Publications by authors named "Alan Hastings"

124 Publications

Directed movement changes coexistence outcomes in heterogeneous environments.

Ecol Lett 2021 Nov 24. Epub 2021 Nov 24.

Department of Environmental Science and Policy, University of California, Davis, Davis, California, USA.

Understanding mechanisms of coexistence is a central topic in ecology. Mathematical analysis of models of competition between two identical species moving at different rates of symmetric diffusion in heterogeneous environments show that the slower mover excludes the faster one. The models have not been tested empirically and lack inclusions of a component of directed movement toward favourable areas. To address these gaps, we extended previous theory by explicitly including exploitable resource dynamics and directed movement. We tested the mathematical results experimentally using laboratory populations of the nematode worm, Caenorhabditis elegans. Our results not only support the previous theory that the species diffusing at a slower rate prevails in heterogeneous environments but also reveal that moderate levels of a directed movement component on top of the diffusive movement allow species to coexist. Our results broaden the theory of species coexistence in heterogeneous space and provide empirical confirmation of the mathematical predictions.
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http://dx.doi.org/10.1111/ele.13925DOI Listing
November 2021

Contrasting plant responses to multivariate environmental variations among species with divergent elevation shifts.

Ecol Appl 2021 Oct 22:e02488. Epub 2021 Oct 22.

Department of Natural Resource Ecology and Management, Oklahoma State University, Stillwater, Oklahoma, 74078, USA.

The general predictions of climate impacts on species shifts (e.g., upward shift) cannot directly inform local species conservation, because local-scale studies find divergent patterns instead of a general one. For example, our previous study found three shift patterns with elevation (strong down-, moderate down-, and up-slope shifts) in temperate mountain forests. The divergent shifts are hypothesized to arise from both multivariate environmental variations with elevation and corresponding species-specific responses. To test this hypothesis, we sampled soils and leaves to measure elevation variations in soil conditions and determined plant responses using discriminations against heavier isotopes, carbon ( C) and nitrogen ( N). Functional traits of the species studied were also extracted from a public trait dataset. We found that: (1) With low soil water contents at low elevations, only the leaves of up-shifters had lower C discriminations at low vs. high elevations; (2) With low soil P contents at high elevations, only the leaves of moderate down-shifters had higher N discriminations at high vs. low elevations; (3) The leaves of strong down-shifters did not show significant elevation patterns of the discriminations; (4) The contrasting responses among the three types of shifters agree with their functional dissimilarity, suggested by their separate locations in a multitrait space. Taken together, the divergent shifts are associated with the elevation variations in environmental conditions and contrasting plant responses. The contrasting responses could result from the functional dissimilarity among species. Therefore, a detailed understanding of both local environmental variations and species-specific responses can facilitate accurate predictions of species shifts to inform local species conservation.
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http://dx.doi.org/10.1002/eap.2488DOI Listing
October 2021

Tipping Cascades in a Multi-patch System with Noise and Spatial Coupling.

Bull Math Biol 2021 Sep 30;83(11):112. Epub 2021 Sep 30.

Department of Environmental Science and Policy, University of California Davis, Davis, CA, 95616, USA.

Forecasting tipping points in spatially extended systems is a key area of interest to ecologists. A slowly declining spatially distributed population is an important example of an ecological system that could exhibit a cascade of tipping points. Here, we develop a spatial two-patch model with environmental stochasticity that is slowly forced through population collapse, in the presence of changing environmental conditions. We begin with a basic spatial model, then introduce a fast-slow version of the model using geometric singular perturbation theory, followed by the inclusion of stochasticity. Using the spectral density of the fluctuating subpopulation in each patch, we derive analytic expressions for candidate indicators of population extinction and evaluate their performance through a simulation study. We find that coupling and spatial heterogeneity decrease the magnitude of the proposed indicators in coupled populations relative to isolated populations. Moreover, the degree of coupling dictates the trends in summary statistics. We conclude that this theory may be applied to other contexts, including the control of invasive species.
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http://dx.doi.org/10.1007/s11538-021-00943-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8484107PMC
September 2021

Towards Building a Sustainable Future: Positioning Ecological Modelling for Impact in Ecosystems Management.

Bull Math Biol 2021 Sep 4;83(10):107. Epub 2021 Sep 4.

Mathematics and Statistics, Unit 5, Irving K. Barber, School of Arts and Sciences, University of British Columbia-Okanagan, Kelowna, British Columbia, V1V 1V7, Canada.

