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.
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
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Abstract Aim We investigate the biogeographical history and diversification in a treefrog lineage distributed in contrasting (open and forested) ecoregions of South America, including three biodiversity hotspots. We evaluate the role of dispersal and whether other factors such as diversity‐dependence or paleotemperatures could explain the diversification pattern for this group. Especially focusing on the savanna endemics, we illuminate the processes governing the species assembly and evolution of the Cerrado savanna.
Location South American ecoregions south of the Amazon (i.e. Atlantic Forest, Cerrado, Araucaria Forest, Pampas, Central and Southern Andes).
Taxon Boana pulchella group.Methods We built the most complete time‐calibrated phylogeny for the group to date. We then reconstructed ancestral ranges using the dispersal‐extinction‐cladogenesis (DEC) model comparing different dispersal scenarios considering distance, adjacency and ecological similarity among regions. Centre‐of‐origin hypotheses in forest and open ecoregions were also tested. Using biogeographical stochastic mapping, we additionally estimated the contribution of range shifts across different biomes. Lastly, we evaluated several diversification models, including the effect of time, diversity‐dependence and temperature‐dependence on speciation and extinction rates.
Results The
Boana pulchella group originated during the Early Miocene (~17.5 MYA) and underwent high speciation rates during the Middle Miocene Climatic Optimum, with a decreasing trend following the Miocene Climatic Transition. We found no support for a single ecoregion acting as a centre of origin and diversification; instead, we inferred recurrent range shifts with dispersal among dissimilar adjacent ecoregions. Speciation linearly dependent on paleotemperatures, with either no or very low constant extinction rates, best explained the slowdown diversification pattern.Main conclusions Our results support a species assembly of Cerrado savanna in South America during the Miocene with intermittent interchange with rain forest habitats. Past climate changes impacted the rate new species originated with apparently no impact on extinction. Finally, the repeated habitat shifts among open/dry and forested/humid ecoregions, rather than long‐term in‐situ diversification in single areas, highlights the very dynamic historical interchange between contrasting habitats in South America, possibly contributing to its high species diversity.
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Abstract The refugia hypothesis, often used to explain Amazonia’s high biodiversity, initially received ample support but has garnered increasing criticism over time. Palynological, phylogenetic, and vegetation model reconstruction studies have been invoked to support the opposing arguments of extensive fragmentation versus a stable Amazonian Forest during Pleistocene glacial maxima. Here, we test the past existence of forest fragments and savanna connectivity by bias-correcting vegetation distributions from a Dynamic Vegetation Model (DVM) driven by paleoclimate simulations for South America during the Last Glacial Maximum (LGM). We find evidence for fragmented forests akin to refugia with extensive tropical humid forests to the west and forest islands in central/southern Amazonia. Drier ecosystems of Northern Llanos, Caatinga and Cerrado may have merged into continuous savanna/grasslands that dominated the continent. However, our reconstructions suggest taller, dense woodland/tropical savanna vegetation and areas of similar bioclimate connected disparate forest fragments across Amazonia. This ecotonal biome may have acted as a corridor for generalist forest and savanna species, creating connectivity that allows for range expansion during glacial periods. Simultaneously, it could have served as a barrier for specialists, inducing diversification through the formation of ‘semi-refugia’.
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Abstract Aim Climate 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.
Location Eastern USA.
Time period Last century to present.
Major taxa studied Temperate broadleaf forests.
Methods We 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.
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Main conclusions As 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.
