Alan Hastings

Santa Fe Institute

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Louis W. Botsford

University of California, Davis

Karen C. Abbott

Case Western Reserve University

Kim Cuddington

University of Waterloo

Jonathan Machta

Barts Health NHS Trust

J. Wilson White

Oregon State University

Kevin S. McCann

University of Guelph

Tad Dallas

University of South Carolina

Marissa L. Baskett

University of California, Davis

Peter J. Mumby

University of Queensland

Carl Boettiger

University of California, Berkeley

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John Wiley & Sons (United States)

207

Ecological Society of America

200

University of California, Davis

145

National Institute of Anthropology and History

Universidad Nacional Agraria La Molina

China National Bamboo Research Center

Western University of Health Sciences

Berkeley College

La Jolla Alcohol Research

RELX Group (Netherlands)

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Timescales and the management of ecological systems

Proceedings of the National Academy of Sciences (2016)

Alan Hastings

Human management of ecological systems, including issues like fisheries, invasive species, and restoration, as well as others, often must be undertaken with limited information. This means that developing general principles and heuristic approaches is important. Here, I focus on one aspect, the importance of an explicit consideration of time, which arises because of the inherent limitations in the response of ecological systems. I focus mainly on simple systems and models, beginning with systems without density dependence, which are therefore linear. Even for these systems, it is important to recognize the necessary delays in the response of the ecological system to management. Here, I also provide details for optimization that show how general results emerge and emphasize how delays due to demography and life histories can change the optimal management approach. A brief discussion of systems with density dependence and tipping points shows that the same themes emerge, namely, that when considering issues of restoration or management to change the state of an ecological system, that timescales need explicit consideration and may change the optimal approach in important ways.

Ecological systems theory

10.1073/pnas.1604974113

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Citations (67)

Coral Reef Habitats as Surrogates of Species, Ecological Functions, and Ecosystem Services

Conservation Biology (2008)

Peter J. Mumby Kenneth Broad Daniel R. Brumbaugh P. DAHLGREN CRAIG Alastair R. Harborne

Habitat maps are often the core spatially consistent data set on which marine reserve networks are designed, but their efficacy as surrogates for species richness and applicability to other conservation measures is poorly understood. Combining an analysis of field survey data, literature review, and expert assessment by a multidisciplinary working group, we examined the degree to which Caribbean coastal habitats provide useful planning information on 4 conservation measures: species richness, the ecological functions of fish species, ecosystem processes, and ecosystem services. Approximately one-quarter to one-third of benthic invertebrate species and fish species (disaggregated by life phase; hereafter fish species) occurred in a single habitat, and Montastraea-dominated forereefs consistently had the highest richness of all species, processes, and services. All 11 habitats were needed to represent all 277 fish species in the seascape, although reducing the conservation target to 95% of species approximately halved the number of habitats required to ensure representation. Species accumulation indices (SAIs) were used to compare the efficacy of surrogates and revealed that fish species were a more appropriate surrogate of benthic species (SAI = 71%) than benthic species were for fishes (SAI = 42%). Species of reef fishes were also distributed more widely across the seascape than invertebrates and therefore their use as a surrogate simultaneously included mangroves, sea grass, and coral reef habitats. Functional classes of fishes served as effective surrogates of fish and benthic species which, given their ease to survey, makes them a particularly useful measure for conservation planning. Ecosystem processes and services exhibited great redundancy among habitats and were ineffective as surrogates of species. Therefore, processes and services in this case were generally unsuitable for a complementarity-based approach to reserve design. In contrast, the representation of species or functional classes ensured inclusion of all processes and services in the reserve network.

Seascape

Marine protected area

10.1111/j.1523-1739.2008.00933.x

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Citations (149)

Multiple attractors and long transients in spatially structured populations with an Allee effect

arXiv (Cornell University) (2020)

Irina Vortkamp Sebastian J. Schreiber Alan Hastings Frank M. Hilker

We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation. While an isolated population can exhibit only bistability and essential extinction, a spatially structured population can exhibit numerous coexisting attractors. We identify mechanisms and parameter ranges that can protect the spatially structured population from essential extinction, whereas it is inevitable in the local system. In the case of weak coupling, a state where one subpopulation density lies above and the other one below the Allee threshold can prevent essential extinction. Strong coupling, on the other hand, enables both populations to persist above the Allee threshold when dynamics are (approximately) out-of-phase. In both cases, attractors have fractal basin boundaries. Outside of these parameter ranges, dispersal was not found to prevent essential extinction. We also demonstrate how spatial structure can lead to long transients of persistence before the population goes extinct.

Allee effect

Extinction (optical mineralogy)

Bistability

Coupling parameter

10.48550/arxiv.2004.11219

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Highly Variable Spread Rates in Replicated Biological Invasions: Fundamental Limits to Predictability

Science (2009)

Brett A. Melbourne Alan Hastings

Limits to Invasion Predictions Using mathematical models linked to experiments on laboratory insect populations, Melbourne and Hastings (p. 1536 ) show that current models seriously underestimate variability in spatial spread. Genetic founder effects resulting from small population sizes are probably responsible for the surprising increase in variability and for increased uncertainty of ecological forecasts. Thus, even without exogenous sources of variability such as weather, fundamental uncertainties arise biologically from inherent differences among individuals and small population sizes.

Predictability

10.1126/science.1176138

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Citations (205)

POPULATION DYNAMICS AND FOOD WEB STRUCTURE—PREDICTING MEASURABLE FOOD WEB PROPERTIES WITH MINIMAL DETAIL AND RESOLUTION

Elsevier eBooks (2005)

John L. Sabo Beatrix E. Beisner Eric L. Berlow Kim Cuddington Alan Hastings

Resilience

10.1016/b978-012088458-2/50041-2

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Citations (7)

Boundary-layer model for the population dynamics of single species

Proceedings of the National Academy of Sciences (1981)

Alan Hastings Juan Manuel Serradilla Francisco J. Ayala

We develop a new discrete-time model, called the boundary-layer model, to describe the dynamics of single species that have a capacity for fast growth at very low population densities. The model explicitly separates the dynamics of the population at very low densities (within the “boundary layer”) and at high densities. The boundary-layer model provides a better fit than other models such as the logistic or the θ model to data from experimental populations of Drosophila willistoni and D. pseudoobscura.

Dynamics

Population model

10.1073/pnas.78.3.1972

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Citations (13)

Optimal management of stochastic invasion in a metapopulation with Allee effects

Journal of Theoretical Biology (2022)

Abhishek Mallela Alan Hastings

Allee effect

Metapopulation

10.1016/j.jtbi.2022.111221

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Citations (1)

How Faculty Members in School Districts Experiencing Enrollment Decline Make Sense of Policy: Evidence from Michigan.

ProQuest LLC eBooks (2016)

Alan Hastings

Open enrollment

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Competition

Springer eBooks (1997)

Alan Hastings

10.1007/978-1-4757-2731-9_7

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Rate-induced tipping in complex high-dimensional ecological networks

arXiv (Cornell University) (2023)

Shirin Panahi Younghae Do Alan Hastings Ying-Cheng Lai

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we discover a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

Tipping point (physics)

Phenomenon

10.48550/arxiv.2311.09140

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