CAUSATION, DETECTION, AND ADAPTATION TO REGIME SHIFTS IN NATURAL SYSTEMS

• Sponsoring Institution: National Institute of Food and Agriculture
• Project Status: TERMINATED
• Funding Source: HATCH
• Reporting Frequency: Annual
• Accession No.: 0230081
• Project No.: CA-D-ESP-2163-H
• Project Start Date: Oct 1, 2012
• Project End Date: Sep 30, 2017

Project Director
Hastings, A.

Recipient Organization
UNIVERSITY OF CALIFORNIA, DAVIS
410 MRAK HALL
DAVIS,CA 95616-8671

Performing Department
Environmental Science and Policy

Non Technical Summary
Especially in light of anthropogenic changes (climate change, increased pressure from humans such as spreading urbanization, increased fishing pressure, or introduction of non-native species) it is important to know when ecological or environmental systems may undergo relatively rapid and relatively irreversible changes. This phenomenon is known as a regime shift, or more popularly as a 'tipping point'. Because of the potential irreversibility, or possible high costs of reversing a change it is important to be able to predict when such changes are likely to occur, so appropriate measures can be taken. Simply taking measures to prevent a regime shift if one is not likely to occur may also not be wise, as the measures (for example, reduced or no fishing) might themselves be very costly. Even when management to prevent a regime shift might not be possible or might be too costly, advance warning might be important to allow for or reduce the costs of adaptation to change. The goal of this project is to develop a deeper understanding of the dynamics underlying regime shifts in ecological or environmental systems. This new knowledge will take several forms. One will be a better understanding of the kinds of ecological systems that are likely to undergo regime shifts. A second will be an understanding of the behavior of ecological systems that are undergoing, or about to undergo a regime shift and the extent to which shifts can be prevented. A third aspect will be to develop better ways to detect impending regime shifts and then determine appropriate measures that can be taken to prevent shifts or allow adaptation. The general results will be applied to problems in ecology and environmental biology and should lead to better design of monitoring of environmental systems. This will be accomplished by providing information of what kinds of data (frequency in time and space, for example) will be most useful in predicting when a regime shift will take place. By explicitly identifying the likelihood of predicting a shift when one is imminent, as well as falsely predicting a shift or missing an impending shift, optimal management approaches can be determined for ecological or environmental systems, thus leading to overall better environmental management and maintenance of ecosystem services.

Animal Health Component

(N/A)

Research Effort Categories

Basic

90%

Applied

10%

Developmental

(N/A)

Classification

Knowledge Area (KA)	Subject of Investigation (SOI)	Field of Science (FOS)	Percent
136	0899	1070	25%
136	0899	2080	25%
136	0899	2090	10%
132	0899	1070	15%
132	0899	2080	15%
132	0899	2090	10%

Knowledge Area
132 - Weather and Climate; 136 - Conservation of Biological Diversity;

Subject Of Investigation
0899 - Wildlife and natural fisheries, general/other;

Field Of Science
1070 - Ecology; 2080 - Mathematics and computer sciences; 2090 - Statistics, econometrics, and biometrics;

Keywords

environmental management

dynamical systems

regime shifts

tipping points

climate change

hysteresis

fishery collapse

statistical approaches

invasive species

ecosystem services

Goals / Objectives
The possibility of relatively rapid or sudden change in ecological systems is an important issue. At a local scale, examples include eutrophication, sudden replacement of a native species by an invasive one, dieoff of a native species, collapse of a fishery, or elimination of an invasive pest. Note that although the majority of items in this list are negative outcomes, elimination of a pest is a positive outcome and understanding how this could be achieved, or signals that it is about to be achieved, is clearly of importance. In California, many of these sudden changes have already occurred, including fisheries collapse and invasion of new species, and many more are expected in the near future. The activities of the project will primarily be focused on the development of both general and specific models that can exhibit sudden collapse. The specific models will be used to develop scenarios that will then be studied using the general models. This work will be done together with graduate students and potentially postdoctoral scholars who will be extensively and intensively mentored in model development, statistical analysis, and the incorporation of economic aspects. As this is an area of great interest, there will also be collaborations to work on specific systems. The primary products of the project will be new knowledge, both basic and applied, software and websites, and individuals trained in this interdisciplinary approach. The new knowledge will be an understanding of the dynamics and predictability of sudden changes in ecological systems. This knowledge will include both aspects related to the ability to predict sudden changes, and an understanding of what management actions could be undertaken to either prevent an undesirable change, or to achieve a desirable change. These products will include analytical models, computer models, and appropriate software. The appropriate software will be made freely available on public websites. The interdisciplinary training of individuals (graduate students and postdoctoral scholars) within the project will produce graduates who have special abilities to deal with complex environmental and ecological problems. The general questions that these individuals will be equipped to deal with range over dynamics found in ecological and agricultural systems.

