Development and application of a novel age x size classified demographic model for individual-level, long-term data

Background/Question/Methods

Matrix population models (MPMs) and integral projection models (IPMs) have become some of the most widely used tools to explore population dynamics in organisms varying wildly in life cycle complexity, ecological strategies, and life expectancy, from bacteria to killer whales or sequoias. In both MPMs and IPMs, individuals are categorized according to a state variable (often size) in order to predict survival, change in state, reproduction, and recruitment, and thus examine the drivers of its population dynamics. Yet, most demographic models are unable to explore the potential interactive effects of size and age. The inclusion of the effects of size and age on vital rates is particularly important in organisms where age and size are not tightly coupled, such as certain modular organisms with the ability to shrink and re-grow quickly.

Here we build a age x size classified matrix population model, using Poisson-based regressions obtained from an IPM, with an IPMs to describe the population dynamics of the desert herbaceous perennial Cryptantha flava (Boraginaceae).  The model is based on 16 years of long-term, publicly available data, including a set of permanent plots with individuals under background precipitation, and two sets of permanent plots with rain-out shelters. The model is developed using the vec-permutation approach, and used to examine the absolute impact of changes in vital rates at all sizes and observed ages on the population growth rate. 

Results/Conclusions

We found significant effects of both age and size, in both the control plots and rain-out shelter experiments, on all vital rates (survival, growth, probability of reproduction, and number of flowering stalks per capita). All vital rates scaled positively with size. Some rates (e.g., the number of flowering rosettes produced per capita) declined in older individuals. This indicates that senescence, the decline in demographic performance due to physiological deterioration, may manifest in some fitness components but not in others. The age x size interactions were positive and significant for some vital rates (e.g. growth in control plants), negative and significant for others (e.g. growth in both treatments), and not significant for other vital rates (e.g. number of flowering rosettes). 

The age x size classified matrix model was then used to contrast the underlying vital rates and to explain why population growth rates in the treated plots were higher than in the plots receiving background precipitation.