Hannah Hawthorne Matrix Models

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Hannah Hawthorne Matrix Models
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The management of tropical rain forests in Central Africa is an essential issue because of the economic importance of the production of timber for the country and of the resource supply to local populations (non wood forest products, proteins via hunting). The sustainable management of these forests often relies on population dynamics models for size-structured tree populations (also called matrix model) that describe forest dynamics and consequently can be used to predict the temporal evolution of the timber stock. The uncertainty on model predictions is directly related to the precision of estimation of the transition parameters of the model. These parameters, also called vital rates, include growth, recruitment and mortality rates. There are two main sources of variability in parameter estimates : sampling variability, and environmental variability. Sampling variability depends on the amount of available data. As tropical rain forests have a high number of species with many rare species, most species-specific parameter estimates have huge errors. One way to solve this problem is to group species with common behaviour to increase the number of available observations. Environmental variability is related to the spatial and temporal variations of transition parameters due to environmental fluctuations (such as climate or soil). This kind of variability is not yet considered in the models used by forest managers. In this study, we address climate variability (rainfall) in forest dynamic predictions and group species according to their response to rainfall. First, the species classification and the relation between growth, mortality and recruitment rates, and climatic covariates for each species group were simultaneously fitted using finite mixture of regression models. Data come from permanent sample plots (40 ha, 25-year monitoring) located at M'Baïki, in the Central African Republic. The plots are located in a semi-deciduous mixed forest, where the climate has a pronounced dry season and where the average annual rainfall is 1739mm. The climatic covariates used are the length of the dry season, the average rainfall during the dry season, and the annual average soil water content. The response of growth, mortality, and recruitment to climatic covariates varied among species. Nine response groups were identified for growth, three for mortality, and five for recruitment. The response groups based on growth showed a correlation between response to drought and species shade-tolerance. Second, we predicted stand dynamics which incorporates rainfall variability and variability in species response to rainfall. Stand dynamics was predicted for three climate scenarios : increase of drought, increase of rainfall, or no change in precipitation. The response of the forest stand was analyzed in terms of changes in stand structure (basal area and density), and relative composition in the species groups previously defined. The analyses showed a gradient in species drought tolerance, which opposed 9 predominantly pioneer species that responded negatively to drought, to 60 predominantly shade-tolerant species that responded positively to drought. The M'Baïki forest stand seems to be relatively drought resistant. Moreover, the response to drought seems to be driven by the mortality response to the climatic covariates, with shade-tolerant species having a lower mortality during the dry season, probably due to an increase in light availability in the understory as a consequence of a longer period of defoliation of canopy deciduous trees during drought. In this study, we also showed that logging increased the proportion of pioneer species in the stand. Consequently, an increase in logging pressure would result in a more drought-sensitive forest stand.
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Amazon forests are a key but poorly understood component of the global carbon cycle. If, as anticipated, they dry this century, they might accelerate climate change through carbon losses and changed surface energy balances. We used records from multiple long-term monitoring plots across Amazonia to assess forest responses to the intense 2005 drought, a possible analog of future events. Affected forest lost biomass, reversing a large long-term carbon sink, with the greatest impacts observed where the dry season was unusually intense. Relative to pre-2005 conditions, forest subjected to a 100-millimeter increase in water deficit lost 5.3 megagrams of aboveground biomass of carbon per hectare. The drought had a total biomass carbon impact of 1.2 to 1.6 petagrams (1.2 × 1015 to 1.6 × 1015 grams). Amazon forests therefore appear vulnerable to increasing moisture stress, with the potential for large carbon losses to exert feedback on climate change.
