Post provided by Quinn Asena

Uncovering signals from the past

Understanding interactions among organisms, and between organisms and their environment, has been a cornerstone of ecology as long as we have been busying ourselves with the lives of other species. How do plants and animals facilitate or compete with each other? How do they respond to the continuous challenge of changing climates or new neighbors? Long time-series observations of shifting community composition and environmental co-variates are foundational to answering these questions, but formal statistical modeling of these processes is challenged by various features of the data. Our goal was to model time series of community count data in such a way that we can estimate species interactions and species-environmental relationships. To this end, we’ve developed a new state-space modeling approach, called multinomialTS, along with a paper (Asena et al. 2026) and tutorials.

Before we go further, I’m going to put the important resources up front:

• The full paper: Asena et al. (2026)
• The multinomialTS R package
• Tutorial resources
• Tutorial resources repo

Community Time Series Data: Features and Challenges

Count data, or multinomially distributed data, are a common form of species community data where the count of species present in a sample is recorded. It may not be possible to obtain the true absolute abundance of every species (i.e., counting every individual of every species present), so we make do with counting enough individuals to get a representative sample of their relative abundances. Knowing only the relative abundances poses statistical and inferential challenges as we can only calculate estimates for each species relative to other species.

To make things more challenging, we are tackling data that are unevenly spaced through time. Most timeseries analyses perform well on evenly spaced data, but real-world observational data often are irregularly spaced in time. We were particularly interested in palaeoecological data, which usually represents sparsely sampled observations at varying time intervals, so the methods presented here work well for such data, but are applicable to any count data.

Palaeoecological data

Palaeodata are often derived from core samples, like sediment or ice cores, which over time accumulate a signal of the surrounding environment as layers build up through deposition. This signal is continuous (unless interrupted by hiatuses, e.g. if a lake dries up) and the amount of time between samples depends both on sampling interval and the deposition rate of sediments. Since deposition rates are usually inconsistent over time, even with a constant depth-interval spacing the temporal spacing of the observations becomes uneven with observations at, for example, 75, 160, 200, 300… years.

Many different proxies can be extracted from these samples, providing both count data about past community composition and associated changes in various environmental covariates. For example, pollen from the vegetation surrounding a lake is deposited in the lake’s sediment layers and can be extracted and taxonomically identified by light microscopy. Accompanying analyses of various stable isotopes and organic compounds can provide estimates of surface air temperature and water balance.

Palaeoecology is more than the description of ecological history (i.e. what happened and when?), it is the study of the processes governing ecological trajectories through time, across a broad range of timescales, that help inform our understanding of present and future ecosystem states. Ecological processes occur at an intragenerational scale, and laboratory studies on bacteria or insects can span multiple generations over days or months. However, on the ecosystem scale, a few thousand years is only a few generations of some tree species such as the Kauri in New Zealand. Many ecosystems have co-evolved with a fire regime, and fires that return on the scale of hundreds of years can be essential determinants of forest demography and ecosystem function (Smithwick et al. 2005). These scales are well beyond the direct observational record, but are short relative to the evolution of ecosystems or their movement through space. Quickly you understand that ‘long time periods’ of decades to millennia are actually not so long, but our paradigm is shaped by our shorter lives! The record we use as an example in our paper is from Sunfish Pond in Pennsylvania, USA, spanning 13,800 years. This record covers the geological epoch of the Holocene, the last 11,700 years, and the last bit of the preceding Pleistocene epoch. The Sunfish record contains pollen data of the surrounding vegetation, and a proxy for the hydroclimate (Ray-Cozzens 2022), an important driving variable to the most abundant species: hemlock, pine, birch and oak (actually, these are genera because of limits in pollen taxonomic identification, but we’ll use ‘species’ throughout for consistency).

State-space modelling

We set out to develop a method that can use count data of species observations, and information about the environment (i.e., driving variables such as temperature changes over time), to estimate coefficients of species-species interactions and environment-species relationships. The approach we used is state-space modelling, specifically using a Kalman filter (Harvey 1990), where the ‘true’ state of a system is modelled from both the processes influencing the system (environmental drivers), and the observations about that system (community count data). State-space models have been used to remarkable effect to model challenges such as animal movement and population dynamics; for a fantastic review, see Auger-Méthé et al. (2021).