As many ecosystems worldwide are in peril, efforts to manage them sustainably require scientific advice. While numerous researchers around the world use a great variety of models to understand ecological dynamics and their responses to disturbances, only a small fraction of these models are ever used to inform ecosystem management. There seems to be a perception that ecological models are not useful for management, even though mathematical models are indispensable in many other fields. We were curious about this mismatch, its roots, and potential ways to overcome it. We searched the literature on recommendations and best practices for how to make ecological models useful to the management of ecosystems and we searched for 'success stories' from the past. We selected and examined several cases where models were instrumental in ecosystem management. We documented their success and asked whether and to what extent they followed recommended best practices. We found that there is not a unique way to conduct a research project that is useful in management decisions. While research is more likely to have impact when conducted with many stakeholders involved and specific to a situation for which data are available, there are great examples of small groups or individuals conducting highly influential research even in the absence of detailed data. We put the question of modelling for ecosystem management into a socio-economic and national context and give our perspectives on how the discipline could move forward.
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http://dx.doi.org/10.1007/s11538-021-00927-yDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8418459PMC
September 2021

Effects of stochasticity on the length and behaviour of ecological transients.

J R Soc Interface 2021 07 7;18(180):20210257. Epub 2021 Jul 7.

Department of Mathematics, Bowdoin College, Brunswick, ME 04011, USA.

There is a growing recognition that ecological systems can spend extended periods of time far away from an asymptotic state, and that ecological understanding will therefore require a deeper appreciation for how long ecological transients arise. Recent work has defined classes of deterministic mechanisms that can lead to long transients. Given the ubiquity of stochasticity in ecological systems, a similar systematic treatment of transients that includes the influence of stochasticity is important. Stochasticity can of course promote the appearance of transient dynamics by preventing systems from settling permanently near their asymptotic state, but stochasticity also interacts with deterministic features to create qualitatively new dynamics. As such, stochasticity may shorten, extend or fundamentally change a system's transient dynamics. Here, we describe a general framework that is developing for understanding the range of possible outcomes when random processes impact the dynamics of ecological systems over realistic time scales. We emphasize that we can understand the ways in which stochasticity can either extend or reduce the lifetime of transients by studying the interactions between the stochastic and deterministic processes present, and we summarize both the current state of knowledge and avenues for future advances.
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http://dx.doi.org/10.1098/rsif.2021.0257DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8261213PMC
July 2021

Scaling up experimental stress responses of grass invasion to predictions of continental-level range suitability.

Ecology 2021 08 13;102(8):e03417. Epub 2021 Jul 13.

School of Forest Resources and Conservation, Fort Lauderdale Research and Education Center, University of Florida, 3205 College Avenue, Davie, Florida, 33314, USA.

Understanding how the biological invasion is driven by environmental factors will improve model prediction and advance early detection, especially in the context of accelerating anthropogenic ecological changes. Although a large body of studies has examined how favorable environments promote biological invasions, a more comprehensive and mechanistic understanding of invasive species response to unfavorable/stressful conditions is still developing. Grass invasion has been problematic across the globe; in particular, C grass invaders, with high drought tolerance, adaptations to high temperatures, and high water use efficiency, could become more severe. Here, we conducted a rigorous microcosm experiment, with one of the most damaging invasive C grass, cogongrass (Imperata cylindrica), to explore how cogongrass responds to soil water and nutrient stress. We further integrated the results of the microcosm study with a species distribution model to (1) corroborate greenhouse results with field observations and (2) validate the robustness of our findings at subcontinental scales. Both the microcosm experiments and species distribution model agreed that soil water stress had a stronger impact on cogongrass than the nutrient one. New vegetative growth of cogongrass continued to be inhibited by the prior water stress. The significant water effect on cogongrass total biomass was supported by the finding that both allometric and biochemical traits of cogongrass did not show significant responses to the changes in water treatment. Different to the conventional wisdom that nutrient enrichment plays a bigger role in facilitating biological invasions, this study highlighted the possibility that water conditions may have a more substantial effect on some aggressive invaders. Therefore, an important implication of this study on biological conservation is that field managers might take advantage of the negative effect of global drought on some invasive species to increase the efficiency of their controlling efforts because invasive species may become more vulnerable under drought effect.
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http://dx.doi.org/10.1002/ecy.3417DOI Listing
August 2021

A Low-Dimensional Network Model for an SIS Epidemic: Analysis of the Super Compact Pairwise Model.

