Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop

This is the author accepted manuscript. The final version is available from the American Institute of Mathematical Sciences via the DOI in this recordWe study a scalar, first-order delay differential equation (DDE) with instantaneous and state-dependent delayed feedback, which itself may be delayed. The state dependence introduces nonlinearity into an otherwise linear system. We investigate the ensuing nonlinear dynamics with the case of instantaneous state dependence as our starting point. We present the bifurcation diagram in the parameter plane of the two feedback strengths showing how periodic orbits bifurcate from a curve of Hopf bifurcations and disappear along a curve where both period and amplitude grow beyond bound as the orbits become saw-tooth shaped. We then 'switch on' the delay within the state-dependent feedback term, reflected by a parameter b>0. Our main conclusion is that the new parameter b has an immediate effect: as soon as b>0 the bifurcation diagram for b=0 changes qualitatively and, specifically, the nature of the limiting saw-tooth shaped periodic orbits changes. Moreover, we show − numerically and through center manifold analysis − that a degeneracy at b=1/3 of an equilibrium with a double real eigenvalue zero leads to a further qualitative change and acts as an organizing center for the bifurcation diagram. Our results demonstrate that state dependence in delayed feedback terms may give rise to new dynamics and, moreover, that the observed dynamics may change significantly when the state-dependent feedback depends on past states of the system. This is expected to have implications for models arising in different application contexts, such as models of human balancing and conceptual climate models of delayed action oscillator type.Natural Sciences and Research Council of CanadaRoyal Society Te ApārangiEngineering and Physical Sciences Research Council (EPSRC

Markedly Divergent Tree Assemblage Responses to Tropical Forest Loss and Fragmentation across a Strong Seasonality Gradient

We examine the effects of forest fragmentation on the structure and composition of tree assemblages within three seasonal and aseasonal forest types of southern Brazil, including evergreen, Araucaria, and deciduous forests. We sampled three southernmost Atlantic Forest landscapes, including the largest continuous forest protected areas within each forest type. Tree assemblages in each forest type were sampled within 10 plots of 0.1 ha in both continuous forests and 10 adjacent forest fragments. All trees within each plot were assigned to trait categories describing their regeneration strategy, vertical stratification, seed-dispersal mode, seed size, and wood density. We detected differences among both forest types and landscape contexts in terms of overall tree species richness, and the density and species richness of different functional groups in terms of regeneration strategy, seed dispersal mode and woody density. Overall, evergreen forest fragments exhibited the largest deviations from continuous forest plots in assemblage structure. Evergreen, Araucaria and deciduous forests diverge in the functional composition of tree floras, particularly in relation to regeneration strategy and stress tolerance. By supporting a more diversified light-demanding and stress-tolerant flora with reduced richness and abundance of shade-tolerant, old-growth species, both deciduous and Araucaria forest tree assemblages are more intrinsically resilient to contemporary human-disturbances, including fragmentation-induced edge effects, in terms of species erosion and functional shifts. We suggest that these intrinsic differences in the direction and magnitude of responses to changes in landscape structure between forest types should guide a wide range of conservation strategies in restoring fragmented tropical forest landscapes worldwide

Basin-wide variation in tree hydraulic safety margins predicts the carbon balance of Amazon forests

Tropical forests face increasing climate risk1,2, yet our ability to predict their response to climate change is limited by poor understanding of their resistance to water stress. Although xylem embolism resistance thresholds (for example, Ψ50) and hydraulic safety margins (for example, HSM50) are important predictors of drought-induced mortality risk3–5, little is known about how these vary across Earth’s largest tropical forest. Here, we present a pan-Amazon, fully standardized hydraulic traits dataset and use it to assess regional variation in drought sensitivity and hydraulic trait ability to predict species distributions and long-term forest biomass accumulation. Parameters Ψ50 and HSM50 vary markedly across the Amazon and are related to average long-term rainfall characteristics. Both Ψ50 and HSM50 influence the biogeographical distribution of Amazon tree species. However, HSM50 was the only significant predictor of observed decadal-scale changes in forest biomass. Old-growth forests with wide HSM50 are gaining more biomass than are low HSM50 forests. We propose that this may be associated with a growth–mortality trade-off whereby trees in forests consisting of fast-growing species take greater hydraulic risks and face greater mortality risk. Moreover, in regions of more pronounced climatic change, we find evidence that forests are losing biomass, suggesting that species in these regions may be operating beyond their hydraulic limits. Continued climate change is likely to further reduce HSM50 in the Amazon6,7, with strong implications for the Amazon carbon sink

