoe, eds., Ecotoxicology: A Hierarchical Treatment. Lewis, Boca Raton, Fla.

Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.

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

Horvitz, C., D.W. Schemske, and Hal Caswell. 1997. The relative "importance" of life-history stages to population growth: Prospective and retrospective analyses. In S. Tuljapurkar and H. Caswell. Structured population models in terrestrial and freshwater systems. Chapman and Hall, New York.

Oostermeijer J.G.B., M.L. Brugman, E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.

Stubben, C & B. Milligan. 2007. Estimating and Analysing Demographic Models Using the popbio Package in R. Journal of Statistical Software 22 (11): 1-23

Stubben, C., B. Milligan, P. Nantel. 2011. Package ‘popbio’. Construction and analysis of matrix population models. Version 2.3.1

ion 2.3.1