Alan Hastings

Alan Hastings
University of California, Davis | UCD

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502
Publications
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31,195
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Publications

Publications (502)
Article
Full-text available
During recent years, the study of long transients has been expanded in ecological theory to account for shifts in long-term behavior of ecological systems. These long transients may lead to regime shifts between alternative states that resemble the dynamics of alternative stable states for a prolonged period of time. One dynamic that potentially le...
Article
Invasive species account for incalculable damages worldwide, in both ecological and bioeconomic terms. The question of how a network of invasive populations can be optimally managed is one that deserves further exploration. A study accounting for partial observability and imperfect detection, in particular, could yield useful insights into species...
Article
Full-text available
Studies of oscillatory populations have a long history in ecology. A first-principles understanding of these dynamics can provide insights into causes of population regulation and help with selecting detailed predictive models. A particularly difficult challenge is determining the relative role of deterministic versus stochastic forces in producing...
Article
Full-text available
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 co...
Article
Full-text available
During their lifetimes, individuals in populations pass through different states, and the notion of an occupancy time describes the amount of time an individual spends in a given set of states. Questions related to this idea were studied in a recent paper by Roth and Caswell for cases where the environmental conditions are constant. However, it is...
Preprint
Full-text available
In this paper, we discuss the conceptual underpinnings of Modern Coexistence Theory (MCT), a quantitative framework for understanding ecological coexistence. In order to use MCT to infer how species are coexisting, one must relate a complex model (which simulates coexistence in the real world) to simple models in which previously proposed explanati...
Preprint
Full-text available
Ecologists have put forward many explanations for coexistence, but these are only partial explanations; nature is complex, so it is reasonable to assume that in any given ecological community, multiple mechanisms of coexistence are operating at the same time. Here, we present a methodology for quantifying the relative importance of different explan...
Preprint
Full-text available
How do species coexist? A framework known as Modern Coexistence Theory measures mechanisms of coexistence by comparing a species perturbed to low density (the invader) to other species that remain at their typical densities (the residents); this invader-resident comparison measures a rare-species advantage that results from specialization. However,...
Preprint
Full-text available
The storage effect is a well-known explanation for the coexistence of competing species in temporally varying environments. Like many complex ecological theories, the storage effect is often used as an explanation for observed coexistence on the basis of heuristic understanding, rather than careful application of a detailed model. But, a careful ex...
Preprint
Full-text available
The storage effect is a general explanation for coexistence in a variable environment. The generality of the storage effect is both a strength - it can be quantified in many systems - and a challenge - there is not a clear relationship between the abstract conditions for storage effect and species' life-history traits (e.g., dormancy, stage-structu...
Preprint
Full-text available
During recent years, the study of long transients has been expanded in ecological theory to account for shifts in long-term behavior of ecological systems. These long transients may lead to regime shifts between alternative states that resemble the dynamics of alternative stable states for a prolonged period of time. One dynamic that potentially le...
Preprint
Climate-driven habitat shifts pose challenges for dispersal-limited, late-maturing taxa such as trees. Older trees are often the most reproductive individuals in the population, but as habitats shift, these individuals can be left behind in the trailing range edge, generating "zombie forests" that may persist long after the suitable habitat has shi...
Preprint
Full-text available
Integrodifference equations are a discrete time spatially explicit model that describes dispersal of ecological populations through space. This framework is useful to study spread dynamics of organisms and how ecological interactions can affect their spread. When studying interactions such as consumption, dispersal rates might vary with life cycle...
Article
Full-text available
One of the main factors that determines habitat suitability for sessile and territorial organisms is the presence or absence of another competing individual in that habitat. This type of competition arises in populations occupying patches in a metacommunity. Previous studies have looked at this process using a continuous-time modeling framework, wh...
Article
Full-text available
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 throug...
Article
The planktonic larvae of many coastal marine invertebrates swim vertically during dispersal to exploit variation in current strength and direction, food abundance and mortality rate throughout the water column and offshore. Prior studies have estimated the effects of vertical swimming upon larval dispersal using mathematical models. However, most s...
Preprint
Full-text available
In restoration ecology, the Field of Dreams Hypothesis posits that restoration efforts that create a suitable environment could lead to eventual recovery of the remaining aspects of the ecosystem through natural processes. Natural processes following partial restoration has lead to ecosystem recovery in both terrestrial and aquatic systems. However...
