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The authors have declared that no competing interests exist.

TLS led the writing of the manuscript with contribution from all of the authors. Conceived and designed the experiments: TLS CRA DGA TE. Performed the experiments: JRS. Analyzed the data: DGA TE KLN TLS CRA SCF ASG. Wrote the paper: TLS DGA TE.

Regime shifts are generally defined as the point of ‘abrupt’ change in the state of a system. However, a seemingly abrupt transition can be the product of a system reorganization that has been ongoing much longer than is evident in statistical analysis of a single component of the system. Using both univariate and multivariate statistical methods, we tested a long-term high-resolution paleoecological dataset with a known change in species assemblage for a regime shift. Analysis of this dataset with Fisher Information and multivariate time series modeling showed that there was a∼2000 year period of instability prior to the regime shift. This period of instability and the subsequent regime shift coincide with regional climate change, indicating that the system is undergoing extrinsic forcing. Paleoecological records offer a unique opportunity to test tools for the detection of thresholds and stable-states, and thus to examine the long-term stability of ecosystems over periods of multiple millennia.

Ecosystems can undergo regime shifts and reorganize into an alternative state when a critical threshold is exceeded

To test for regime shifts in the paleoecological record, we used a long-term high-resolution sedimentological record from Foy Lake (Montana, USA) that showed abrupt changes in diatom community structure at ∼1.3 ka (thousands of years before present, with present defined as AD 1950). Foy Lake (48.1648°N, 1143589°W, 1005 m elevation) is a deep freshwater lake situated in the drought-sensitive Flathead River Basin in the Northern Rocky Mountains

To determine if regimes shifts could be anticipated in this paleoecological data set we (i) plotted several indicators proposed to be early-warning signals of approaching critical thresholds (increasing variance, skewed responses, kurtosis, and the autocorrelation at lag-1)

Of the indicators used, we found that univariate species-level indicators were weak predictors of regime shifts. Skewness, kurtosis, and critical slowing down showed minor changes in the frequency patterns of some variables. Several species showed increased variance prior to the abrupt change in species composition at ∼1.3 ka. However, most of the species provided no warning signal; hence, conclusions about the dynamics of the overall system were unclear (

Several populations of species experienced increased variability in the Foy Lake record; this increased variability peaks prior to ∼1.3 ka (

While

Fisher information identified a substantial regime shift in the system prior to the abrupt community change. The mean FI results indicated that the system was in a steady state (regime one) from ∼7.0 to ∼4.5 ka. This was followed by a ∼2 kyr period of instability, before it returned to a steady state (regime two) at ∼1.3 ka (

Prior to ∼4.5 ka the system had episodic fluctuations in species composition and mean FI, but the overall mean of the FI is unchanging; this suggests that this period was a stable regime characterized by high variability. At ∼4.5 ka species evenness decreases, and the system begins a ∼2 kyr gradual decrease in mean FI. Decreases in FI suggest the system is becoming unstable; as instability increases resilience decreases, warning of a possible regime shift. The system was in this unstable transitional period until ∼2 ka, but it did not attain a new stable-state until ∼1.3 ka.

Multivariate time series modeling revealed eight different temporal patterns in the diatom data set that were associated with eight significant canonical axes in the redundancy analysis (RDA) model. Each of these canonical axes reflects a modeled frequency pattern of individual species or groups of species in the diatom data set. The first three canonical axes capture 55% of the variance used to summarize the transitional dynamics and regime shifts (

The proportion of variance explained by each axis is 29%, 18%, and 8% respectively. The amplitude of the frequency is low in axis one (

The regimes, transitional period, and regime shift detected by FI and time series modeling are consistent with ecological and regional climate patterns. Foy Lake was a moderately deep lake with a diverse planktic and benthic flora during regime one. Throughout the period of instability, the lake was much shallower and dominated by a benthic flora, and during the more recent regime two, Foy Lake was a deep lake dominated by

Paleoenvironmental and paleoecological data provide a vital and fundamental perspective on the long-term functioning of complex ecological systems. Here we reveal that climate-driven regime shifts may be infrequent over time in systems not impacted by anthropogenic change, and that transitional periods leading to a regime shift can last a relatively long time (∼2.0 kyr). Delayed responses and time lags have been found in other ecosystems

Rising variance, skewness, kurtosis, and critical slowing down are statistical measures that have been proposed and employed as indicators of impending regime shifts

Fisher information (FI) can be used to evaluate the dynamic order of ecosystems, including regimes and regime shifts

Here, p(s) is the probability of observing the system in a particular condition (state, s) of the system. This equation was adapted ^{2}(s)≡p(s)) in order to minimize calculation errors from very small p(s). From

Assessing the dynamic changes in system behavior requires gathering information on its condition (state) through time; hence, measurable variables (x_{i}) are selected such that a time varying system has a trajectory in a phase space defined by the n-dimensions of its system variables and time. Each point in the trajectory is defined by specific values for each of the _{1}(t_{i}), x_{2}(t_{i}) x_{3}(t_{i})…x_{n} (t_{i})]). Since uncertainty is inherent in any measurement and system variables may fluctuate within a stable state, a state is defined as a region bounded by a level of uncertainty (or size of states for each dimension (i): sost_{i}), such that if |x_{i}(t_{i}) - x_{i} (t_{j})| ≤ sost_{i} is true for all variables then the two points at times i and j are indistinguishable and are identified as being in the same state of the system. There are a number of methods for defining the sizes of states parameter, but the general idea is to assign a level of uncertainty for each variable based on either knowledge of the system (empirically or theoretically) or estimation

The basic steps employed to compute FI for the Foy Lake system were as follows: (1) the diatom time series data (consisting of the relative abundances of all 109 species) were divided into a sequence of overlapping time windows with each window containing 10 time steps. Since the goal is to capture changing patterns, there is no particular window size that must be used to compute FI. The window size is set based on available data and from empirical studies, it is typically at least eight time steps

Assessing system behavior using FI is based on the fundamental idea that different regimes (set of system conditions) exhibit different degrees of dynamic order

To assess patterns and scales of diatom fluctuations, we constructed time series models based on redundancy analysis (RDA)

The RDA retains significant PCNM variables, and these are linearly combined to extract temporal patterns from the Hellinger-transformed species matrices

(CSV)

We thank two anonymous reviewers for comments that greatly enhanced this manuscript. Data reported in this paper are archived at the National Climatic Data Center, Data Contribution Series # 2008-070. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. The views expressed in this paper are those of the authors and do not necessarily represent the views or policies of the U.S. Environmental Protection Agency.