Intact ecosystems have the capacity for self-regulation, which keeps their complex structure of species – such as animals, plants, fungi and bacteria – in balance. For example, when the population of a species increases, its per capita growth rate decreases, keeping population growth in check. Ecological stability is an important indicator of how well self-regulation works and how “healthy” ecosystems are. Measuring and assessing the stability of ecosystems is therefore crucial for monitoring and conserving biodiversity.

However, quantifying ecological stability is not easy, for three reasons. Firstly, it can be measured at different levels of biological organisation: from the health and physiological condition of individual organisms to populations of individual species to communities of multiple species that can interact and depend on each other. Secondly, it can be assessed using a variety of metrics that capture different levels of the dynamics of the system (individuals, populations or communities) at different stages of response to disturbances. For example, the immediate response of the system to a disturbance may convey a different picture than the long-term recovery rate. Thirdly, biodiversity is currently threatened by a variety of disturbances with very different effects that put species under pressure to adapt. Some disturbances have immediate effects, such as habitat destruction through urbanisation or land use change, which can directly result in the death or displacement of individuals. Other disturbances, such as climate change, affect the viability of species over longer periods of time.

“Although such processes have long been scientifically described and analysed by wildlife biologists and ecologists, there is still no software that allows the quantification of ecological stability taking all these scenarios into account”, says Dr Ludmilla Figueiredo, data and code curator at the German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig and first author of the paper. According to the authors, their work therefore closes an important methodological gap in biodiversity research.

Advanced mathematics made applicable to biodiversity research

The “estar” package was developed for the R programming language, which is widely used in ecological research. R is a free, open-source tool for statistical analysis, data visualisation and machine learning. The package offers functions for calculating eleven established ecosystem stability indicators using corresponding time series data. For example, a time series of immunological measurements for individuals allows the quantification of the stability of their immunological status over time, while a time series of population abundance allows the measurement of population stability. “estar” standardises and facilitates the calculation of these indicators, which are used to evaluate the responses of ecosystems to disturbances at various ecological levels (e.g. population, community).
‘Our R package can be used in two different ways. On the one hand, it offers functions that quantify stability at every organisational level, from the individual to the community, and can be applied to a time series of a system's state variables (e.g. body mass, population numbers or species diversity)”, explains Dr Viktoriia Radchuk, scientist in the Department of Ecological Dynamics at the Leibniz Institute for Zoo and Wildlife Research (Leibniz-IZW) and senior author of the paper. “The stability metrics included in this set comprise invariability, resistance, extent and rate of recovery, persistence, and overall ecological vulnerability.” For example, House sparrows (Passer domesticus) are very common and everyone knows and sees them regularly in cities such as Berlin. Despite being a widely spread species, they have been experiencing a notable decline in population numbers in Europe over the last decades. Not much is known, however, about how variable their population numbers have been. Yet, quantifying invariability – one of the stability metrics in the “estar” software – gives an insight that is complementary to the recorded precipitous decline of this species. Species whose population numbers are highly invariable will be less prone to decline, while those that are varying more over time will be more susceptible to going extinct locally under unfavourable conditions.
The second group of functions measures the stability of a community on short and long-time scales using so-called Jacobian matrices. This is the first time that what has previously been described mainly in theoretical terms has been translated into a practical statistical software package: complex relationships in species communities strongly shape the self-regulation capacity and stability of these communities. “In ‘estar’, we have mathematically mapped multidimensional matrices for the strength of species interactions in communities, enabling us to quantify community stability”, explain Radchuk and Figueiredo.
The package also includes practical instructions for scientists who wish to collect empirical data on ecological stability and process it using the new tool, as described in the article. The team hopes that this will bridge the gap between theory and practice in measuring ecological stability and thus stimulate further important research in this area.