Project Methods
The approach taken in the project will be based on developing both approaches that are predictive and ones that can match up to data. The challenges arise from the following general characteristics of the problem. Often there is not a good dynamical description of the ecological or environmental system. There are often large perturbations from outside influences, or in other words stochastic factors are large, and external influences may be changing through time due to anthropogenic forces. Limited and noisy data are available from natural systems. Data is often available only from a single system (a single realization of a highly variable process), so estimates of parameters as well as estimates of underlying system dynamics are very difficult. If the goal is management to either adapt to anticipated change, or to prevent potential change, the approach used in model development and analysis cannot be based on typical statistical ideas formulated as significance tests. The first step will be to consider a range of descriptive dynamical models of ecological systems, using evolution equations (ordinary differential equations, partial differential equations, delay equations, or integro-difference equations) which incorporate parameters that would represent changing conditions. Using these models I will consider the kinds of bifurcations that arise that would correspond to possible sudden changes in system behavior. Current research has focused primarily on the simplest kinds of bifurcations, with some notable exceptions, and more work is needed to consider different kinds of bifurcations. Possible scenarios will be built up by starting with descriptions of particular systems involving invasive species, fisheries, and other biological systems. The next step will be to make the models stochastic, to represent unknown external influences, and also to consider errors in measurement of state variables to produce models that generate observable aspects of systems undergoing sudden changes. The generation of these models will be one set of milestones. The next steps will be to evaluate the outputs of these models to determine how well sudden changes in system behavior can be anticipated. One major tool will be the use of receiver operator curves as a way to understand the tradeoff between false positives (predicting a sudden shift in system behavior when one does not occur) and missed signals (not predicting a sudden shift that does occur). This approach provides a way of moving to the next step of determining when it is worthwhile to take an action if the costs of acting, of missing a shift, and the ongoing costs or profits can all be identified. The final steps will be implementation of the results both in a statistical sense and in the development of appropriate computer software. This will also involve dissemination, and application to appropriate and specific environmental and ecological problems in California.

Progress 10/01/12 to 09/30/17

Outputs
Target Audience:I made a detailed presentation as part of a Sackler Colloquium held at the National Academy of Sciences in Washington D.C. on this topic. Presentations were also made at annual meetings (including symposia) at the Society for Mathematical Biology and the Ecological Society of America. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?Individuals working on the project have had an opportunity to participate in an interdisciplinary project. This has provided exposure to how matheamtical tools provide isnights into the management of biological populations. How have the results been disseminated to communities of interest?Results have been presented in symposia (including at the National Academy of Sciences), and at the annual meetings of the Ecological Society of America and the Society for Mathematical Biology. What do you plan to do during the next reporting period to accomplish the goals? Nothing Reported

Impacts
What was accomplished under these goals? Further identification of approaches for including time scales in the understanding of management of ecological systems was the major accomplishment during this last period. We have also been focused on developing two new modeling approaches. One is the development of the simplest model that could exhibit cascading effects of systems that undergo regime shifts. This has led to the development of a system with two compartments and we have approached analyzing this system using deterministic ideas. The second approach has been the development of ideas based on dynamic game theory to look at how different groups would interact in dealing with environmental problems.

Publications

• Type: Journal Articles Status: Submitted Year Published: 2018 Citation: Lampert, Adam; Hastings, Alan; Sanchirico, James. (2018) Slow treatment promotes control of harmful species by multiple agents. Submitted to Conservation Letters
• Type: Journal Articles Status: Published Year Published: 2017 Citation: Chad�s. I., Nicol, S., Rout, T.M., P�ron, M., Dujardin, Y., Pichancourt, J-B., Hastings, A., Cindy E. Hauser, C.E. (2017) Optimization methods to solve adaptive management problems. Theoretical Ecology 10:1-20. doi:10.1007/s12080-016-0313-0

Progress 10/01/15 to 09/30/16

Outputs
Target Audience: Nothing Reported Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?Individuals working on the project have had an opportunity to participate in an interdisciplinary project. This has provided exposure to how matheamtical tools provide isnights into the management of biological populations. How have the results been disseminated to communities of interest?Results have been presented in symposia (including at the National Academy of Sciences), and at the annual meetings of the Ecological Society of America and the Society for Mathematical Biology. What do you plan to do during the next reporting period to accomplish the goals? Nothing Reported

Impacts
What was accomplished under these goals? Further identification of approaches for including time scales in the understanding of management of ecological systems was the major accomplishment during this last period. We have also been focused on developing two new modeling approaches. One is the development of the simplest model that could exhibit cascading effects of systems that undergo regime shifts. This has led to the development of a system with two compartments and we have approached analyzing this system using deterministic ideas. The second approach has been the development of ideas based on dynamic game theory to look at how different groups would interact in dealing with environmental problems.