Article
Full-text available
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 b...
Article
Full-text available
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...
Preprint
Full-text available
Nonlinear physics and agroecosystems can be of great relevance in the synchronisations of chaotic oscillators. The endogenous dynamics of the seed production of perennial plant species which include alternate bearing and masting, portray typical synchronisation patterns in nature and can be modelled using a tent map known as a resource budget model...
Preprint
Collective dynamics of chaotic oscillators has attracted much attention in many fields even including agriculture and forestry. Alternate bearing of tree crops is a phenomenon in which a year of heavy yield is followed by a light yield. This phenomenon has been modelled using a tent map known as a resource budget model (RBM). We applied in-phase/ou...
Article
Full-text available
Many benthic animals begin life with a planktonic larval stage during which coastal currents may move individuals far from shore. This trait is believed to allow individuals to develop away from nearshore predators and sibling competition, based on the assumption that mortality rates are weaker offshore. However, larvae developing offshore often fa...
Preprint
Full-text available
Studies of populations oscillating through time have a long history in ecology as these dynamics can help provide insights into the causes of population regulation. A particularly difficult challenge is determining the relative role of deterministic versus stochastic forces in producing this oscillatory behavior. Another classic ecological study ar...
Article
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...
Article
Full-text available
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 mechanisti...
Article
Full-text available
Adaptive management of marine protected areas (MPAs) to determine whether they are meeting their intended goals requires predicting how soon those goals will be realized. Such predictions have been made for increases in fish abundance and biomass inside MPAs. However, projecting increases in fishery yield (“fishery spillover”) is more complex becau...
Article
Full-text available
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 importan...
Conference Paper
Two types of physical disturbances that are impeding our understanding of ocean productivity are: 1) pulses of adverse conditions (e.g.,marine heat waves, pulses of low pH), and 2) changing frequencies of cycles in productivity (e.g.,ENSO fluctuations). Managers of fisheries and MPAs need to understand these better to maintain healthy oceans. We ha...
Article
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...
Preprint
Full-text available
Marine reserves are becoming an increasingly important tool in fisheries management. Particularly for species with relatively sedentary adults, the basic approach taken is to permanently close areas to fishing which allows species to recover inside the reserve and export larvae outside the reserve which eventually can be harvested. Two key issues a...
Preprint
Full-text available
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...
Article
1. 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). 2. However, incorporating stochasticity into population‐ or community‐level processes into models is necessar...
Article
Full-text available
We present a single-species metapopulation model structured by population size that is discrete in time. The novel formulation of our model allows for explicit incorporation of both the local, in space, dynamics and new details of the dispersal process. To study the impact of between-patch dynamics in the model, we construct various functions to de...
Article
Simple models in theoretical ecology have a long‐standing history of being used to understand how specific processes influence population dynamics as well as providing a foundation for future endeavors. The Levins model is the seminal example of this for continuous‐time metapopulation dynamics. However, many natural populations have a distinct sepa...
Article
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 > 1,000 / m²) and have unusually long life-spans (13 or 17 years). They spend most of their lives underground feeding on pl...
Article
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 ab...
Preprint
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 importan...
Article
Catastrophic events, like oil spills and hurricanes, occur in many marine systems. One potential role of marine reserves is buffering populations against disturbances, including the potential for disturbance-driven population collapses under Allee effects. This buffering capacity depends on reserves in a network providing rescue effects, setting up...
Article
Seasonality is an important feature of essentially all natural systems but the consequences of seasonality have been vastly underappreciated. Early work emphasized the role of seasonality in driving cyclic population dynamics, but the consequences of seasonality for ecological processes are far broader. Yet, seasonality is often not explicitly incl...
Article
Full-text available
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...
Preprint
Full-text available
During their lifetimes, individuals in populations pass through different states, and the notion of an occupancy time describes the amount of time an individual spends in a given set of states. Questions related to this idea were studied in a recent paper by Roth and Caswell for cases where the environmental conditions are constant. However, it is...
Preprint
Full-text available
Background Soil microbiomes play important roles in invasion biology, yet it is often treated as a ‘black box’ in modeling or large-scale field studies. Hence, investigating the change of association between invasive vegetation and soil microbes under changing environmental conditions, and exploring the genetic functions of associated microbiomes w...
