Clustering species using a model of population dynamics and aggregation theory

The high species diversity of some ecosystems like tropical rainforests goes in pair with the scarcity of data for most species. This hinders the development of models that require enough data for fitting. The solution commonly adopted by modellers consists in grouping species to form more sizeable data sets. Classical methods for grouping species such as hierarchical cluster analysis do not take account of the variability of the species characteristics used for clustering. In this study a clustering method based on aggregation theory is presented. It takes account of the variability of species characteristics by searching for the grouping that minimizes the quadratic error (square bias plus variance) of some model’s prediction. This method allows one to check whether the gain in variance brought by data pooling compensate for the bias that it introduces. This method was applied to a data set on 94 tree species in a tropical rainforest in French Guiana, using a Usher matrix model to predict species dynamics. An optimal trade-off between bias and variance was found when grouping species. Grouping species appeared to decrease the quadratic error, except when the number of groups was very small. This clustering method yielded species groups similar to those of the hierarchical cluster analysis using Ward’s method when variance was small, that is when the number of groups was small.     

Coupling soil water and shoot dynamics in three grass species: A spatial stochastic model on water competition in Neotropical savanna

Savannas are ecosystems known for their high environmental and economic value. They cover at least 20% of the global land surface and, in some cases, can act as a boundary between tropical rainforest and deserts. Water is an important determinant of savanna ecosystems.In this paper, we present a theoretical stochastic model of root competition for water, which couples, soil water availability, phenology, and root and shoot architecture applied to three Neotropical savanna grasses. Soil moisture was simulated using a daily balance, as proposed by Rodriguez-Iturbe et al. [Rodriguez-Iturbe, I., Porporato, A., Ridolfi, L., Isham, V., Cox, D.R., 1999. Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation. Proc. R. Soc. London, Ser. A 455, 3789–3805.]. To simulate rainfall stochasticity, we used daily precipitation data from the airport weather station in the State of Barinas, Venezuela, for the period 1991–2007. Competition among neighbouring plants took into account the spatial distribution of the individuals. As a final step, the model allowed us to calculate the shoot dynamic of the species as a function of soil water availability.Using these data, we compared the behaviour of isolated plants, pairs and trios, and we found below-ground competition to be a fundamental component of global (shoot + root) competition. Finally, our model suggests various circumstances that allow poor competitor plants to coexist in competition for water with more successful competitors. Apparently, this is not only due to transpiration rates, but also to differences in shoot emergence and shoot growth.     

Local population dynamics of an invasive tree species with a complex life-history cycle: A stochastic matrix model

Biological invasions are widely accepted as having a major impact on ecosystem functioning worldwide, giving urgency to a better understanding of the factors that control their spread. Modelling tools have been developed for this purpose but are often discrete-space, discrete-time spatial-mechanistic models that adopt a computer simulation approach and resist mathematical analysis. We constructed a simple demographic matrix model to explore the local population dynamics of an invasive species with a complex life history and whose invasive success depends on resource availability, which occurs stochastically. As a case study we focused on the American black cherry (Prunus serotina Ehrh.), a gap-dependent tree able both to constitute a long-living seedling bank under unfavourable light conditions and to resprout vigorously once cut-down, which is invading European temperate forests. The model used was a stage-classified matrix population model (i.e., Lefkovitch matrix), integrating environmental stochasticity. Stochastic matrix projection analysis was combined with elasticity analysis and stochastic simulations to search for the species’ ‘Achille heel’. As expected, the population growth rate (i.e., Lyapunov exponent), which measures the risk of P. serotina invasion at the stand scale, increased with light frequency. There was a critical value above which the population of P. serotina explodes and below which it locally goes extinct. The resprouting capacity usually speed up the invasion but appeared to play a minor role. The mean duration of stand invasion was measured and important life stage transitions that mostly contribute to the local stochastic growth rate were identified. Some relevant management implications are discussed and the interest of such models for the understanding of demographic characteristics of invasive species is stressed.     