Bull Math Biol 2021 May 21;83(7):77. Epub 2021 May 21.

Department of Environmental Science and Policy, University of California, Davis, USA.

Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive important epidemiological quantities for the system. We derive the epidemic threshold and analyze the bifurcation that occurs, and we use asymptotic techniques to derive an approximation for the endemic equilibrium when it exists. We consider the sensitivity of this approximation to network parameters, and the implications for disease control measures are found to be in line with the results of existing studies.
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http://dx.doi.org/10.1007/s11538-021-00907-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8139886PMC
May 2021

The Role of Stochasticity in Noise-Induced Tipping Point Cascades: A Master Equation Approach.

Bull Math Biol 2021 03 31;83(5):53. Epub 2021 Mar 31.

Department of Environmental Science and Policy, University of California Davis, Davis, CA, 95616, USA.

Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less explored and is an important one. A study of noise-induced tipping, in particular, could provide key insights into tipping cascades. Here, we consider a specific example of a simple model system that could have cascading tipping points. This model consists of two interacting populations with underlying Allee effects and stochastic dynamics, in separate patches connected by dispersal, which can generate bistability. From an ecological standpoint, we look for rescue effects whereby one population can prevent the collapse of a second population. As a way to investigate the stochastic dynamics, we use an individual-based modeling approach rooted in chemical reaction network theory. Then, using continuous-time Markov chains and the theory of first passage times, we essentially approximate, or emulate, the original high-dimensional model by a Markov chain with just three states, where each state corresponds to a combination of population thresholds. Analysis of this reduced model shows when the system is likely to recover, as well as when tipping cascades through the whole system.
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http://dx.doi.org/10.1007/s11538-021-00889-1DOI Listing
March 2021

Initial abundance and stochasticity influence competitive outcome in communities.

J Anim Ecol 2021 07 30;90(7):1691-1700. Epub 2021 Apr 30.

Department of Environmental Science and Policy, University of California-Davis, Davis, CA, USA.

Predicting competitive outcomes in communities frequently involves inferences based on deterministic population models since these provide clear criteria for exclusion (e.g. R* rule) or long-term coexistence (e.g. mutual invasibility). However, incorporating stochasticity into population- or community-level processes into models is necessary if the goal is to explain variation in natural systems, which are inherently stochastic. Similarly, in systems with demographic or environmental stochasticity, weaker competitors have the potential to exclude superior competitors, contributing to what is known as 'competitive indeterminacy'. The importance of such effects for natural communities is unknown, in part because it is difficult to demonstrate that multiple forms of stochasticity are present in these communities. Moreover, the effects of multiple forms of stochasticity on competitive outcomes are largely untested, even in theory. Here, we address these issues by examining the role of stochasticity in replicated communities of flour beetles (Tribolium sp.). To do so, we developed a set of two-species stochastic Ricker models incorporating four distinct forms of stochasticity: environmental stochasticity, demographic stochasticity, demographic heterogeneity and stochastic sex determination. By fitting models to experimental data, and simulating fit models to examine long- term behaviour, we found that both the duration of transient coexistence and the degree of competitive indeterminacy were sensitive to the forms of stochasticity included in our models. These findings suggest the current estimates of extinction risk, coexistence and time until competitive exclusion in communities may not be accurate when based on models that exclude relevant forms of stochasticity.
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http://dx.doi.org/10.1111/1365-2656.13485DOI Listing
July 2021

Sharp boundary formation and invasion between spatially adjacent periodical cicada broods.

J Theor Biol 2021 04 26;515:110600. Epub 2021 Jan 26.

Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA.

Periodical cicadas, Magicicada spp., are a useful model system for understanding the population processes that influence range boundaries. Unlike most insects, these species typically exist at very high densities (occasionally >1000/ m) and have unusually long life-spans (13 or 17 years). They spend most of their lives underground feeding on plant roots. After the underground period, adults emerge from the ground to mate and oviposit over a period of just a few days. Collections of populations that are developmentally synchronized across large areas are known as "broods". There are usually sharp boundaries between spatially adjacent broods and regions of brood overlap are generally small. The exact mechanism behind this developmental synchronization and the sharp boundary between broods remain unknown: previous studies have focused on the impacts of predator-driven Allee-effects, competition among nymphs, and their impacts on the persistence of off-synchronized emergence events. Here, we present a nonlinear Leslie-type matrix model to additionally consider cicada movement between spatially separated broods, and examine its role in maintaining brood boundaries and within-brood developmental synchrony that is seen in nature. We successfully identify ranges of competition and dispersal that lead to stable coexistence of broods that differ between spatial patches.
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http://dx.doi.org/10.1016/j.jtbi.2021.110600DOI Listing
April 2021

Management implications of long transients in ecological systems.