Publications

• Type: Journal Articles Status: Published Year Published: 2016 Citation: Hastings, A. (2016) Time scales and the management of ecological systems. PNAS 113: 14568 -14573, doi: 10.1073/pnas.1604974113

Progress 10/01/14 to 09/30/15

Outputs
Target Audience:The primary publication described here was reported on in a number of media sites so the information about synchrony as a regime shift was available to multiple audiences. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided?Both graduate students and postdoctoral investigators have received training in interdisciplianry approaches involving mathematics, ecology, and economics. How have the results been disseminated to communities of interest?I gave a presentation at the 2015 Ecological Society of America meeting in Baltimore and the results on synchrony were discussed with media. What do you plan to do during the next reporting period to accomplish the goals?We will continue to focus on objectives 1, 3, and 4 by continuing the development of models that will focus on specific systems. In particular, we are continuing to examine a set of models that have previously been used to model two classes of systems that undergo critical transitions:coral-algal-grazer systems, and forest-grassland systems where fire plays a role. Doing so will uncover common features that will apply broadly and in particular to systems in California. We are also applying ideas from the previously developed models for transitions to and from spatial synchrony to look at aspects of the dynamics of yield from trees. This will both provide insight into these specific systems and general understanding of these kinds of transitions.

Impacts
What was accomplished under these goals? Under objectives 1, 3 and 4 we continued to investigate models that considered the control of invasive species, as well as understanding the time scale of the dynamics of responses of human systems to these kinds of challenges. We also developed general approaches for understanding transitions to and from spatial synchrony of dynamics in ecological systems. The nature of the approach, which was based on universality, means that these ideas can be applied to broad classes of systems. These approaches thus can both give signs of impending transitions and provide insights into managment approaches to prevent transitions.

Publications

• Type: Journal Articles Status: Published Year Published: 2015 Citation: Noble, A.E., Machta, J., and Hastings, A. (2015) Emergent long-range synchronization of oscillating ecological populations without external forcing described by Ising universality. Nature Communications 6, 6664 DOI:10.1038/ncomms7664
• Type: Journal Articles Status: Published Year Published: 2015 Citation: Li, Y., Liu, Y., Zhao, L., Hastings, A., Guo, H. (2015) Exploring change of internal nutrients cycling in a shallow lake: A dynamic nutrient driven phytoplankton model Ecological Modeling 313:137-148
• Type: Journal Articles Status: Published Year Published: 2016 Citation: Wilson, R. S., Hardisty, D. J., Epanchin-Niell, R.S., Runge, M.C., Cottingham, K. L.., Urban, D.L., Maguire, L.A., Hastings, A., Mumby, P.J., Peters, D.P.C (2016) A typology of timescale mismatches and behavioral interventions to diagnose and solve conservation problems. Conservation Biology 30:42-49

Progress 10/01/13 to 09/30/14

Outputs
Target Audience: During this period we had meetings with the Invasive Spartina Projectto discuss ideas and issues related to management oiif invasive species. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided? Both graduate students and postdoctoral investigators have received training in interdisciplianry approaches involving mathematics, ecology, and economics. How have the results been disseminated to communities of interest? I gave presentations at the 2014 annual meeting of the Ecological Society of America, held in Sacramento, and also at the 2014 annual meeting of the Society for Mathematical Biology. As noted above, we have discussed our approaches and results with the Invasive Spartina Project and relevant state agencies. What do you plan to do during the next reporting period to accomplish the goals? We will continue to focus on objectives 1, 3, and 4 by continuing the development of models that will focus on specific systems. In particular, we will examine a set of models that have previously been used to model two classes of systems that undergo critical transitions:coral-algal-grazer systems, and forest-grassland systems where fire plays a role. Doing so will uncover common features that will apply broadly and in particular to systems in California.

Impacts
What was accomplished under these goals? Under objectives 1, 3 and 4 we developed and carefully investigated models that considered the control of a particular invasive species, hybrids between Spartina alterniflora and Spartina foliosa, in San Francisco Bay with the additional complication that the invasive species is used by an endangered species, California Clapper Rail, as habitat. The issues that arose in describing a particular species, in both stochastic and deterministic models provide insights that will be used in the development of modeling approaches that both apply more generally and to other particular species.

Publications

• Type: Journal Articles Status: Published Year Published: 2014 Citation: Lampert, A. and Hastings, A. (2014) Optimal control of population recovery - the role of economic restoration threshold. Ecology Letters 17:28-35.
• Type: Journal Articles Status: Published Year Published: 2014 Citation: Lampert, A., Hastings, A., Grosholz, E., Jardine, S., Sanchirico, J.N. (2014) Optimal approaches for balancing invasive species eradication and endangered species management. Science 344:1028-1031.