In population ecology, species spatial patterns are studied in order to infer the existence of underlying processes, such as interactions within and between species, and species response to environmental heterogeneity. We propose to analyze spatial multi-species data by defining species abundance assemblages. Species assemblages are one of the signatures of the local spatial interactions between species and with their environment. Species assemblages are defined here by a non spatial classification of the multivariate observations of species abundances. Model-based clustering procedures using mixture models were chosen in order to have an estimation of the classification uncertainty and to model an assemblage by a multivariate probability distribution. We propose : 1. An exploratory tool for the study of spatial multivariate observations of species abundances, which defines species assemblages by a model-based clustering procedure, and then maps and analyzes the spatial structure of the assemblages. Common distributions, such as the multivariate Gaussian, are used to model the assemblages. 2. A hierarchical model for abundance assemblages which cannot be modeled with common distributions. This model can be easily adapted to mixed mode data, which are frequent in ecology. 3. A clustering procedure for mixed-mode data based on mixtures of hierarchical models. Two ecological case-studies guided and illustrated this work: the small-scale study of the assemblages of two aphid species on leaves of Citrus trees, and the large-scale study of the assemblages of a host plant, Plantago lanceolata, and its pathogen, the powdery mildew, on the Aland islands in south-west Finland
Tropical Rainforest Responses to Climatic Change, Second Edition, looks at how tropical rain forest ecology is altered by climate change, rather than simply seeing how plant communities were altered. Shifting the emphasis on to ecological processes, e.g. how diversity is structured by climate and the subsequent impact on tropical forest ecology, provides the reader with a more comprehensive coverage. A major theme of the book is the interaction between humans, climate and forest ecology. The authors, all foremost experts in their fields, explore the long term occupation of tropical systems, the influence of fire and the future climatic effects of deforestation, together with anthropogenic emissions. Incorporating modelling of past and future systems paves the way for a discussion of conservation from a climatic perspective, rather than the usual plea to stop logging. This second edition provides an updated text in this rapidly evolving field. The existing chapters are revised and updated and two entirely new chapters deal with Central America and the effect of fire on wet forest systems. In the first new chapter, the paleoclimate and ecological record from Central America (Lozano, Correa, Bush) is discussed, while the other deals with the impact of fire on tropical ecosystems.
To assess the diversity of tropical tree life histories, a conceptual framework is needed to guide quantitative comparative study of many species. We propose one such framework, which focuses on long-term performance through ontogeny and over the natural range of microsites. For 6 yr we annually evaluated survival, growth, and microsite conditions of six non-pioneer tree species in primary tropical wet forest at the La Selva Biological Station, Costa Rica. The species were: Lecythis ampla, Hymenolobium mesoamericanum, Dipteryx panamensis, Pithecellobium elegans, Hyeronima alchorneoides (all emergents), and Minquartia guianensis (a canopy species). The study was based on long-term measurement of individuals from all post-seedling size classes. Trees were sampled from 150 ha of primary forest spanning several watersheds and soil types. To evaluate individuals' microsites we recorded the number of overtopping crowns, forest phase (gap, building, mature), and crown illumination index (an estimate of the tree's light environment). For comparison, we also evaluated the microsites of three species that have been categorized as pioneers (Cecropia insignis, C. obtusifolia) or high-light demanders (Simarouba amara). For the six species of non-pioneers, mortality rates declined with increasing juvenile size class. As a group, these emergent and canopy trees showed a much lower exponential annual mortality rate (0.44%/yr at >10 cm diameter) than has been found for the La Selva forest as a whole. Growth rates increased with juvenile size class for all six species. As adults (trees >30 cm in diameter), all five emergent species showed substantial annual diameter increments (medians of 5-14 mm/yr). Small saplings and adults of all species had significant year-to-year variation in diameter growth, with much greater growth occurring in the year of lowest rainfall. Passage time analysis suggests that all six species require >150 yr for growth from small saplings to the canopy. Evaluation of all nine species revealed four patterns of microsite occupancy by juveniles. Among the non-pioneers, one species pair (Lecythis and Minquartia: Group A) was associated with low crown illumination and mature-phase forest in all juvenile stages. For two species (Dipteryx and Hymenolobium: Group B) the smallest saplings were in predominantly low-light, mature-forest sites, but crown illumination and association with gap- or building-phase sites increased with juvenile size (Simarouba also showed this