Out of the jungle of demographic analyses

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By Satu Ramula Associate Editor

Demographic models have been used for decades in biology to assess population status or extinction risk, to guide management, and to explore evolutionary responses. Interestingly, these models are now more popular than ever. For instance, Crone et al. (2011) showed in their review that the use of matrix population models are currently expanding in plant ecology, and surely these are not the only types of demographic models that are doing so well. So, why is this expansion happening now?

A gap between models and their potential users – Caswell’s book (2001) gave a gentle introduction to matrix models and was accompanied with some code snippets to calculate demographic parameters. At about the same time, some applications of demographic models were illustrated in the book “Population Viability Analysis” edited by Beissinger and McCullough (2002). After reading this book, it was easy to become inspired about stochastic or Bayesian population models. However, there was still a gap between demographic models and their potential users, because the translation of demographic analyses into computer codes required advanced programming skills, which might have been beyond the repertoire of an ordinary biologist.

Life is getting easier – Morris and Doak began to fill the gap between demographic models and their use in practice by providing Matlab codes for the analyses of population dynamics in their book (2002). They went through a number of examples for various purposes, from simple count-based models to more complex stochastic models together with computer codes. These codes were definitely great news for those who could afford a commercial software license! A few years later another big step forward happened, when Stubben and Milligan (2007) launched the package ‘popbio’ for matrix models using R: the software that is freely available and commonly used among biologists. ‘Popbio’ contains basic functions for deterministic and stochastic matrix models to calculate, for example, the long-term population growth rate, sensitivities and elasticities to changes in matrix elements or in underlying vital rates.

Further advances – Since more and more biologists have adopted R, a large number of R packages are available to ease the use of demographic models. Stott et al. (2012) developed the R package ‘popdemo’ that is targeted to analyse short-term, transient population dynamics based on matrix population models. It is a nice complement to ‘popbio’ and can be particularly useful when used to explore potential management options for populations of rare or invasive species that are rarely at stable state. Transient analyses may well reveal that populations are growing or declining much faster in the short-run than predicted by the analyses of their long-term dynamics.

The most recent R package for structured demographic models is ‘IPMpack’ (Metcalf et al. 2013), which is based on integral projection models (IPMs). IPMs are similar to matrix models, but describe demographic processes as a continuous function of, for example. individuals’ size or age, potentially containing multiple covariates. These models have become increasingly popular over the past ten years because of their flexibility to address various eco-evolutionary questions. However, IPMs are more challenging to construct than the matrix models, and ‘IPMpack’ is the first R package providing a practical guide for their construction. It contains functions to explore model structure and to calculate demographic parameters, including some stochastic ones.

In addition to structured population models, R packages are of course available for non-structured models as well. For instance, the package ‘marked’ (Laake et al. 2013) produces survival and abundance estimates for animals based on large mark-recapture data, and the package ‘BaSTA’ estimates survival based on incomplete mark-recapture data of natural populations (Colchero et al. 2012).

There has been considerable change to the demographic field, from the days when programming skills were required, to today when many demographic models can, in principle, be used without any previous experience of programming. The rapid development of numerous open-source demographic packages means that demographic models and related analyses are widely available for all biologists. It also provides a great opportunity to introduce these methods to students at the beginning of their studies. Taking the first step is now easy!

By Satu Ramula
Associate Editor, Methods in Ecology and Evolution

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2 thoughts on “Out of the jungle of demographic analyses

  1. An excellent advertisement for demographic models — nice to see! One small comment: IPMs are perhaps easier to construct than matrix models, and certainly not harder. Christ, even I can do it!

  2. Depends what you mean by “construct” an IPM.

    It’s as easy to write down the equation representing an IPM as it is to write down the equation representing a matrix model. But analyzing an IPM involves some harder mathematical concepts than analysis of a matrix model (see, for example, appendix C in Ellner and Rees 2006, Am Nat 167:410-428). And even when you’ve got the concepts sorted, the numerical techniques can still be quite hard (see Baker, 1977, The Numerical Treatment of Integral Equations). For example, Williams et al 2012 (Ecology 93:2008-2014) is exactly the kind of complicated numerical problem that you would really like somebody else to have solved for you in software.

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