Disentangling the effects of heterogeneity, stochastic dynamics and sampling in a community of aquatic insects

A dynamic and heterogeneous species abundance model generating the lognormal species abundance distribution is fitted to time series of species data from an assemblage of stoneflies and mayflies (Plecoptera and Ephemeroptera) of an aquatic insect community collected over a period of 15 years. In each year except one, we analyze 5 parallel samples taken at the same time of the season giving information about the over-dispersion in the sampling relative to the Poisson distribution. Results are derived from a correlation analysis, where the correlation in the bivariate normal distribution of log abundance is used as measurement of similarity between communities. The analysis enables decomposition of the variance of the lognormal species abundance distribution into three components due to heterogeneity among species, stochastic dynamics driven by environmental noise, and over-dispersion in sampling, accounting for 62.9, 30.6 and 6.5% of the total variance, respectively. Corrected for sampling the heterogeneity and stochastic components accordingly account for 67.3 and 32.7% of the among species variance in log abundance. By using this method, it is possible to disentangle the effect of heterogeneity and stochastic dynamics by quantifying these components and correctly remove sampling effects on the observed species abundance distribution.     

Selecting parameters for calibration via sensitivity analysis: An individual-based model of mosquitofish population dynamics

A stochastic individual-based model (IBM) of mosquitofish population dynamics in experimental ponds was constructed in order to increase, virtually, the number of replicates of control populations in an ecotoxicology trial, and thus to increase the statistical power of the experiments. In this context, great importance had to be paid to model calibration as this conditions the use of the model as a reference for statistical comparisons. Accordingly, model calibration required that both mean behaviour and variability behaviour of the model were in accordance with real data. Currently, identifying parameter values from observed data is still an open issue for IBMs, especially when the parameter space is large. Our model included 41 parameters: 30 driving the model expectancy and 11 driving the model variability. Under these conditions, the use of “Latin hypercube” sampling would most probably have “missed” some important combinations of parameter values. Therefore, complete factorial design was preferred. Unfortunately, due to the constraints of the computational capacity, cost-acceptable “complete designs” were limited to no more than nine parameters, the calibration question becoming a parameter selection question. In this study, successive “complete designs” were conducted with different sets of parameters and different parameter values, in order to progressively narrow the parameter space. For each “complete design”, the selection of a maximum of nine parameters and their respective n values was carefully guided by sensitivity analysis. Sensitivity analysis was decisive in selecting parameters that were both influential and likely to have strong interactions. According to this strategy, the model of mosquitofish population dynamics was calibrated on real data from two different years of experiments, and validated on real data from another independent year. This model includes two categories of agents; fish and their living environment. Fish agents have four main processes: growth, survival, puberty and reproduction. The outputs of the model are the length frequency distribution of the population and the 16 scalar variables describing the fish populations. In this study, the length frequency distribution was parameterized by 10 scalars in order to be able to perform calibration. The recently suggested notion of “probabilistic distribution of the distributions” was also applied to our case study, and was shown to be very promising for comparing length frequency distributions (as such).     

Predicting tree species presence and basal area in Utah: A comparison of stochastic gradient boosting,generalized additive models,and tree-based methods

Many efforts are underway to produce broad-scale forest attribute maps by modelling forest class and structure variables collected in forest inventories as functions of satellite-based and biophysical information. Typically, variants of classification and regression trees implemented in Rulequest's^© See5 and Cubist (for binary and continuous responses, respectively) are the tools of choice in many of these applications. These tools are widely used in large remote sensing applications, but are not easily interpretable, do not have ties with survey estimation methods, and use proprietary unpublished algorithms. Consequently, three alternative modelling techniques were compared for mapping presence and basal area of 13 species located in the mountain ranges of Utah, USA. The modelling techniques compared included the widely used See5/Cubist, generalized additive models (GAMs), and stochastic gradient boosting (SGB). Model performance was evaluated using independent test data sets. Evaluation criteria for mapping species presence included specificity, sensitivity, Kappa, and area under the curve (AUC). Evaluation criteria for the continuous basal area variables included correlation and relative mean squared error. For predicting species presence (setting thresholds to maximize Kappa), SGB had higher values for the majority of the species for specificity and Kappa, while GAMs had higher values for the majority of the species for sensitivity. In evaluating resultant AUC values, GAM and/or SGB models had significantly better results than the See5 models where significant differences could be detected between models. For nine out of 13 species, basal area prediction results for all modelling techniques were poor (correlations less than 0.5 and relative mean squared errors greater than 0.8), but SGB provided the most stable predictions in these instances. SGB and Cubist performed equally well for modelling basal area for three species with moderate prediction success, while all three modelling tools produced comparably good predictions (correlation of 0.68 and relative mean squared error of 0.56) for one species.     

