pe_mv: Estimate the mean-variance portfolio effect
In seananderson/ecofolio: Tools to quantify metapopulation portfolio effects

Description Usage Arguments Details Value References Examples

View source: R/pe_mv.r

Takes a matrix of abundance or biomass data and returns various estimates of the mean-variance portfolio effect. Options exist to fit various mean-variance models and to detrend the time series data.

1 2	pe_mv(x, type = c("linear", "linear_robust", "quadratic", "linear_quad_avg", "linear_detrended", "loess_detrended"), ci = FALSE, na.rm = FALSE)

`x`	A matrix or dataframe of abundance or biomass data. The columns should represent different subpopulations or species. The rows should represent the values through time.
`type`	Type of model to fit to the log(variance)-log(mean) data. Options are: `linear`: linear regression (the default), `linear_robust`: robust linear regression `quadratic`: quadratic regression `linear_quad_avg`: AICc-weighted model averaging of linear and quadratic regression `linear_detrended`: detrend the time series with a linear model before estimating z from a linear regression `loess_detrended`: detrend the time series with a loess smoother before estimating z from a linear regression
`ci`	Logical value describing whether a 95% confidence interval should be calculated and returned (defaults to `TRUE`).
`na.rm`	A logical value indicating whether `NA` values should be row-wise deleted.

This version of the portfolio effect consists of dividing the CV of a theoretical single population (single asset system) that has the same overall mean but with the variance scaled according to the mean-variance relationship by the CV of the combined total population. The calculation of the portfolio CV is the same as in pe_avg_cv but the calculation of the single asset system CV is different.

Currently, confidence intervals can only be returned for linear, linear_detrended, and loess_detrended. Otherwise, the value of ci will be automatically turned to FALSE. It is not obvious what a confidence interval should be given that the quadratic term in the quadratic and linear-quadratic averaged versions are bounded at 0.

A numeric value representing the portfolio effect that takes into account the mean-variance relationship. If confidence intervals were requested then a list is returned with the portfolio effect (pe) and 95% confidence interval (ci).

Anderson, S.C., A.B. Cooper, N.K. Dulvy. 2013. Ecological prophets: Quantifying metapopulation portfolio effects. Methods in Ecology and Evolution. In Press.

Doak, D., D. Bigger, E. Harding, M. Marvier, R. O'Malley, and D. Thomson. 1998. The Statistical Inevitability of Stability-Diversity Relationships in Community Ecology. Amer. Nat. 151:264-276.

Tilman, D., C. Lehman, and C. Bristow. 1998. Diversity-Stability Relationships: Statistical Inevitability or Ecological Consequence? Amer. Nat. 151:277-282.

Tilman, D. 1999. The Ecological Consequences of Changes in Biodiversity: A Search for General Principles. Ecology 80:1455-1474.

Taylor, L. 1961. Aggregation, Variance and the Mean. Nature 189:732-735. doi: 10.1038/189732a0.

Taylor, L., I. Woiwod, and J. Perry. 1978. The Density-Dependence of Spatial Behaviour and the Rarity of Randomness. J. Anim. Ecol. 47:383-406.

data(pinkbr)
pe_mv(pinkbr[,-1], ci = TRUE)
## Not run: 
pe_mv(pinkbr[,-1], type = "quadratic") # same as linear in this case
pe_mv(pinkbr[,-1], type = "linear_quad_avg")
pe_mv(pinkbr[,-1], type = "linear_robust")
pe_mv(pinkbr[,-1], type = "linear_detrended", ci = TRUE)
pe_mv(pinkbr[,-1], type = "loess_detrended", ci = TRUE)

## End(Not run)