Individual History and the Matrix Projection Model

Post provided by Rich Shefferson

A single time-step projection of a historical matrix projection model (hMPM), for a 7 life stage life history model of Cypripedium parviflorum, the small yellow lady’s slipper. In this case, the vector of biologically plausible stage pairs in time 2 is equal to the full projection matrix multiplied by the vector of biologically plausible stage pairs in time 1.

Matrix projection modeling is a mainstay of population ecology. Ecologists working in natural area management and conservation, as well as in theoretical and academic realms such as the study of life history evolution, develop and use these models routinely. Matrix projection models (MPMs) have advanced dramatically in complexity over the years, originating from age-based and stage-based matrix models parameterized directly from the data, to complex matrices developed from statistical models of vital rates such as integral projection models (IPMs) and age-by-stage models. We consider IPMs to be a class of function-based MPM, while age-by-stage MPMs may be raw or function-based, but are typically the latter due to a better ability to handle smaller dataset. The rapid development of these methods can leave many feeling bewildered if they need to use these methods but lack sufficient understanding of scientific programming and of the background theory to analyze them properly.

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Exploring Population Responses to Environmental Change When There’s Never Enough Data

Post provided by Bethan Hindle

Understanding Population Responses to Environmental Change

Rapid climatic change has increased interest about how populations respond to environmental change. This has broad applications, for example in the management of endangered and economically important species, the control of harmful species, and the spread of disease. At the population level changes in abundance are driven by changes in vital rates, such as survival and fecundity. So studies that track individual survival and reproduction over time can provide useful insights into the drivers of such changes. They allow us to make future population level predictions on things like abundance, extinction risk and evolutionary strategies.

Archbold Biological Station - site of numerous long-term demographic studies, including that of Eryngium cuneifolium used in this paper. ©Reed Bowman

Archbold Biological Station – site of numerous long-term demographic studies, including that of Eryngium cuneifolium used in this paper. ©Reed Bowman

Predicting the future isn’t a simple task though. Anyone whose washing has got soaked through after the weather forecast suggested the day would be dry and sunny will know that (though the accuracy of short term weather forecasts has increased dramatically in recent years). Ideally, if we want to predict what will happen to populations as their environment changes, we would identify the drivers of variation in their survival and reproduction. We do this by asking questions like ‘are years of low survival associated with high rainfall?’ But, this is not a simple task; identifying drivers and the time periods over which they act and accurately estimating their effects requires long-term demographic data.   Continue reading