Progress 01/01/13 to 09/30/13

Outputs
Target Audience: Workshops and a summer school sponsored through Mathematics of Planet Earth 2013 were targeted to a mix of biology and mathematics students. These efforts educated a number of young individuals on both the biological issues and the technical approaches to solving the problem. Changes/Problems: Nothing Reported What opportunities for training and professional development has the project provided? I actively participated in activities in 2013 under the special year on Mathematics of Planet Earth (organizing a number of workshops, making presentations, and lecturing in a summer school). These led to substantial training of a variety of individuals with varying backgrounds. How have the results been disseminated to communities of interest? I gave presentations at a number of workshops and conferences, including a special session at the Fall 2013 American Geophysical Meeting attended by Governor Jerry Brown. What do you plan to do during the next reporting period to accomplish the goals? Under the first objective, I will move from general considerations of the kinds of changes in system behavior are possible to relating these more carefully to underlying biological mechanisms. During the next year as well, stochastic versions of these explicitly biological models will be developed.

Impacts
What was accomplished under these goals? Per the first objective, a range of different kinds of bifurcations (changes in system behavior) that arise in a variety of biologically motivated models under parameter change were cataloged. This development indicated what kinds of changing behavior need further study (Boettiger et al 2013, Hastings 2013). Under the second and fourth objectives in the project, the kinds of changes in system dynamics that are due to underlying changes in parameters versus changes in system states that occur simply due to stochastic factors were carefully studied (Boettiger and Hastings 2013). This analysis will help develop tools for determining when various signals of system behavior would indicate impending changes due to underlying parameter changes.

Publications

• Type: Journal Articles Status: Published Year Published: 2013 Citation: Boettiger, C. and Hastings, A. (2013) Tipping points: From patterns to predictions. Nature 493:157-158.
• Type: Journal Articles Status: Published Year Published: 2013 Citation: Hastings, A. (2013) Multiple stable states and regime shifts in ecological systems. Mathematics Today February 2013 37-39
• Type: Journal Articles Status: Published Year Published: 2013 Citation: Cuddington, K., Fortin, M.-J., Gerber, L., Hastings, A, Leibhold, A., O'Connor, M., and Ray, C. (2013) Process-based models are required to manage ecological systems in a changing world. Ecosphere 4 (no. 2) Article 20.
• Type: Journal Articles Status: Published Year Published: 2013 Citation: Boettiger, C. and Hastings, A. (2013) No early warning signals for stochastic transitions: insights from large deviation theory. Proceedings Royal Society B 280: 1372.
• Type: Journal Articles Status: Published Year Published: 2013 Citation: Dakos, V. and Hastings, A. (2013) Editorial: special issue on regime shifts and tipping points in ecology. Theoretical Ecology 253-254.
• Type: Journal Articles Status: Published Year Published: 2013 Citation: Boettiger, C., Ross, N. and Hastings, A. (2013) Early warning signals: The charted and uncharted territories. Theoretical Ecology 255.264.

Progress 01/01/12 to 12/31/12

Outputs
OUTPUTS: I have been active in organizing and participating in events related to Mathematics of Planet Earth 2013, which is a worldwide effort to develop the mathematical tools and background that will, in part, be used to manage natural systems. Regime shifts and the potential for prediction, prevention, or adaptation are a large part of this effort. Specifically during this time period I participated in a workshop at the Institute Henri Poincare on management of natural systems and a working group at the National Institute for Mathematical Biology and Synthesis on approximate methods of control that would apply, For the former, I presented a tutorial on approaches to spatial management and ecology that was attended by a large number of scientists from developing countries. PARTICIPANTS: Carl Boettiger, former graduate student Noam Ross, current graduate student Peter Mumby, Professor, University of Queensland, collaborator The graduate students have received interdisciplinary training. TARGET AUDIENCES: Nothing significant to report during this reporting period. PROJECT MODIFICATIONS: Not relevant to this project.

Impacts
We have been developing approaches for detection of impending regime shifts and have focused on the development of understanding of regime shifts in a variety of systems, including marine systems. These techniques will guide management decisions that will compare cost of action or adaptation to possible costs of damages resulting from a regime shift. The approaches will also focus on the idea of cascading regime shifts (for example the spread of an invasive species through space with concomitant negative effects) with the goal again of prevention or adaptation.

Publications

• Mumby, P.J., Steneck, R.S. and Hastings, A. (2013) Evidence for and against the existence of alternate attractors on coral reefs. Oikos 122: 481-491
• Boettiger, C. and Hastings, A. (2013) Tipping points: From patterns to predictions. Nature 493:157-158
• Hastings, A. (2013) Multiple stable states and regime shifts in ecological systems. Mathematics Today February 2013 37-39.