Simple Ecological Models Research Articles

A niche for null models in adaptive resource management.

As global systems rapidly change, our collective ability to predict future ecological dynamics will become increasingly important for successful natural resource management. By merging stakeholder objectives with system uncertainty, and by adapting actions to changing systems and knowledge, adaptive resource management (ARM) provides a rigorous platform for making sound decisions in a changing world. Critically, however, applications of ARM could be improved by employing benchmarks (i.e., points of reference) for determining when learning is occurring through the cycle of monitoring, modeling, and decision‐making steps in ARM. Many applications of ARM use multiple model‐based hypotheses to identify and reduce systematic uncertainty over time, but generally lack benchmarks for gauging discovery of scientific evidence and learning. This creates the danger of thinking that directional changes in model weights or rankings are indicative of evidence for hypotheses, when possibly all competing models are inadequate. There is thus a somewhat obvious, but yet to be filled niche for including benchmarks for learning in ARM. We contend that carefully designed “ecological null models,” which are structured to produce an expected ecological pattern in the absence of a hypothesized mechanism, can serve as suitable benchmarks. Using a classic case study of mallard harvest management that is often used to demonstrate the successes of ARM for learning about ecological mechanisms, we show that simple ecological null models, such as population persistence (Nt +1 = Nt ), provide more robust near‐term forecasts of population abundance than the currently used mechanistic models. More broadly, ecological null models can be used as benchmarks for learning in ARM that trigger the need for discarding model parameterizations and developing new ones when prevailing models underperform the ecological null model. Identifying mechanistic models that surpass these benchmarks will improve learning through ARM and help decision‐makers keep pace with a rapidly changing world.

Biodiversity assessment across a dynamic riverine system: A comparison of eDNA metabarcoding versus traditional fish surveying methods

AbstractWhile many studies have considered the ability of eDNA to assess animal communities in lacustrine settings, fewer have considered riverine systems, particularly those spanning the environmental gradients present in large river basins. Such dynamic systems are challenging for eDNA biomonitoring due to differing eDNA transport distances in rivers and the effects of river chemistry. To address this challenge, we focused on the Thames River system, UK, which has exceptional historical fish records providing a baseline to test the accuracy of eDNA metabarcoding in recovering fish community structure across both fresh and tidal zones. Two primer sets targeting 12S and CO1 regions were used to capture fish communities across the Thames catchment, from the upper freshwaters to the mid estuary. eDNA was collected at 35 sites, 14 of which were simultaneously paired with traditional fish surveys for direct comparison. We demonstrated that eDNA metabarcoding consistently detected more freshwater species than traditional methods, despite extensive sampling effort using the latter. In contrast, metabarcoding did not perform as well as traditional approaches in estuarine waters, although results included the novel detection of the protected sea lamprey. We further demonstrated that minor variations in the recovery of all approaches would not impact on the assessment of simple ecological models of community structure and, thus, some variability between approaches should not be viewed as a serious hindrance to uptake. Rather, our findings support a growing consensus that eDNA can reliably detect fish communities across dynamic freshwater habitats.

Developmental Change in Predators Drives Different Community Configurations.

AbstractTheoreticians who first observed alternative stable states in simple ecological models warned of grave implications for unexpected and irreversible collapses of natural systems (i.e., regime shifts). Recent ecosystem-level shifts engendering considerable economic losses have validated this concern, positioning bistability at the vanguard of coupled human-environment systems management. While the perturbations that induce regime shifts are known, the ecological forces that uphold alternative stable states are often unresolved or complex and system specific. Thus, the search continues for general mechanisms that can produce alternative stable states under realistic conditions. Integrating model predictions with long-term zooplankton community experiments, we show that the core feature of ontogenetic development, food-dependent maturation, enables a single community to reach different configurations within the same constant environment. In one configuration, predators regulate prey to foster coexistence, while in the other, prey counterintuitively exclude their predators via maturation-limiting competition. The concordance of these findings with the unique outcome and underlying mechanism of a general model provides empirical evidence that developmental change, a fundamental property of life, can support bistability of natural systems.