Nat Ecol Evol 2021 03 18;5(3):285-294. Epub 2021 Jan 18.

Department of Mathematics, Bowdoin College, Brunswick, ME, USA.

The underlying biological processes that govern many ecological systems can create very long periods of transient dynamics. It is often difficult or impossible to distinguish this transient behaviour from similar dynamics that would persist indefinitely. In some cases, a shift from the transient to the long-term, stable dynamics may occur in the absence of any exogenous forces. Recognizing the possibility that the state of an ecosystem may be less stable than it appears is crucial to the long-term success of management strategies in systems with long transient periods. Here we demonstrate the importance of considering the potential of transient system behaviour for management actions across a range of ecosystem organizational scales and natural system types. Developing mechanistic models that capture essential system dynamics will be crucial for promoting system resilience and avoiding system collapses.
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http://dx.doi.org/10.1038/s41559-020-01365-0DOI Listing
March 2021

Spatial Dynamics and Spread of Ecosystem Engineers: Two Patch Analysis.

Bull Math Biol 2020 11 19;82(12):149. Epub 2020 Nov 19.

Department of Environmental Science and Policy, University of California Davis, Davis, CA, USA.

Ecosystem engineers are organisms characterized by interacting with other organisms thorough physical modifications or modifying their habitat. Examples of ecosystem engineers include Spartina alterniflora cordgrass or the zebra mussel Dreissena polymorpha. For both of these, the effect of modifying the environment can be nonlocal, affecting other regions farther away from the region populated by the ecosystem engineer. This shows the importance of understanding the population dynamics of ecosystem engineers in a spatial context. To do this, we have developed an extension of the ecosystem engineer population model of Cuddington et al. (Am Natur, 2009. https://doi.org/10.1086/597216 ) to the simplest spatial model, incorporating two local populations. We use this model to understand the relationship between dispersal and engineering effects, both at local and regional scales. Our main result is that the delayed Allee effect induced in the nonspatial model is extended to the spatial model, so the spread dynamics of an ecosystem engineer can be similar to the Allee case. However, there are more complex possibilities due to the two components of the dynamics. We also find quantitative guidelines that explain the interaction between spread of the environment modification and organism spread.
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http://dx.doi.org/10.1007/s11538-020-00833-9DOI Listing
November 2020

Mutualistic networks emerging from adaptive niche-based interactions.

Nat Commun 2020 10 29;11(1):5470. Epub 2020 Oct 29.

Department of Computer Science, University of California at Davis, Davis, CA, 95616, USA.

Mutualistic networks are vital ecological and social systems shaped by adaptation and evolution. They involve bipartite cooperation via the exchange of goods or services between actors of different types. Empirical observations of mutualistic networks across genres and geographic conditions reveal correlated nested and modular patterns. Yet, the underlying mechanism for the network assembly remains unclear. We propose a niche-based adaptive mechanism where both nestedness and modularity emerge simultaneously as complementary facets of an optimal niche structure. Key dynamical properties are revealed at different timescales. Foremost, mutualism can either enhance or reduce the network stability, depending on competition intensity. Moreover, structural adaptations are asymmetric, exhibiting strong hysteresis in response to environmental change. Finally, at the evolutionary timescale we show that the adaptive mechanism plays a crucial role in preserving the distinctive patterns of mutualism under species invasions and extinctions.
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http://dx.doi.org/10.1038/s41467-020-19154-5DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7596068PMC
October 2020

Dynamical Ising model of spatially coupled ecological oscillators.

J R Soc Interface 2020 10 28;17(171):20200571. Epub 2020 Oct 28.

Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA.

Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of 'universal' properties at the point of synchronization. Common biological systems of coupled oscillators have been shown to be members of the Ising universality class, meaning that the very simple Ising model replicates certain spatial statistics of these systems at stationarity. This observation is useful because it reveals which aspects of spatial pattern arise independently of the details governing local dynamics, resulting in both deeper understanding of and a simpler baseline model for biological synchrony. However, in many situations a system's dynamics are of greater interest than their static spatial properties. Here, we ask whether a dynamical Ising model can replicate universal and non-universal features of ecological systems, using noisy coupled metapopulation models with two-cycle dynamics as a case study. The standard Ising model makes unrealistic dynamical predictions, but the Ising model with memory corrects this by using an additional parameter to reflect the tendency for local dynamics to maintain their phase of oscillation. By fitting the two parameters of the Ising model with memory to simulated ecological dynamics, we assess the correspondence between the Ising and ecological models in several of their features (location of the critical boundary in parameter space between synchronous and asynchronous dynamics, probability of local phase changes and ability to predict future dynamics). We find that the Ising model with memory is reasonably good at representing these properties of ecological metapopulations. The correspondence between these models creates the potential for the simple and well-known Ising class of models to become a valuable tool for understanding complex biological systems.
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http://dx.doi.org/10.1098/rsif.2020.0571DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7653388PMC
October 2020

Interspecific competition slows range expansion and shapes range boundaries.

Proc Natl Acad Sci U S A 2020 10 14;117(43):26854-26860. Epub 2020 Oct 14.

Department of Ecology and Evolutionary Biology, University of Colorado, Boulder, CO 80309;

Species expanding into new habitats as a result of climate change or human introductions will frequently encounter resident competitors. Theoretical models suggest that such interspecific competition can alter the speed of expansion and the shape of expanding range boundaries. However, competitive interactions are rarely considered when forecasting the success or speed of expansion, in part because there has been no direct experimental evidence that competition affects either expansion speed or boundary shape. Here we demonstrate that interspecific competition alters both expansion speed and range boundary shape. Using a two-species experimental system of the flour beetles and , we show that interspecific competition dramatically slows expansion across a landscape over multiple generations. Using a parameterized stochastic model of expansion, we find that this slowdown can persist over the long term. We also find that the shape of the moving range boundary changes continuously over many generations of expansion, first steepening and then becoming shallower, due to the competitive effect of the resident and density-dependent dispersal of the invader. This dynamic boundary shape suggests that current forecasting approaches assuming a constant shape could be misleading. More broadly, our results demonstrate that interactions between competing species can play a large role during range expansions and thus should be included in models and studies that monitor, forecast, or manage expansions in natural systems.
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http://dx.doi.org/10.1073/pnas.2009701117DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7604451PMC
October 2020

Density dependent Resource Budget Model for alternate bearing.

J Theor Biol 2021 01 21;509:110498. Epub 2020 Sep 21.

Physics Department, University of Massachusetts, Amherst, MA 01003, USA. Electronic address:

Alternate bearing, seen in many types of plants, is the variable yield with a strongly biennial pattern. In this paper, we introduce a new model for alternate bearing behavior. Similar to the well-known Resource Budget Model, our model is based on the balance between photosynthesis or other limiting resource accumulation and reproduction processes. We consider two novel features with our model, 1) the existence of a finite capacity in the tree's resource reservoir and 2) the possibility of having low (but non-zero) yield when the tree's resource level is low. We achieve the former using a density dependent resource accumulation function, and the latter by removing the concept of the well-defined threshold used in the Resource Budget Model. At the level of an individual tree, our model has a stable two-cycle solution, which is suitable to model plants in which the alternate bearing behavior is pronounced. We incorporate environmental stochasticity by adding two uncorrelated noise terms to the parameters of the model associated with the nutrient accumulation and reproduction processes. Furthermore, we examine the model's behavior on a system of two coupled trees with direct coupling. Unlike the coupled Resource Budget Model, for which the only stable solution is the out-of-phase solution, our model with direct coupling has stable in-phase period-2 solutions. This suggests that our model might serve to explain spatial synchrony on a larger scale.
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http://dx.doi.org/10.1016/j.jtbi.2020.110498DOI Listing
January 2021

Forecasting resilience profiles of the run-up to regime shifts in nearly-one-dimensional systems.

J R Soc Interface 2020 09 16;17(170):20200566. Epub 2020 Sep 16.

Institute for Environmental Systems Research and Institute of Mathematics, University of Osnabrück, Barbarastraße 12, 49076 Osnabrück, Germany.