pattern). Two species (Pithecellobium and Hyeronima: Group C) were strongly associated with gap or building phase as small juveniles (@<4 cm diameter) and again as subcanopy trees (>10-20 cm diameter), but were predominantly in mature-phase sites at intermediate sizes. Juveniles of the two pioneer species (Cecropia: Group D) showed the highest crown illumination and association with gap or building sites. Among the six non-pioneer species, only one aspect of juvenile performance clearly varied according to microsite group. The smallest saplings (@<1 cm diameter) of Groups B and C showed significant mortality differences across a small gradient in crown illumination; neither of the Group A species showed this pattern. Otherwise, juvenile performance was strikingly similar among the six species. All showed a capacity for growth responses to small increases in light, substantial height and diameter increments at higher light levels, equal ability to survive 4-yr periods of no growth, and very low mortality rates at intermediate-to-large juvenile sizes. Species differed significantly in growth rates, but relative differences shifted with tree size and were unrelated to microsite group. These findings do not support prevailing paradigms concerning trade-offs and correlated suites of traits. For non-pioneer tropical trees, life history classification based on generalized concepts such as gap dependence and shade tolerance is inadequate to describe the complex size-dependent patterns of life history differences and similarities that exist among species.
Matrix models are critical for conservation planning of endangered species or any species with limited data. Sufficient growth data to construct growth-transition matrices required for size-structured population dynamics models may be lacking using traditional methods. We present a simple semi-empirical method for converting limited growth data into estimated transition probabilities required as elements in structured matrix models. Rather than approximating transition probabilities by counting actual transition frequencies between sparsely populated size classes, we assume that a selected function represents the entire data set, we obtain the model parameters by conventional curve fitting, and we construct the matrix model from the assumed model function. To illustrate the method, we use a sparse, scattered sample of growth data from the endangered white abalone. We use the slope and intercept of the von Bertalanffy model function to determine the growth-transition matrix elements, where the paucity and or scatter of the data preclude using the traditional counting method. The method we propose can accommodate both linear and non-linear mappings of size into growth rate, as we demonstrate with a Gaussian function which has been used to model growth of red abalone and red sea urchins. We illustrate how our method can convert confidence intervals from the model function into confidence intervals for the matrix elements. We suggest that this modelling procedure, which is simple to use and is suitable in data poor situations, will be broadly applicable for conservation practitioners in developing quantitative models to evaluate the population viability of endangered species.
Global climate change may be affecting forests around the world. However, the impact of climate change on forest population dynamics, especially at the landscape or regional level, has hardly been addressed before. A new methodology was proposed to enable matrix transition models to account for climate impact on forest population dynamics. The first climate-sensitive matrix (CSMatrix) model was developed for the Alaska boreal forest based on observations from over 15years of forest inventory. The spatially explicit model was used to map climate-induced forest population dynamics across the region. The model predicted that the basal area increment in the region under natural succession would be hindered by global warming, more so for dry upland areas than for moist wetlands. It was suggested that temperature-induced drought stress could more than offset a predicted increase of future precipitation in the region to lower overall forest productivity. At the same time, stand diversity would increase across the region through transient species redistribution. Accounting for climate conditions made the CSMatrix model more accurate than conventional matrix models.
Projection matrix models are intensely used in ecology to model the dynamics of structured populations. When dealing with size-structured populations, there is no satisfactory algorithm to partition size into discrete classes. We show that the Vandermeer–Moloney algorithm for choosing classes is inconsistent with the Usher model, and systematically selects the finest classes. Considering that the matrix model is a discrete approximation of a continuous model, we define an approximation error as the sum of a distribution error (the difference between the discrete distribution and its continuous counterpart), and a sample error. The optimal partition of size into classes is the one that minimizes the approximation error. This method for choosing classes also shows that the choice of the class width cannot be disconnected from the choice of the time step. When applied to 520 trees of Dicorynia guianensis in French Guiana, this algorithm identified 8 classes of 11.4cm in width, which is in agreement with the empirical choice of foresters.