Biased-corrected richness estimates for the Amazonian tree flora

Amazonian forests are extraordinarily diverse, but the estimated species richness is very much debated. Here, we apply an ensemble of parametric estimators and a novel technique that includes conspecific spatial aggregation to an extended database of forest plots with up-to-date taxonomy. We show that the species abundance distribution of Amazonia is best approximated by a logseries with aggregated individuals, where aggregation increases with rarity. By averaging several methods to estimate total richness, we confirm that over 15,000 tree species are expected to occur in Amazonia. We also show that using ten times the number of plots would result in an increase to just ~50% of those 15,000 estimated species. To get a more complete sample of all tree species, rigorous field campaigns may be needed but the number of trees in Amazonia will remain an estimate for years to come

Basin-wide variation in tree hydraulic safety margins predicts the carbon balance of Amazon forests

This is the final version. Available on open access from Nature Research via the DOI in this recordData availability: The pan-Amazonian HT dataset (Ψ 50, Ψ dry and HSM50) and branch wood density per species per site, as well as forest dynamic and climate data per plot presented in this study are available as a ForestPlots.net data package at https://forestplots.net/data-packages/Tavares-et-al-2023. Basal area weighted mean LMA is shown in Supplementary Table 2. Species stem wood density data were obtained from Global Wood Density database65,66. Species WDA data were extracted from ref. 45.Code availability: The codes to recreate the main analyses and the main figures presented in this study are available as a ForestPlots.net data package at https://forestplots.net/data-packages/Tavares-et-al-2023.Tropical forests face increasing climate risk, yet our ability to predict their response to climate change is limited by poor understanding of their resistance to water stress. Although xylem embolism resistance thresholds (for example, Ψ 50) and hydraulic safety margins (for example, HSM50) are important predictors of drought-induced mortality risk, little is known about how these vary across Earth’s largest tropical forest. Here, we present a pan-Amazon, fully standardized hydraulic traits dataset and use it to assess regional variation in drought sensitivity and hydraulic trait ability to predict species distributions and long-term forest biomass accumulation. Parameters Ψ 50 and HSM50 vary markedly across the Amazon and are related to average long-term rainfall characteristics. Both Ψ 50 and HSM50 influence the biogeographical distribution of Amazon tree species. However, HSM50 was the only significant predictor of observed decadal-scale changes in forest biomass. Old-growth forests with wide HSM50 are gaining more biomass than are low HSM50 forests. We propose that this may be associated with a growth–mortality trade-off whereby trees in forests consisting of fast-growing species take greater hydraulic risks and face greater mortality risk. Moreover, in regions of more pronounced climatic change, we find evidence that forests are losing biomass, suggesting that species in these regions may be operating beyond their hydraulic limits. Continued climate change is likely to further reduce HSM50 in the Amazon, with strong implications for the Amazon carbon sink

Geographic patterns of tree dispersal modes in Amazonia and their ecological correlates

This is the final version. Available on open access from Wiley via the DOI in this recordData availability statement: The percentages of dispersal modes per plot are included as Supporting Information (Table S7, based on 5433 species and morphospecies within 1877 tree-inventory plots across terra-firme, seasonally flooded, and permanently flooded forests in Amazonia). The dispersal modes assigned to these 5433 species and morphospecies are also included as Supporting Information (Table S8).Aim: To investigate the geographic patterns and ecological correlates in the geographic distribution of the most common tree dispersal modes in Amazonia (endozoochory, synzoochory, anemochory and hydrochory). We examined if the proportional abundance of these dispersal modes could be explained by the availability of dispersal agents (disperser-availability hypothesis) and/or the availability of resources for constructing zoochorous fruits (resource-availability hypothesis). Time period: Tree-inventory plots established between 1934 and 2019. Major taxa studied: Trees with a diameter at breast height (DBH) ≥ 9.55 cm. Location: Amazonia, here defined as the lowland rain forests of the Amazon River basin and the Guiana Shield. Methods: We assigned dispersal modes to a total of 5433 species and morphospecies within 1877 tree-inventory plots across terra-firme, seasonally flooded, and permanently flooded forests. We investigated geographic patterns in the proportional abundance of dispersal modes. We performed an abundance-weighted mean pairwise distance (MPD) test and fit generalized linear models (GLMs) to explain the geographic distribution of dispersal modes. Results: Anemochory was significantly, positively associated with mean annual wind speed, and hydrochory was significantly higher in flooded forests. Dispersal modes did not consistently show significant associations with the availability of resources for constructing zoochorous fruits. A lower dissimilarity in dispersal modes, resulting from a higher dominance of endozoochory, occurred in terra-firme forests (excluding podzols) compared to flooded forests. Main conclusions: The disperser-availability hypothesis was well supported for abiotic dispersal modes (anemochory and hydrochory). The availability of resources for constructing zoochorous fruits seems an unlikely explanation for the distribution of dispersal modes in Amazonia. The association between frugivores and the proportional abundance of zoochory requires further research, as tree recruitment not only depends on dispersal vectors but also on conditions that favour or limit seedling recruitment across forest types.Colombian institution Departamento Administrativo de Ciencia, Tecnología e Innovación COLCIENCIASFaculty of Sciences, Universidad de los Ande