The effect of species response form on species distribution model prediction and inference

Ecological theory and current evidence support the validity of various species response curves according to a variety of environmental gradients. Various methods have been developed for building species distribution models but it is not well known how these methods perform under various assumptions about the form of the underlying species response. It is also not well known how spatial correlation in species occurrence affects model performance. These effects were investigated by applying an environmental envelope method (BIOCLIM) and three regression-based methods: logistic regression (LR), generalized additive modelling (GAM), and classification and regression tree (CART) to simulated species occurrence data. Each simulated species was constructed as a sum of responses with varying weights. Three basic species response curves were assumed: Gaussian (bell-shaped), Beta (skew) and linear. The two non-linear responses conform to standard ecological niche theory. All three responses were applied in turn to three simulated environmental variables, each with varying degrees of spatial autocorrelation. GAM produced the most consistent model performance over all forms of simulated species response. BIOCLIM and CART were inclined to underrate the performance of variables with a linear response. BIOCLIM was less sensitive to data density. LR was susceptible to model misspecification. The use of a linear function in LR underestimated the performance of variables with non-linear species response and contributed to increased spatial autocorrelation in model residuals. Omission of important environmental variables with non-linear species response also contributed to increased spatial autocorrelation in model residuals. Adding a spatial autocovariate term to the LR model (autologistic model) reduced the spatial autocorrelation and improved model performance, but did not correct the misidentification of the dominant environmental determinant. This is to be expected since the autologistic approach was designed primarily for prediction and not for inference. Given that various forms of species response to environmental determinants arise commonly in nature: (1) higher order functions should always be tested when applying LR in modelling species distribution; (2) spatial autocorrelation in species distribution model residuals can indicate that environmental determinants with non-linear response are missing from the model; and (3) deficiencies in LR model performance due to model misspecification can be addressed by adding a spatial autocovariate to the model, but care should be taken when interpreting the coefficients of the model parameters.     

Impact of the quality of climate models for modelling species occurrences in countries with poor climatic documentation: a case study from Bolivia

The quality of climate models has largely been overlooked as a possible source of uncertainty that may affect the outcomes of species distribution models, especially in the tropics, where comparatively few climatic stations are available. We compared the geographical discrepancies and potential conservation implications of using two different climate models (Saga and Worldclim) in combination with the species modelling approach Maxent in Bolivia. We estimated ranges of selected bird and fern species biogeographically restricted to either humid montane forest of the northern Bolivian Andes or seasonal dry tropical forests (in the Andes and southern lowlands). Saga and Worldclim predicted roughly similar climate patterns of temperature that were significantly correlated. Precipitation layers of both climate models were also roughly similar, but showed important differences. Species ranges estimated with Worldclim and Saga likewise produced different results. Ranges of species endemic to humid montane forests estimated with Saga had higher AUC (Area under the curve) values than those estimated with Worldclim, which for example predicted the occurrence of humid montane forest bird species near Lake Titicaca, an area that is clearly unsuitable for these species. Likewise, Worldclim overpredicted the occurrence of fern and bird species in the lowlands of the Chapare region and well south of the Andean Elbow, where more seasonal biomes occur. By contrast, Saga predictions were coherent with the known distribution of humid montane forests in the northern Bolivian Andes. Estimated ranges of species endemic to seasonal dry tropical forests predicted with Saga and Worldclim were not statistically different in most cases. However, detailed comparisons revealed that Saga was able to distinguish fragments of seasonal dry tropical forests in rain-shadow valleys of the northern Bolivian Andes, whereas Worldclim was not. These differences highlight the neglected influence of climate layers on modelling results and the importance of using the most accurate climate data available when modelling species distributions.     