The forecasting of sudden, irreversible shifts in natural systems is a challenge of great importance, whose realization could allow pre-emptive action to be taken to avoid or mitigate catastrophic transitions, or to help systems adapt to them. In recent years, there have been many advances in the development of such early warning signals. However, much of the current toolbox is based around the tracking of statistical trends and therefore does not aim to estimate the future time scale of transitions or resilience loss. Metric-based indicators are also difficult to implement when systems have inherent oscillations which can dominate the indicator statistics. To resolve these gaps in the toolbox, we use additional system properties to fit parsimonious models to dynamics in order to predict transitions. Here, we consider nearly-one-dimensional systems-higher dimensional systems whose dynamics can be accurately captured by one-dimensional discrete time maps. We show how the nearly one-dimensional dynamics can be used to produce model-based indicators for critical transitions which produce forecasts of the resilience and the time of transitions in the system. A particularly promising feature of this approach is that it allows us to construct early warning signals even for critical transitions of chaotic systems. We demonstrate this approach on two model systems: of phosphorous recycling in a shallow lake, and of an overcompensatory fish population.
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http://dx.doi.org/10.1098/rsif.2020.0566DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7536042PMC
September 2020

Robert May, 1936-2020: A man for all disciplines.

Proc Natl Acad Sci U S A 2020 09 10;117(38):23199-23201. Epub 2020 Sep 10.

Emerging Pathogens Institute, University of Florida, Gainesville, FL 32611.

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http://dx.doi.org/10.1073/pnas.2016616117DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7519286PMC
September 2020

Community context and dispersal stochasticity drive variation in spatial spread.

J Anim Ecol 2020 11 28;89(11):2657-2664. Epub 2020 Sep 28.

Department of Environmental Science and Policy, University of California-Davis, Davis, CA, USA.

Dispersal is a key process in shaping species spatial distributions. Species interactions and variation in dispersal probabilities may jointly influence species spatial dynamics. However, many studies examine dispersal as a neutral process, independent of community context or intraspecific variation in dispersal behaviour. Here, we use controlled, replicated communities of two Tribolium species (T. castaneum and T. confusum) to examine how intraspecific variation in dispersal behaviour and community context influence dispersal dynamics in simple experimental landscapes composed of homogeneous habitat patches. We found considerable individual-level variation in dispersal probability that was unrelated to body size variation. Further, the context of dispersal mattered, as T. castaneum dispersal was reduced in two-species communities, while T. confusum dispersal was unaffected by community composition. Incorporating individual-level variation into a two-species stochastic spatial Ricker model, we provide evidence that individual-level variability in dispersal behaviour results in more variable spatial spread than assuming individuals have the same dispersal probability. Further, interspecific competition resulted in more variable spatial spread. The variability in spatial spread observed in our tightly controlled and replicated experimental system and in our stochastic model simulations points to potential fundamental limitations in forecasting species shifting ranges without considering potential interspecific interactions and demographic variability in dispersal behaviour.
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http://dx.doi.org/10.1111/1365-2656.13331DOI Listing
November 2020

Multiple Attractors and Long Transients in Spatially Structured Populations with an Allee Effect.

Bull Math Biol 2020 06 16;82(6):82. Epub 2020 Jun 16.

Institute of Mathematics and Institute of Environmental Systems Research, Osnabrück University, 49076, Osnabrück, Germany.

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.
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http://dx.doi.org/10.1007/s11538-020-00750-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7295732PMC
June 2020

Advancing an interdisciplinary framework to study seed dispersal ecology.

AoB Plants 2020 Apr 19;12(2):plz048. Epub 2019 Aug 19.

Department of Wildland Resources & Ecology Center, Utah State University, Logan, UT, USA.

Although dispersal is generally viewed as a crucial determinant for the fitness of any organism, our understanding of its role in the persistence and spread of plant populations remains incomplete. Generalizing and predicting dispersal processes are challenging due to context dependence of seed dispersal, environmental heterogeneity and interdependent processes occurring over multiple spatial and temporal scales. Current population models often use simple phenomenological descriptions of dispersal processes, limiting their ability to examine the role of population persistence and spread, especially under global change. To move seed dispersal ecology forward, we need to evaluate the impact of any single seed dispersal event within the full spatial and temporal context of a plant's life history and environmental variability that ultimately influences a population's ability to persist and spread. In this perspective, we provide guidance on integrating empirical and theoretical approaches that account for the context dependency of seed dispersal to improve our ability to generalize and predict the consequences of dispersal, and its anthropogenic alteration, across systems. We synthesize suitable theoretical frameworks for this work and discuss concepts, approaches and available data from diverse subdisciplines to help operationalize concepts, highlight recent breakthroughs across research areas and discuss ongoing challenges and open questions. We address knowledge gaps in the of seeds and the integration of that could benefit from such a synthesis. With an interdisciplinary perspective, we will be able to better understand how global change will impact seed dispersal processes, and potential cascading effects on plant population persistence, spread and biodiversity.
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http://dx.doi.org/10.1093/aobpla/plz048DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7179845PMC
April 2020

Long transients in ecology: Theory and applications.