Ecological and evolutionary diversification in the Australo-Papuan scrubwrens (Sericornis) and mouse-warblers (Crateroscelis), with a revision of the subfamily Sericornithinae (Aves: Passeriformes: Acanthizidae)

Understanding how the complex geotectonic and climatic history of the Australo-Papuan region has promoted the ecological and evolutionary diversification of its avifauna remains a challenge. Outstanding questions relate to the nature and timing of biogeographical connections between Australia and the emerging island of New Guinea and the mechanisms by which distinctive altitudinal replacement sequences have evolved amongst congeneric species in montane New Guinea. Here, we combine analyses of phylogenetic and eco-morphological data to investigate ecological and evolutionary patterns of diversification in the largely mesic-adapted Australo-Papuan scrubwrens (Sericornis) and mouse-warblers (Crateroscelis). We find evidence of ecological convergence and present a revised taxonomic and systematic treatment of the subfamily integrating information from new (ND2) and existing molecular phylogenetic reconstructions. Biogeographical connections indicate at least three phases of faunal interchange between Australia and New Guinea commencing in the mid to late Miocene. We also find little support for the proposed time dependency of ecological sorting mechanisms linked to divergence in foraging niche amongst altitudinal replacements. Instead, physiological adaptations to hypoxia and increased thermal efficiency at higher altitudes may better account for observed patterns of diversification in montane New Guinea. Indirect support for this hypothesis is derived from molecular clock calibrations that indicate a pulse of diversification across the Miocene-Pliocene boundary coincident with a phase of rapid mountain uplift. Simple ecological and climatic models appear inadequate for explaining observed patterns and mechanisms of diversification in the New Guinean montane avifauna. Further insights will require multidisciplinary research integrating geotectonic, palaeoclimatic, genetic, ecological and physiological approaches.

Dry season streamflow persistence in seasonal climates

AbstractSeasonally dry ecosystems exhibit periods of high water availability followed by extended intervals during which rainfall is negligible and streamflows decline. Eventually, such declining flows will fall below the minimum values required to support ecosystem functions or services. The time at which dry season flows drop below these minimum values (Q*), relative to the start of the dry season, is termed the “persistence time” ( ). The persistence time determines how long seasonal streams can support various human or ecological functions during the dry season. In this study, we extended recent work in the stochastic hydrology of seasonally dry climates to develop an analytical model for the probability distribution function (PDF) of the persistence time. The proposed model accurately captures the mean of the persistence time distribution, but underestimates its variance. We demonstrate that this underestimation arises in part due to correlation between the parameters used to describe the dry season recession, but that this correlation can be removed by rescaling the flow variables. The mean persistence time predictions form one example of the broader class of streamflow statistics known as crossing properties, which could feasibly be combined with simple ecological models to form a basis for rapid risk assessment under different climate or management scenarios.

Notes from the field: Lessons learned from using ecosystem service approaches to inform real-world decisions

While there have been rapid advances in assessments of biodiversity and ecosystem services (BES), a critical remaining challenge is how to move from scientific knowledge to real-world decision making. We offer 6 lessons from our experiences applying new approaches and tools for quantifying BES in 20 pilot demonstrations: (1) Applying a BES approach is most effective in leading to policy change as part of an iterative science-policy process; (2) simple ecological production function models have been useful in a diverse set of decision contexts, across a broad range of biophysical, social, and governance systems. Key limitations of simple models arise at very small scales, and in predicting specific future BES values; (3) training local experts in the approaches and tools is important for building local capacity, ownership, trust, and long-term success; (4) decision makers and stakeholders prefer to use a variety of BES value metrics, not only monetary values; (5) an important science gap exists in linking changes in BES to changes in livelihoods, health, cultural values, and other metrics of human wellbeing; and (6) communicating uncertainty in useful and transparent ways remains challenging.

Catastrophic Collapse Can Occur without Early Warning: Examples of Silent Catastrophes in Structured Ecological Models

Catastrophic and sudden collapses of ecosystems are sometimes preceded by early warning signals that potentially could be used to predict and prevent a forthcoming catastrophe. Universality of these early warning signals has been proposed, but no formal proof has been provided. Here, we show that in relatively simple ecological models the most commonly used early warning signals for a catastrophic collapse can be silent. We underpin the mathematical reason for this phenomenon, which involves the direction of the eigenvectors of the system. Our results demonstrate that claims on the universality of early warning signals are not correct, and that catastrophic collapses can occur without prior warning. In order to correctly predict a collapse and determine whether early warning signals precede the collapse, detailed knowledge of the mathematical structure of the approaching bifurcation is necessary. Unfortunately, such knowledge is often only obtained after the collapse has already occurred.