The derivation of species response curves with Gaussian logistic regression is sensitive to sampling intensity and curve characteristics

We investigated quantitatively the sensitivity of plant species response curves to sampling characteristics (number of plots, occurrence and frequency of species), along a simulated pH gradient. We defined 54 theoretical unimodal response curves, issued from combinations of six values for optimum (opt = 3, 4, …, 8), three values for tolerance (tol = 0.5, 1.0, and 1.5, sensu ter Braak and Looman [ter Braak, C.J.F., Looman, C.W.N., 1986. Weighted averaging, logistic regression and the Gaussian response model. Vegetatio 65, 3–11]), and three values for maximum probability of presence (p_max = 0.05, 0.20, and 0.50). For each of these 54 theoretical response curves, we built artificial binary data sets (presence/absence) to test the influence of species occurrence, frequency, or number of available plots. With real data extracted from EcoPlant, a phytoecological database for French forests [Gégout, J.-C., Coudun, Ch., Bailly, G., Jabiol, B., 2005. EcoPlant: a forest sites database linking floristic data with soil characteristics and climatic conditions. J. Veg. Sci. 16, 257–260], we compared the ecological response of 50 plant species to soil pH, based first on a small data set (100 randomly sampled plots), and then based on the whole data set available (3810 plots).     

Development and validation of an individual based Daphnia magna population model: The influence of crowding on population dynamics

An individual-based model was developed to predict the population dynamics of Daphnia magna at laboratory conditions from individual life-history traits observed in experiments with different feeding conditions. Within the model, each daphnid passes its individual life cycle including feeding on algae, aging, growing, developing and – when maturity is reached – reproducing. The modelled life cycle is driven by the amount of ingested algae and the density of the Daphnia population. At low algae densities the population dynamics is mainly driven by food supply, when the densities of algae are high, the limiting factor is “crowding” (a density-dependent mechanism due to chemical substances released by the organisms or physical contact, but independent of food competition).     

The behavioural basis of a species replacement: differential aggresssion and predation between the introduced Gammarus pulex and the native G. duebeni celticus (Amphipoda)

Previous studies have shown that differential predation by males on moulted female congenerics may be largely responsible for the elimination and replacement of the native Irish freshwater amphipod Gammarus duebeni celticus by the introduced G. pulex. Predation of moulted females occurs both shortly after their release from precopulatory mate-guarding and whilst they are being guarded by their mates. In the present study, two hypotheses concerning the underlying cause(s) of the differential predation pattern are tested. Firstly, female G. d. celticus may be more vulnerable to predation than female G. pulex due to the former being released from precopula guarding with the new exoskeleton in a less hardened state. Secondly, G. pulex may be an inherently more aggressive species than G. d. celticus during predatory interactions over guarded females. The first experiment indicated that differential predation was not mediated by species differences in the state of the female exoskeleton at the time of release from precopula by guarding males. The second experiment, however, showed that male G. pulex were significantly more aggressive than male G. d. celticus in attacking both guarding male congenerics and guarded moulted female congenerics. In addition, in defence against predatory attacks, paired male and female G. pulex were significantly more aggressive than paired male and female G. d. celticus. These differences in aggressive behaviour led to a significantly higher frequency of predation on G. d. celticus females than on G. pulex females, and also explains this finding in previous studies. It is concluded that differential predation due to differences in aggressive behaviour may explain the pattern of replacement between these species.     

It's a dirty job but someone has to do it: The role of marine benthic macrofauna in organic matter turnover and nutrient recycling to the water column

Benthic macrofaunal populations through their feeding, bioturbation, burrow construction and sediment irrigation activities have profound influences on organic matter inputs to marine sediments (biodeposition) and on the vertical distribution of deposited organic matter within the sediment. These effects in turn influence the rates and pathways of organic matter mineralisation, and element cycles. Similarly, bioturbation, burrow construction and burrow irrigation are major determinants of sediment-water column fluxes of oxygen and nutrients.