We propose assessing a mixture model in a cluster analysis setting with the inegrated classification likelihood. With this purpose, the observed data are assigned to unknown clusters using a maximum a posteriori operator. The integrated completed likelihood approximation is derived without the theoretical difficulties encountered when approximating the integrated observed likelihood. Numerical experiments on simulated and real data of the resulting ICL criterion show that it performs well both for choosing a mixture model and a relevant number of clusters. In particular, ICL appears to be more robust than BIC to violation of some of the mixture model assumptions and it can select a number of clusters leading to a sensible partitioning of the data.
The management of a renewable resource, classified by size classes, is considered. A mathematical model which predicts the stable structure of such a resource in developed. Data on the percentage recruitment of organisms from one class to the class above and data on the regeneration of young organisms are used as elements of a matrix. The largest real latent root of this matrix gives the maximum exploitation, and the latent vector associated with this root gives the stable structure. The model is illustrated by reference to a Scots pine forest in Inverness-shire. An iterative process for finding the latent root and vector is described. This matrix method is compared with a geometric method.
Chapter 1. Cretaceous and Tertiary climate change and the past distribution of megathermal rain forest. R. J. Morley.- 2. Andean Montane forests and climate change. M. B. Bush, J. A. Hanselman, and H. Hooghiemstra.- 3. Climate change in the lowlands of the Amazon Basin. M. B. Bush, W. D. Gosling and P. A. Colinvaux.- 4. NEW CHAPTER: Quaternary climate change in Central American forests. M. B. Bush, S. Lozano.- 5. The Quaternary history of far eastern rainforests. A. P. Kershaw, S. van der Kaars and J. R. Flenley.- 6. Rain Forest responses to past climatic changes in Tropical Africa. R. Bonnefille.- 7. Tropical environmental dynamics: a modelling perspective. R. Marchant and J. Lovett.- 8. Prehistoric human occupation and impacts on Neotropical forest landscapes during the Late Pleistocene and Early/Middle Holocene. D. Piperno.- 9. Ultraviolet insolation and the Tropical Rain Forest: altitudinal variations, Quaternary and recent change, extinctions and biodiversity. J. R. Flenley.- 10. Climate change and hydrological models of the wet tropics. J. Marengo.- 11. Plant species diversity in Amazonian Forests. M. R. Silman.- 12. Nutrient cycling and climate change in tropical forests. M. E. McGroddy and W. L. Silver.- 13. NEW Chapter The effect of fire on tropical forest systems.- 14. The response of South American tropical forests to contemporary atmospheric change. O. L. Phillips, S. L. Lewis, T. R. Baker, and Y. Malhi.- 15. Ecophysiological response of lowland tropical plants to Pleistocene climate. S.A. Cowling.- 16. Modeling Future effects of climate change on tropical forests. L. Hannah, R. Betts, and H.H. Shugart.- 17. Conservation, climate change, and tropical forests. L.Hannah and T. Lovejoy.
The rich ecology of tropical forests is intimately tied to their moisture status. Multi-site syntheses can provide a macro-scale view of these linkages and their susceptibility to changing climates. Here, we report pan-tropical and regional-scale analyses of tree vulnerability to drought. We assembled available data on tropical forest tree stem mortality before, during, and after recent drought events, from 119 monitoring plots in 10 countries concentrated in Amazonia and Borneo. In most sites, larger trees are disproportionately at risk. At least within Amazonia, low wood density trees are also at greater risk of drought-associated mortality, independent of size. For comparable drought intensities, trees in Borneo are more vulnerable than trees in the Amazon. There is some evidence for lagged impacts of drought, with mortality rates remaining elevated 2 yr afte
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