Conceptual modelling of Lake Manyas, Turkey

Previously determined biological and physico-chemical properties of Lake Manyas are employed in modelling the sensitivity of water quality and ecosystem integrity to the (a) water residence time and (b) nutrient inputs from anthropogenic sources. In that context, simple ecological conceptual models are simulated for predicting changes in the aquatic ecosystem with respect to these driving variables. Results yield thresholds where major changes in system behaviour are expected. Based on model predictions, recommendations for the restoration of water quality and ecosystem integrity are made.

Continuous Bayesian Network for Studying the Causal Links between Phosphorus Loading and Plankton Patterns in Lake Simcoe, Ontario, Canada

An ecosystem perspective to restoring beneficial uses in Areas of Concern can be interpreted as a shift from the traditional elucidation of simple cause-effect relationships to a multicausal way of thinking that more effectively accommodates ecosystem complexity. This holistic management paradigm has also pervaded the contemporary ecological modeling practice, making compelling the adoption of more sophisticated ecosystem modeling tools. In this study, our primary objective is to develop a Bayesian hierarchical network of simple ecological models for Lake Simcoe, Ontario, Canada, aiming to establish a realistic representation of the causal connections among exogenous nutrient loading, ambient nutrient conditions, and epilimnetic plankton dynamics. In particular, we used a spatially explicit simple mass-balance model forced with idealized sinusoidal loading to predict total phosphorus concentrations. A structural equation model was then used to delineate the interplay among nutrients, ambient light conditions, phytoplankton, and herbivorous biomass. Our analysis highlights the strength of the causal linkages between total phosphorus and water clarity with phytoplankton as well as the capacity of zooplankton grazing to modulate the algal standing crop. Our Bayesian network is also used to examine the exceedance frequency of threshold values for total phosphorus (15 μg/L) and chlorophyll a (4 μg/L) concentrations under scenarios of phosphorus loading reduction. Our study suggests that a 15% phosphorus loading decrease will still result in >25% violations of the 4 μg chla/L value in the two embayments of Lake Simcoe (Cook's Bay and Kempenfelt Bay). The TP levels will decrease in response to the exogenous loading reductions and this improvement will be primarily manifested in the northcentral segments of the system.

Giant number fluctuations in microbial ecologies

Statistical fluctuations in population sizes of microbes may be quite large depending on the nature of their underlying stochastic dynamics. For example, the variance of the population size of a microbe undergoing a pure birth process with unlimited resources is proportional to the square of its mean. We refer to such large fluctuations, with the variance growing as square of the mean, as giant number fluctuations (GNF). Luria and Delbrück showed that spontaneous mutation processes in microbial populations exhibit GNF. We explore whether GNF can arise in other microbial ecologies. We study certain simple ecological models evolving via stochastic processes: (i) bi-directional mutation, (ii) lysis–lysogeny of bacteria by bacteriophage, and (iii) horizontal gene transfer (HGT). For the case of bi-directional mutation process, we show analytically exactly that the GNF relationship holds at large times. For the ecological model of bacteria undergoing lysis or lysogeny under viral infection, we show that if the viral population can be experimentally manipulated to stay quasi-stationary, the process of lysogeny maps essentially to one-way mutation process and hence the GNF property of the lysogens follows. Finally, we show that even the process of HGT may map to the mutation process at large times, and thereby exhibits GNF.

Modelling and mapping spread in pest risk analysis: a generic approach*

Assessing the likelihood and magnitude of spread is one of the cornerstones of pest risk analysis (PRA), and is usually based on qualitative expert judgment. This paper proposes a suite of simple ecological models to support risk assessors who also wish to estimate the rate and extent of spread, e.g. when modelling the dynamics of invasion and the economic impacts that may result. Models are based on simple ecological principles, such as logistic growth, radial range expansion and population growth in combination with dispersal. Different models capture different perspectives of the spread process, being based on pest density or simply presence/absence, and they compare spatially explicit and spatially implicit approaches. A case study on Diabrotica virgifera virgifera is provided for illustration. The suite of models requires further development and testing with the risk assessment community building familiarity before their more general application in PRA.