In this review, I discuss the influences of the different benthic macrofaunal feeding (functional) groups on mineralisation processes and sediment-water column fluxes of particulate and dissolved nutrients. How these effects influence diagenic processes, the balance between aerobic and anaerobic processes, and the redox status of the surficial sediments. Finally, I discuss some of the limitations of the predominantly laboratory techniques which have been used to study “macrofaunal effects” and how this hinders the inclusion of the effects in quantitative sediment biogeochemical models.     

It's a dirty job but someone has to do it: The role of marine benthic macrofauna in organic matter turnover and nutrient recycling to the water column

Benthic macrofaunal populations through their feeding, bioturbation, burrow construction and sediment irrigation activities have profound influences on organic matter inputs to marine sediments (biodeposition) and on the vertical distribution of deposited organic matter within the sediment. These effects in turn influence the rates and pathways of organic matter mineralisation, and element cycles. Similarly, bioturbation, burrow construction and burrow irrigation are major determinants of sediment-water column fluxes of oxygen and nutrients.

In this review, I discuss the influences of the different benthic macrofaunal feeding (functional) groups on mineralisation processes and sediment-water column fluxes of particulate and dissolved nutrients. How these effects influence diagenic processes, the balance between aerobic and anaerobic processes, and the redox status of the surficial sediments. Finally, I discuss some of the limitations of the predominantly laboratory techniques which have been used to study “macrofaunal effects” and how this hinders the inclusion of the effects in quantitative sediment biogeochemical models.     

Risk aversion and adaptive management: Insights from a multi-armed bandit model of invasive species risk

This article explores adaptive management (AM) for decision-making under environmental uncertainty. In the context of targeting invasive species inspections of agricultural imports, I find that risk aversion increases the relative value of AM and can increase the rate of exploratory action. While calls for AM in natural resource management are common, many analyses have identified modest gains from this approach. I analytically and numerically examine the distribution of outcomes from AM under risk neutrality and risk aversion. The inspection decision is framed as a multi-armed bandit problem and solved using the Lagrangian decomposition method. Results show that even when expected gains are modest, asymmetry in the distribution of outcomes has important implications. Notably, AM can serve to buffer against large losses, even if the most likely outcome is a small loss.     

A method for building spatial model of annual weed seed dispersal from experimental data and its application to simulating Bromus sterilis population dispersal

Spatial model of annual weed seed dispersal, in this article, was theoretically derived. According to the requirements of building the spatial model, we designed and done an indoor experiment of weed seed dispersal by wind. In the experiment, the seeds of Bromus sterilis were released at 100 cm height under different wind velocity conditions. Based on the experimental data, the spatial models of seed dispersal of the weed species were built, which were divided into three types according to the coefficient β < 0, β = 0, β > 0. The results showed that dispersal of annual weed seed in any direction obeyed an approximate Gaussian distribution; under the experimental conditions, spatial distribution type of weed seed dispersal changed with variation of wind velocity. Well-known Howard et al.'s model (Howard et al., 1991) of Bromus sterilis seed dispersal is an especial example of the model built in this article. The result of model analysis indicated that the distribution type described by Howard's model was similar to that of seed dispersal of the weed species at the height of 100 cm under the condition of lower wind velocity (about 2.18 m/s). Using CA simulation analysis we found that mean control agent applying to a cell with weed should have a decrease with an increase of wind velocity to prevent weed with the initial configuration from spreading, which implicated less herbicide needs spraying in every cell with weed on average when wind velocity increases.     

