An official website of the United States government
The frequency distributions can characterize the population-potential landscape related to the stability of ecological states. We illustrate the practical utility of this approach by analyzing a forest–savanna model. Savanna and forest states coexist under certain conditions, consistent with past theoretical work and empirical observations. However, a grassland state, unseen in the corresponding deterministic model, emerges as an alternative quasi-stable state under fluctuations, providing a theoretical basis for the appearance of widespread grasslands in some empirical analyses. The ecological dynamics are determined by both the population-potential landscape gradient and the steady-state probability flux. The flux quantifies the net input/output to the ecological system and therefore the degree of nonequilibriumness. Landscape and flux together determine the transitions between stable states characterized by dominant paths and switching rates. The intrinsic potential landscape admits a Lyapunov function, which provides a quantitative measure of global stability. We find that the average flux, entropy production rate, and free energy have significant changes near bifurcations under both finite and zero fluctuation. These may provide both dynamical and thermodynamic origins of the bifurcations. We identified the variances in observed frequency time traces, fluctuations, and time irreversibility as kinematic measures for bifurcations. This framework opens the way to characterize ecological systems globally, to uncover how they change among states, and to quantify the emergence of quasi-stable states under stochastic fluctuations.
more »
« less
Pattern Formation in Mesic Savannas
Abstract We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Homogeneous solutions dominate the dynamics of the standard forest-savanna model, regardless of the length scales of the various spatial processes considered. However, several different pattern-forming scenarios are possible upon including spatial resource limitation, such as competition for water, soil nutrients, or herbivory effects. Using numerical simulations and continuation, we study the nature of the resulting patterns as a function of system parameters and length scales, uncovering subcritical pattern-forming bifurcations and observing significant regions of multistability for realistic parameter regimes. Finally, we discuss our results in the context of extant savanna-forest modeling efforts and highlight ongoing challenges in building a unifying mathematical model for savannas across different rainfall levels.
more »
« less
- PAR ID:
- 10476006
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Bulletin of Mathematical Biology
- Volume:
- 86
- Issue:
- 1
- ISSN:
- 0092-8240
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
ABSTRACT Predator‐prey models, such as the Leslie‐Gower model, are essential for understanding population dynamics and stability within ecosystems. These models help explain the balance between species under natural conditions, but the inclusion of factors like the Allee effect and intraspecific competition adds complexity and realism to these interactions, enhancing our ability to predict system behavior under stress. To detect early indicators of population collapse, this study investigates the intricate dynamics of a modified Leslie‐Gower predator‐prey model with both Allee effect and intraspecific competition. We analyze the existence and stability of equilibria, as well as bifurcation phenomena, including saddle‐node bifurcations of codimension 2, Hopf bifurcations of codimension 2, and Bogdanov‐Takens bifurcations of codimension at least 4. Detailed transitions between bifurcation curves–specifically saddle‐node, Hopf, homoclinic, and limit cycle bifurcations–are also examined. We observe a novel transition phenomenon, where a system jumps from saddle‐node bifurcation to homoclinic and limit cycle bifurcations. This suggests that burst oscillations may serve as an early warning of system collapse rather than simply a tipping point. Our findings indicate that moderate levels of intraspecific competition or Allee effect support coexistence of both populations, while excessive levels may destabilize the entire biological system, leading to collapse. These insights offer valuable implications for ecological management and the early detection of risks in population dynamics.more » « less
-