Trophic responses to nutrient enrichment in a temperate seagrass food chain

Simple ecological models that predict trophic responses to bottom-up forcing are valuable tools for ecosystem managers. Traditionally, theoretical ecologists have used resource-dependent functional responses to explain the modification of food chains exposed to bottom-up perturbations. These models predict alternating positive, negative and zero responses at each trophic level. More recently, ratio-dependent functional response models that predict proportional increases at each level have challenged this paradigm. The present study tested the predictions of the 2 hypotheses empirically by comparing the relative biomasses of 4 trophic levels of an estuarine seagrass food chain in relatively undisturbed, low-nutrient catchments and 'developed' catchments subjected to a prolonged period of nutrient enrichment. We found that nutrient-enriched sites had significantly greater biomass of both epiphytic algae and grazing invertebrates; however, the bottom-up forcing of nutrients was attenuated at higher trophic levels (occupied by juvenile and piscivorous fish), with no significant effect of catchment development. This disconnect in the upward cascade of energy may be due to a number of possible reasons including high levels of diversity and omnivory, trophic subsidy within the system or the strength or nature of perturbations. Although the predictions of both hypotheses failed to hold across all trophic groups, ratio dependence was prevalent at the lower levels of the food chain, which has implications for catchment management.

Competition, predation and coexistence in a three trophic system

Simple ecological models that mostly operate with population densities using continuous variables, explain quite well the behavior of real populations. In this work we propose and discuss the continuous dynamics of a system of three species, which belongs to the well-known family of Lotka–Volterra models. In particular, the proposed model includes direct effects such as predation and competition among species, and indirect effects such as refuge. The model is proposed to explain recent studies about a group of crustacean (amphipods of genus Hyallela) found in all the plain streams and shallow lakes of the American continent. The studied system includes three compartments: algae, a strictly herbivore amphipod and an omnivore (herbivore and carnivore) one. The analysis of the model shows that there are stable extinction equilibria throughout all the parameters’ space. There are also equilibria with stable coexistence of the three species and two interesting binary equilibria: one with stable coexistence of algae and herbivore and other with coexistence between algae and omnivore amphipods. The presence of Allee effect in the algae growth and the existence of refuge for the herbivore amphipod (prey) determine a bottom-up control.

High-amplitude fluctuations and alternative dynamical states of midges in Lake Myvatn

Complex dynamics are often shown by simple ecological models and have been clearly demonstrated in laboratory and natural systems. Yet many classes of theoretically possible dynamics are still poorly documented in nature. Here we study long-term time-series data of a midge, Tanytarsus gracilentus (Diptera: Chironomidae), in Lake Myvatn, Iceland. The midge undergoes density fluctuations of almost six orders of magnitude. Rather than regular cycles, however, these fluctuations have irregular periods of 4-7 years, indicating complex dynamics. We fit three consumer-resource models capable of qualitatively distinct dynamics to the data. Of these, the best-fitting model shows alternative dynamical states in the absence of environmental variability; depending on the initial midge densities, the model shows either fluctuations around a fixed point or high-amplitude cycles. This explains the observed complex population dynamics: high-amplitude but irregular fluctuations occur because stochastic variability causes the dynamics to switch between domains of attraction to the alternative states. In the model, the amplitude of fluctuations depends strongly on minute resource subsidies into the midge habitat. These resource subsidies may be sensitive to human-caused changes in the hydrology of the lake, with human impacts such as dredging leading to higher-amplitude fluctuations. Tanytarsus gracilentus is a key component of the Myvatn ecosystem, representing two-thirds of the secondary productivity of the lake and providing vital food resources to fish and to breeding bird populations. Therefore the high-amplitude, irregular fluctuations in midge densities generated by alternative dynamical states dominate much of the ecology of the lake.

Changing skewness: an early warning signal of regime shifts in ecosystems

Empirical evidence for large-scale abrupt changes in ecosystems such as lakes and vegetation of semi-arid regions is growing. Such changes, called regime shifts, can lead to degradation of ecological services. We study simple ecological models that show a catastrophic transition as a control parameter is varied and propose a novel early warning signal that exploits two ubiquitous features of ecological systems: nonlinearity and large external fluctuations. Either reduced resilience or increased external fluctuations can tip ecosystems to an alternative stable state. It is shown that changes in asymmetry in the distribution of time series data, quantified by changing skewness, is a model-independent and reliable early warning signal for both routes to regime shifts. Furthermore, using model simulations that mimic field measurements and a simple analysis of real data from abrupt climate change in the Sahara, we study the feasibility of skewness calculations using data available from routine monitoring.