Online single particle analysis of chemical composition and mixing state of crop straw burning particles: from laboratory study to field measurement

Fresh straw burning (SB) particles were generated in the laboratory by the combustion of rice straw and corn straw. The chemical composition and mixing state of the fresh SB particles were investigated by an Aerosol Time-of-Flight Mass Spectrometer (ATOFMS). Based on the mass spectral patterns, the SB particles were clustered into four major types: Salt, Organic Carbon (OC), Elemental Carbon (EC), and internally mixed particles of EC and OC (EC-OC). In addition, particles containing ash, polycyclic aromatic hydrocarbons, heavy metals or nicotine were also observed. Physical and chemical changes of the SB particles immediately after the emission were analyzed with highly time-resolved data. During the aging processes, the average particle size increased steadily. Freshly emitted organic compounds were gradually oxidized to more oxygenated compounds in the OC-containing particles. Meanwhile, an important displacement reaction (2KCl+ SO42−→ K₂SO₄ + 2Cl⁻) was observed. The marker ions for SB particles were optimized and applied to identify the SB particles in the ambient atmosphere. The fluctuation of the number fraction of ambient SB particles sorted by ATOFMS agrees well with that of water soluble K⁺ measured by an online ion chromatography, demonstrating that the optimized marker ions could be good tracers for SB particles in field measurements.     

The effect of pollution on crime: Evidence from data on particulate matter and ozone

We estimate the effect of short-term air pollution exposure (PM_2.5 and ozone) on several categories of crime, with a particular emphasis on aggressive behavior. To identify this relationship, we combine detailed daily data on crime, air pollution, and weather for an eight-year period across the United States. Our primary identification strategy employs extremely high dimensional fixed effects and we perform a series of robustness checks to address confounding variation between temperature and air pollution. We find a robust positive effect of increased air pollution on violent crimes, and specifically assaults, but no relationship between increases in air pollution and property crimes. The effects are present in and out of the home, at levels well below Ambient Air Pollution Standards, and PM_2.5 effects are strongest at lower temperatures. The results suggest that a 10% reduction in daily PM_2.5 and ozone could save $1.4 billion in crime costs per year, a previously overlooked cost associated with pollution.     

Identifying key life-traits for the dynamics and gene flow in a weedy crop relative: Sensitivity analysis of the GeneSys simulation model for weed beet (Beta vulgaris ssp. vulgaris)

The benefits of genetically modified herbicide-tolerant (GMHT) sugar beet (Beta vulgaris) varieties stem from their presumed ability to improve weed control and reduce its cost, particularly targeting weed beet, a harmful annual weedy form of the genus Beta (i.e. B. vulgaris ssp. vulgaris) frequent in sugar beet fields. As weed beet is totally interfertile with sugar beet, it is thus likely to inherit the herbicide-tolerance transgene through pollen-mediated gene flow. Hence, the foreseeable advent of HT weed beet populations is a serious threat to the sustainability of GM sugar beet cropping systems. For studying and quantifying the long-term effects of cropping system components (crop succession and cultivation techniques) on weed beet population dynamics and gene flow, we developed a biophysical process-based model called GeneSys-Beet in a previous study. In the present paper, the model was employed to identify and rank the weed life-traits as function of their effect on weed beet densities and genotypes, using a global sensitivity analysis to model parameters. Monte Carlo simulations with simultaneous randomization of all life-trait parameters were carried out in three cropping systems contrasting for their risk for infestation by HT weed beets. Simulated weed plants and bolters (i.e. beet plants with flowering and seed-producing stems) were then analysed with regression models as a function of model parameters to rank processes and life-traits and quantify their effects. Key parameters were those determining the timing and success of growth, development, seed maturation and the physiological end of seed production. Timing parameters were usually more important than success parameters, showing for instance that optimal timing of weed management operations is more important than its exact efficacy. The ranking of life-traits though depended on the cropping system and, to a lesser extent, on the target variable (i.e. GM weeds vs. total weed population). For instance, post-emergence parameters were crucial in rotations with frequent sugar beet crops whereas pre-emergence parameters were most important when sugar beet was rare. In the rotations with frequent sugar beet and insufficient weed control, interactions between traits were small, indicating diverse populations with contrasted traits could prosper. Conversely, when sugar beet was rare and weed control optimal, traits had little impact individually, indicating that a small number of optimal combinations of traits would be successful. Based on the analysis of sugar beet parameters and genetic traits, advice for the future selection of sugar beet varieties was also given. In climatic conditions similar to those used here, the priority should be given to limiting the presence of hybrid seeds in seed lots rather than decreasing varietal sensitivity to vernalization.