Phys Life Rev 2020 03 13;32:1-40. Epub 2019 Sep 13.

Mathematics, Bowdoin College, Brunswick, USA.

This paper discusses the recent progress in understanding the properties of transient dynamics in complex ecological systems. Predicting long-term trends as well as sudden changes and regime shifts in ecosystems dynamics is a major issue for ecology as such changes often result in population collapse and extinctions. Analysis of population dynamics has traditionally been focused on their long-term, asymptotic behavior whilst largely disregarding the effect of transients. However, there is a growing understanding that in ecosystems the asymptotic behavior is rarely seen. A big new challenge for theoretical and empirical ecology is to understand the implications of long transients. It is believed that the identification of the corresponding mechanisms along with the knowledge of scaling laws of the transient's lifetime should substantially improve the quality of long-term forecasting and crisis anticipation. Although transient dynamics have received considerable attention in physical literature, research into ecological transients is in its infancy and systematic studies are lacking. This text aims to partially bridge this gap and facilitate further progress in quantitative analysis of long transients in ecology. By revisiting and critically examining a broad variety of mathematical models used in ecological applications as well as empirical facts, we reveal several main mechanisms leading to the emergence of long transients and hence lays the basis for a unifying theory.
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http://dx.doi.org/10.1016/j.plrev.2019.09.004DOI Listing
March 2020

Success and failure of ecological management is highly variable in an experimental test.

Proc Natl Acad Sci U S A 2019 11 28;116(46):23169-23173. Epub 2019 Oct 28.

Department of Environmental Science and Policy, University of California, Davis, CA 95616.

When managing natural systems, the importance of recognizing the role of uncertainty has been formalized as the precautionary approach. However, it is difficult to determine the role of stochasticity in the success or failure of management because there is almost always no replication; typically, only a single observation exists for a particular site or management strategy. Yet, assessing the role of stochasticity is important for providing a strong foundation for the precautionary approach, and learning from past outcomes is critical for implementing adaptive management of species or ecosystems. In addition, adaptive management relies on being able to implement a variety of strategies in order to learn-an often difficult task in natural systems. Here, we show that there is large, stochastically driven variability in success for management treatments to control an invasive species, particularly for moderate, and more feasible, management strategies. This is exactly where the precautionary approach should be important. Even when combining management strategies, we show that moderate effort in management either fails or is highly variable in its success. This variability allows some management treatments to, on average, meet their target, even when failure is probable. Our study is an important quantitative replicated experimental test of the precautionary approach and can serve as a way to understand the variability in management outcomes in natural systems which have the potential to be more variable than our tightly controlled system.
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http://dx.doi.org/10.1073/pnas.1911440116DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6859370PMC
November 2019

Harnessing tipping points in complex ecological networks.

J R Soc Interface 2019 09 11;16(158):20190345. Epub 2019 Sep 11.

School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA.

Complex and nonlinear ecological networks can exhibit a tipping point at which a transition to a global extinction state occurs. Using real-world mutualistic networks of pollinators and plants as prototypical systems and taking into account biological constraints, we develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with a tipping point. If conditions are changing so as to approach a tipping point, the management strategy we describe can prevent sudden drastic changes. Additionally, if the system has already moved past a tipping point, we show that a full recovery can occur for reasonable parameter changes only if there is active management of abundance, again due essentially to removal of the hysteresis. This recovery point in the aftermath of a tipping point can be predicted by a universal, two-dimensional reduced model.
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http://dx.doi.org/10.1098/rsif.2019.0345DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6769319PMC
September 2019

Consequences of intraspecific variation in seed dispersal for plant demography, communities, evolution and global change.

AoB Plants 2019 Aug 21;11(4):plz016. Epub 2019 Mar 21.

Department of Wildland Resources and Ecology Center, Utah State University, Logan, UT, USA.