Abstract AimClimate and disturbance alter forest dynamics, from individual trees to biomes and from years to millennia, leaving legacies that vary with local, meso‐ and macroscales. Motivated by recent insights in temperate forests, we argue that temporal and spatial extents equivalent to that of the underlying drivers are necessary to characterize forest dynamics across scales. We focus specifically on characterizing mesoscale forest dynamics because they bridge fine‐scale (local) processes and the continental scale (macrosystems) in ways that are highly relevant for climate change science and ecosystem management. We revisit ecological concepts related to spatial and temporal scales and discuss approaches to gain a better understanding of climate–forest dynamics across scales. LocationEastern USA. Time periodLast century to present. Major taxa studiedTemperate broadleaf forests. MethodsWe review regional literature of past tree mortality studies associated with climate to identify mesoscale climate‐driven disturbance events. Using a dynamic vegetation model, we then simulate how these forests respond to a typical climate‐driven disturbance. ResultsBy identifying compound disturbance events from both a literature review and simulation modelling, we find that synchronous patterns of drought‐driven mortality at mesoscales have been overlooked within these forests. Main conclusionsAs ecologists, land managers and policy‐makers consider the intertwined drivers of climate and disturbance, a focus on spatio‐temporal scales equivalent to those of the drivers will provide insight into long‐term forest change, such as drought impacts. Spatially extensive studies should also have a long temporal scale to provide insight into pathways for forest change, evaluate predictions from dynamic forest models and inform development of global vegetation models. We recommend integrating data collected from spatially well‐replicated networks (e.g., archaeological, historical or palaeoecological data), consisting of centuries‐long, high‐resolution records, with models to characterize better the mesoscale response of forests to climate change in the past and in the future.more » « less
-
Abstract Global change is shifting disturbance regimes that may rapidly change ecosystems, sometimes causing ecosystems to shift between states. Interactions between disturbances such as fire and disease could have especially severe effects, but experimental tests of multi‐decadal changes in disturbance regimes are rare. Here, we surveyed vegetation for 35 years in a 54‐year fire frequency experiment in a temperate oak savanna–forest ecotone that experienced a recent outbreak of oak wilt. Different fire regimes determined whether plots were savanna or forest by regulating tree abundance (r2 = 0.70), but disease rapidly reversed the effect of fire exclusion, increasing mortality by 765% in unburned forests, but causing relatively minor changes in frequently burned savannas. Model simulations demonstrated that disease caused unburned forests to transition towards a unique woodland that was prone to transition to savanna if fire was reintroduced. Consequently, disease–fire interactions could shift ecosystem resilience and biome boundaries as pathogen distributions change.more » « less
-
Abstract Tropical ecosystems are undergoing unprecedented rates of degradation from deforestation, fire, and drought disturbances. The collective effects of these disturbances threaten to shift large portions of tropical ecosystems such as Amazon forests into savanna‐like structure via tree loss, functional changes, and the emergence of fire (savannization). Changes from forest states to a more open savanna‐like structure can affect local microclimates, surface energy fluxes, and biosphere–atmosphere interactions. A predominant type of ecosystem state change is the loss of tree cover and structural complexity in disturbed forest. Although important advances have been made contrasting energy fluxes between historically distinct old‐growth forest and savanna systems, the emergence of secondary forests and savanna‐like ecosystems necessitates a reframing to consider gradients of tree structure that span forest to savanna‐like states at multiple scales. In this Innovative Viewpoint, we draw from the literature on forest–grassland continua to develop a framework to assess the consequences of tropical forest degradation on surface energy fluxes and canopy structure. We illustrate this framework for forest sites with contrasting canopy structure that ranges from simple, open, and savanna‐like to complex and closed, representative of tropical wet forest, within two climatically distinct regions in the Amazon. Using a recently developed rapid field assessment approach, we quantify differences in cover, leaf area vertical profiles, surface roughness, albedo, and energy balance partitioning between adjacent sites and compare canopy structure with adjacent old‐growth forest; more structurally simple forests displayed lower net radiation. To address forest–atmosphere feedback, we also consider the effects of canopy structure change on susceptibility to additional future disturbance. We illustrate a converse transition—recovery in structure following disturbance—measuring forest canopy structure 10 yr after the imposition of a 5‐yr drought in the ground‐breaking Seca Floresta experiment. Our approach strategically enables rapid characterization of surface properties relevant to vegetation models following degradation, and advances links between surface properties and canopy structure variables, increasingly available from remote sensing. Concluding, we hypothesize that understanding surface energy balance and microclimate change across degraded tropical forest states not only reveals critical atmospheric forcing, but also critical local‐scale feedbacks from forest sensitivity to additional climate‐linked disturbance.more » « less