Sudden Shifts in Ecological Systems: Intermittency and Transients in the Coupled Ricker Population Model

Many real ecological systems show sudden changes in behavior, phenomena sometimes categorized as regime shifts in the literature. The relative importance of exogenous versus endogenous forces producing regime shifts is an important question. These forces' role in generating variability over time in ecological systems has been explored using tools from dynamical systems. We use similar ideas to look at transients in simple ecological models as a way of understanding regime shifts. Based in part on the theory of crises, we carefully analyze a simple two patch spatial model and begin to understand from a mathematical point of view what produces transient behavior in ecological systems. In particular, since the tools are essentially qualitative, we are able to suggest that transient behavior should be ubiquitous in systems with overcompensatory local dynamics, and thus should be typical of many ecological systems.

Estuarine classification and response to nitrogen loading: Insights from simple ecological models

Estuaries exhibit a large range in their responses to nitrogen loadings determined in part by characteristics of the driver, such as magnitude and frequency, but also by such intrinsic characteristics as physical/chemical factors (e.g., depth, volume, hypsometry, salinity, turbidity) and biological factors (e.g., nature of ecological communities, trophic interactions). To address the richness of estuarine response to driver variables, the aim ultimately is to establish a simple estuarine classification scheme, beginning with a river-dominated subset of estuarine systems and focusing on the role of water residence time in the estuary. Residence time (or flushing time) is related to other drivers (streamflow, nutrient, and sediment loads) and drives much of the biological response of estuaries because of flushing effects on plankton, temperature, nutrients, and light. Toward this goal, nutrient–phytoplankton–zooplankton (NPZ) models have been used to examine a range of subjects including effects of nutrient limitation and zooplankton predation on phytoplankton dynamics and fish predation. This class of model can admit a wide range of behavior, including multiple steady-states and oscillatory behavior. The NPZ equations include terms for nutrient recycling, phytoplankton settling, benthic regeneration, and zooplankton mortality. Analysis of the equations suggests that both the nature of nitrogen loading (i.e., whether it is correlated with discharge or independent of it) and residence time are critical in determining the steady-state response of the system.

Trophic structure and dynamical complexity in simple ecological models

We study the dynamical complexity of five non-linear deterministic predator–prey model systems. These simple systems were selected to represent a diversity of trophic structures and ecological interactions in the real world while still preserving reasonable tractability. We find that these systems can dramatically change attractor types, and the switching among different attractors is dependent on system parameters. While dynamical complexity depends on the nature (e.g., inter-specific competition versus predation) and degree (e.g., number of interacting components) of trophic structure present in the system, these systems all evolve principally on intrinsically noisy limit cycles. Our results support the common observation of cycling and rare observation of chaos in natural populations. Our study also allows us to speculate on the functional role of specialist versus generalist predators in food web modeling.

Temporal and spatial aspects of peatland initiation following deglaciation in North America

A set of simple ecological models accounts well for the cumulative initiation of peatlands throughout North America in relation to glacial retreat. The most parsimonious form incorporates, first, a delay term to account for the lag during which newly deglaciated land became suitable for peatland initiation and, second, an intrinsic rate of initiation related to the probability of migration and establishment of plant propagules from elsewhere. The goodness of fit of the models, based on 1680 basal-peat dates throughout the continent, allows projection of past trends into the future. Factors contributing to the lag of about 4000 years between deglaciation and peatland initiation are suggested and data on colonization of deglaciated land by beavers (known to initiate peatlands) are presented. The rate of peatland initiation peaked between 7000 and 8000 years ago, but remains appreciable today. A marked depression of peatland initiation (8360–8040BP) interrupted the peak rate. The time of the interruption matches the 8200BP cold–dry event recorded in Greenland ice cores, and suggests that this event caused a substantial, continent-wide depression of an important ecosystem function, i.e., carbon sequestration from the atmosphere by peat deposition. Spontaneous initiation of new peatlands is projected to continue for millennia to come.

Coupled oscillations in food webs: balancing competition and mutualism in simple ecological models.

As in other oscillating systems, oscillations of consumer resource pairs in ecological systems may be coupled such that complex behavior results. The form of that coupling may determine the nature and extent of this behavior. Two biologically significant forms of coupling are here investigated: first, where consumers consume each other's resources (CR coupling, representing competition between the two consumers), and second, where the resources are in competition with one another (RR coupling, potentially representing indirect mutualism between the two consumers). Interestingly, CR coupling leads to in-phase synchrony of the oscillations, whereas RR coupling leads to antiphase synchrony. With either form of coupling, if the coupling remains weak, synchronous behavior is generated in the two systems. At strong levels of coupling, when the two forms act simultaneously, a balance between competition and mutualism is generated, which is manifest differently at different levels of resource coupling.