As the single opportunity for plants to move, seed dispersal has an important impact on plant fitness, species distributions and patterns of biodiversity. However, models that predict dynamics such as risk of extinction, range shifts and biodiversity loss tend to rely on the mean value of parameters and rarely incorporate realistic dispersal mechanisms. By focusing on the mean population value, variation among individuals or variability caused by complex spatial and temporal dynamics is ignored. This calls for increased efforts to understand individual variation in dispersal and integrate it more explicitly into population and community models involving dispersal. However, the sources, magnitude and outcomes of intraspecific variation in dispersal are poorly characterized, limiting our understanding of the role of dispersal in mediating the dynamics of communities and their response to global change. In this manuscript, we synthesize recent research that examines the sources of individual variation in dispersal and emphasize its implications for plant fitness, populations and communities. We argue that this intraspecific variation in seed dispersal does not simply add noise to systems, but, in fact, alters dispersal processes and patterns with consequences for demography, communities, evolution and response to anthropogenic changes. We conclude with recommendations for moving this field of research forward.
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http://dx.doi.org/10.1093/aobpla/plz016DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6644487PMC
August 2019

Rapid changes in seed dispersal traits may modify plant responses to global change.

AoB Plants 2019 Jun 28;11(3):plz020. Epub 2019 Mar 28.

Nature Conservation and Landscape Ecology, University of Freiburg, Freiburg, Germany.

When climatic or environmental conditions change, plant populations must either adapt to these new conditions, or track their niche via seed dispersal. Adaptation of plants to different abiotic environments has mostly been discussed with respect to physiological and demographic parameters that allow local persistence. However, rapid modifications in response to changing environmental conditions can also affect seed dispersal, both via plant traits and via their dispersal agents. Studying such changes empirically is challenging, due to the high variability in dispersal success, resulting from environmental heterogeneity, and substantial phenotypic variability of dispersal-related traits of seeds and their dispersers. The exact mechanisms that drive rapid changes are often not well understood, but the ecological implications of these processes are essential determinants of dispersal success, and deserve more attention from ecologists, especially in the context of adaptation to global change. We outline the evidence for rapid changes in seed dispersal traits by discussing variability due to plasticity or genetics broadly, and describe the specific traits and biological systems in which variability in dispersal is being studied, before discussing some of the potential underlying mechanisms. We then address future research needs and propose a simulation model that incorporates phenotypic plasticity in seed dispersal. We close with a call to action and encourage ecologists and biologist to embrace the challenge of better understanding rapid changes in seed dispersal and their consequences for the reaction of plant populations to global change.
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http://dx.doi.org/10.1093/aobpla/plz020DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6548345PMC
June 2019

Setting expected timelines of fished population recovery for the adaptive management of a marine protected area network.

Ecol Appl 2019 09 26;29(6):e01949. Epub 2019 Jul 26.

Department of Fisheries and Wildlife, Coastal Oregon Marine Experiment Station, Oregon State University, Newport, Oregon, 97365, USA.

Adaptive management of marine protected areas (MPAs) requires developing methods to evaluate whether monitoring data indicate that they are performing as expected. Modeling the expected responses of targeted species to an MPA network, with a clear timeline for those expectations, can aid in the development of a monitoring program that efficiently evaluates expectations over appropriate time frames. Here, we describe the expected trajectories in abundance and biomass following MPA implementation for populations of 19 nearshore fishery species in California. To capture the process of filling in the age structure truncated by fishing, we used age-structured population models with stochastic larval recruitment to predict responses to MPA implementation. We implemented both demographically open (high larval immigration) and closed (high self-recruitment) populations to model the range of possible trajectories as they depend on recruitment dynamics. From these simulations, we quantified the time scales over which anticipated increases in abundance and biomass inside MPAs would become statistically detectable. Predicted population biomass responses range from little change, for species with low fishing rates, to increasing by a factor of nearly seven, for species with high fishing rates before MPA establishment. Increases in biomass following MPA implementation are usually greater in both magnitude and statistical detectability than increases in abundance. For most species, increases in abundance would not begin to become detectable for at least 10 years after implementation. Overall, these results inform potential indicator metrics (biomass), potential indicator species (those with a high fishing : natural mortality ratio), and time frame (>10 yr) for MPA monitoring assessment as part of the adaptive management process.
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http://dx.doi.org/10.1002/eap.1949DOI Listing
September 2019

Topological Data Analysis.

Bull Math Biol 2019 07;81(7):2051

, Davis, USA.

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http://dx.doi.org/10.1007/s11538-019-00610-3DOI Listing
July 2019
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