Preprint
Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator-prey type. In the parameter regime where there is phase synchronization among all...
Article
Full-text available
The abundant-center hypothesis posits that species density should be highest in the center of the geographic range or climatic niche of a species, based on the idea that the center of either will be the area with the highest demographic performance (e.g., greater fecundity, survival, or carrying capacity). While intuitive, current support for the h...
Preprint
Full-text available
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 well studied and is an important one. A study of noise-induced tipping, in particular, could provide key insights into tipping cascades. Here, we cons...
Article
Full-text available
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 un...
Article
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...
Article
Full-text available
Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator-prey type. In the parameter regime where there is phase synchronization among all...
Article
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 mo...
Article
Full-text available
Whether fishing around the marine reserve edge can enhance harvested yields is an important issue in fisheries management. To solve the conundrum is difficult because of the lack of a matched boundary condition. Here, we derive a new boundary condition by considering individual losing at habitat boundaries. With the suitable boundary condition, our...
Article
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....
Article
1. Dispersal is a key process in shaping species spatial distributions. Species interactions and variation in dispersal probabilities may jointly influence species spatial dynamics. 2. However, many studies examine dispersal as a neutral process, independent of community context or intraspecific variation in dispersal behavior. 3. Here, we use cont...
Article
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,...
Preprint
Full-text available
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 mode...
Preprint
Full-text available
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 (carbon accumulation) and reproduction processes. We consider two n...
Article
Full-text available
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 ide...
Preprint
Full-text available
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 ide...
Conference Paper
Full-text available
Fishing reduces the resilience of fish populations to environmental variability. This occurs in part due to ‘cohort resonance’: as older fish are removed, generation time shrinks, and the population becomes more sensitive to variability at frequencies occurring on time scales near the generation time. This leaves populations more vulnerable to incr...
Article
Surrogates and indicators of biodiversity are used to infer the state and dynamics of species populations and ecosystems, as well as to inform conservation and management actions. Despite their widespread use, few studies have examined how ecological theory can guide the selection or surrogates and indicators, and thus reduce the likelihood of fail...
Article
A combination of laboratory experiments and mathematical and statistical analysis provides an affirmative answer to a decades-old question — can a predator and its prey coexist indefinitely? Long-sought evidence that predator-prey cycles can endure.
Article
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 si...
Preprint
Full-text available
Seasonality is an important feature of essentially all natural systems but the consequences of seasonality have been vastly underappreciated. Early work emphasized the role of seasonality in driving cyclic population dynamics, but the consequences of seasonality for ecological processes are far broader. Yet, seasonality is often not explicitly incl...
Article
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 m...
Chapter
This chapter describes how models can aid in managing populations to prevent extinction, given uncertainty about their state. From previous chapters, it is clear that avoiding extinction requires keeping both abundance and the replacement rate high. However, for both, the question remains, how high? The question of how high abundance should be to a...
Chapter
This chapter begins by revisiting the M’Kendrick/von Foerster model, but using size instead of age as the state variable. It then uses the lessons from that model to describe how individual growth and mortality rates determine both stand distributions (a population of mixed ages) and cohort distributions (all one age). In particular, incorporating...
Chapter
Most ecological populations exist in a randomly fluctuating environment, and these fluctuations influence vital rates, thus changing population dynamics. These changes are the focus of this chapter. The primary practical concern about environmental variability is the possibility that it could cause a population to go extinct, so the chapter describ...
Chapter
This chapter traces the evolution of models for fishery management, focusing on the problem of maintaining both replacement and a desirable level of yield. Early models from the 1950s led to management for maximum sustainable yield (MSY). Later, recruitment and egg production data from populations at low abundance were used to set critical replacem...
Chapter
This chapter introduces basic concepts in population modeling that will be applied throughout the book. It begins with the oldest example of a population model, the rabbit problem, which was described by Leonardo of Pisa (“Fibonacci”) and whose solution is the Fibonacci series. The chapter then explores what is known about simple models of populati...
Chapter
This chapter examines age-structured models with density-dependent recruitment. In particular, it focuses on populations with over-compensatory density dependence, such as may occur due to cannibalism or some types of space competition. When the slope (at the equilibrium point) of the relationship between egg production and subsequent recruitment i...