Estimating these coefficients and using them to test hypotheses about the underlying drivers of community changes over time is the key advancement in our approach relative to other standard multivariate methods used by community paleoecologists. Because statistically modeling the relationship between paleoecological and paleoenvironmental time series isn’t easy, paleoecologists often use descriptive statistics to represent patterns (e.g., to cluster species) or use ‘wiggle matching’ to visually describe the relationships between environmental and compositional time series. Using this state-space approach we can set up multiple working hypotheses (Chamberlin 1897) and fit the model to address each hypothesis. We can ask questions of the data such as: ‘are species interactions or environmental drivers the stronger influence on community change?’ and lend statistical support to our inferences.

What we cannot do with this modeling approach is definitively prove ‘causal links’ because this is not a mechanistic model; we are inferring underlying processes from observable patterns given the data. This is why we must assess a range of hypotheses and not disregard any one, but view them in the context of their likelihoods of being true. Definitive proof of causality with retrospective observational data are always challenging, and palaeoecological data carry various sources of uncertainty, and so certainty regarding any one inference is rarely appropriate.

Inference from pattern

The most fascinating part of estimating species interactions and driver-species relationships from palaeoecological data is that it is even possible to take patterns of change (i.e., species compositions and environmental drivers over time), and infer how they influenced each other. We can verify our inferences, to some degree, against known contemporary species ranges, autoecology, and environmental tolerances; and in simulation by generating species under known parameters and attempting to recover those parameters by fitting the model to the simulated data.

At Sunfish Pond, we found support for the idea that water availability was an important driver of past forest dynamics, consistent with what we know about the ecology of pine and hemlock today, both of which tend to be more abundant under wetter conditions. We also detected signals of species interactions among pine, oak, and beech playing out over millennia. This work shows how, amazingly, we can take grains of pollen from thousands of years ago and use them, along with other proxy data and this modeling framework, to better tackle cornerstone questions in ecology about why communities change over time. When phrased like that, it seems impossible, but the ecological signals are literally out there buried in mud, ready to be uncovered by hard field work and new statistical methods.

Acknowledgements

I have had the privilege to contribute to this amazing work; however, Tony Ives is the mathematician behind developing the model. Even now, after more than two years working with the model, I bring questions to Tony and ask for an explanation in crayon. Jack Williams is the palaeoecological expert who can make sense of model outputs based on decades of experience analysing palaeoecological data. Bryan Shuman, Jonathan Johnson, Vania Stefanova, and Tessa Ray-Cozzens, were pivitol in gathering the data from Sunfish Pond that we used in our paper.

About the author

I am an ecologist and data scientist currently working at the Cary Institute of Ecosystem Studies on modelling boreal ecosystems and wildfire. Much of my background is in palaeoecology looking into long-term ecological trajectories, using real-world and modeled time series. Together these experiences span my interest in spatiotemporal ecological change that I continue to build on.

References

Asena, Quinn, John W. Williams, Jonathan Johnson, Bryan Shuman, Vania Stefanova, and Anthony Ives. 2026. “Statistical Analyses of Ecological Multinomial Time Series to Identify Environmental Drivers and Biotic Interactions.” Methods in Ecology and Evolution, May, 2041–210x.70315. https://doi.org/10.1111/2041-210x.70315.
Auger-Méthé, Marie, Ken Newman, Diana Cole, Fanny Empacher, Rowenna Gryba, Aaron A. King, Vianey Leos-Barajas, et al. 2021. “A Guide to State–Space Modeling of Ecological Time Series.” Ecological Monographs 91 (4): e01470. https://doi.org/10.1002/ecm.1470.
Chamberlin, T. C. 1897. “The Method of Multiple Working Hypotheses.” The Journal of Geology 5: 837–48.
Harvey, Andrew C. 1990. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781107049994.
Ray-Cozzens, Tessa. 2022. “Stratigraphic Evidence of Water-Level Changes in Small Lakes in the Southern Great Lakes Region During the Late-Quaternary – ProQuest.” PhD thesis, University of Wyoming.
Smithwick, Erica A. H., Monica G. Turner, Michelle C. Mack, and F. Stuart Chapin. 2005. “Postfire Soil N Cycling in Northern Conifer Forests Affected by Severe, Stand-Replacing Wildfires.” Ecosystems 8 (2): 163–81. https://doi.org/10.1007/s10021-004-0097-8.