Effect of temperature and light on the photosynthesis as measured by chlorophyll fluorescence of cultured Eucheuma denticulatum and Kappaphycus sp. (Sumba strain) from Indonesia

The photosynthetic performance of two Indonesian carrageenophytes (Solieriaceae), Eucheuma denticulatum and Kappaphycus sp. (so-called Sumba strain), was investigated under a variety of temperature and light conditions regarding their mariculture performance. A pulse amplitude modulated-chlorophyll fluorometer (Diving-PAM) was used to generate rapid light curves (RLCs) to provide estimates of the relative electron transport rates (rETR) for over 10 temperatures (i.e., from 16 to 34 °C) and at nine levels of photosynthetic active radiation, which ranged from 0 to 1,000?μmol photons m^?2 s^?1. Underwater irradiance in a cultivation area was also measured at the collection site in South Sulawesi, Indonesia. The initial slope (α), photoinhibition coefficient (β), and the coefficient of maximum photosynthesis assuming no photoinhibition (γ) was calculated by fitting the RLCs to a nonlinear model of the form $ {\text{rETR}} = \gamma \left( {1 - \exp \left( { - \frac{\alpha }{\gamma }{\text{PAR}}} \right)} \right)\left( {\exp \left( { - \frac{\beta }{\gamma }{\text{PAR}}} \right)} \right) $ using a two-level hierarchical Bayesian model. The experiments revealed that E. denticulatum and Kappaphycus sp. required temperatures ranging from 23 to 32 °C and 22 to 33 °C to maintain high rates of photosynthetic activity, respectively. Clearly, both species appear to be well-adapted to the natural light and temperature conditions at the cultivation site, and we expect the results of this study will be useful for the design and sustainable management of similar mariculture activity.     

A review and reassessment of lake phosphorus retention and the nutrient loading concept

1. We conducted a statistical reassessment of data previously reported in the lake total phosphorus (TP) input/output literature (n = 305) to determine which lake characteristics are most strongly associated with lake phosphorus concentration and retention. We tested five different hypotheses for predicting lake TP concentrations and phosphorus retention. 2. The Vollenweider phosphorus mass loading model can be expressed as: TP_out = TP_in/(1 + στ_w), where TP_in is the flow‐weighted input TP concentration, τ_w is the lake hydraulic retention time and σ is a first‐order rate constant for phosphorus loss. 3. The inflow‐weighted TP input concentration is a moderately strong predictor (r² = 0.71) of lake phosphorus concentrations when using log–log transformed data. Lake TP retention is negatively correlated with lake hydraulic retention time (r² = 0.35). 4. Of the approaches tested, the best fit to observed data was obtained by estimating σ as an inverse function of the lake's hydraulic retention time. Although this mass balance approach explained 84% of the variability in log–log transformed data, the prediction error for individual lakes was quite high. 5. Estimating σ as the ratio of a putative particle settling velocity to the mean lake depth yielded poorer predictions of lake TP (r² = 0.77) than the approach described above, and in fact did not improve model performance compared with simply assuming that σ is a constant for all lakes. 6. Our results also demonstrate that changing the flow‐weighted input concentration should always have a directly proportionate impact on lake phosphorus concentrations, provided the type of phosphorus loaded (e.g. dissolved or particulate) does not vary.     

Relative strengths of benthic algal nutrient and grazer limitation along a lake productivity gradient

The relative effects of nutrients and herbivores on primary producers are rarely compared across ecosystems that vary in potential primary productivity. Furthermore, proposed mechanisms to explain such patterns remain understudied. Here, I examine the strength of nutrient and grazer (herbivore) limitation (i.e., the extent to which producers’ growth is limited by insufficient nutrient supply or herbivory) of benthic algae across 13 southwest Michigan lakes that vary widely in productivity (i.e., resource supply). I compare the observed patterns of algal limitation and species composition to those predicted by two simple models: one that includes multiple species and species’ traits (the food-web model) and one that includes no variation in species or traits (the food-chain model). Species in the food-web model are assumed to display a tradeoff between resource competitive ability and resistance to herbivory (the “keystone predator” tradeoff). Among these lakes, benthic algal nutrient limitation was positive and declined significantly along a lake N:P gradient. In contrast, grazer limitation was negative and was not significantly related to any of the measured lake productivity variables. Negative grazer limitation indicated that the removal of grazers caused unexpected declines in algal biomass, which were potentially due to indirect, positive effects (e.g., nutrient recycling) of grazers. Nutrient limitation was significantly stronger than grazer limitation across lakes, which was more consistent with the food-web versus food-chain model. Changes in algal composition were also broadly consistent with predictions of the food-web model in that vulnerable, superior nutrient competitors dominated in low productivity lakes and more grazer-resistant species were observed in high productivity lakes. In general, these results point to the importance of examining limiting factors across systems and the consideration of key species’ traits when predicting and interpreting patterns.     

When mechanism matters: Bayesian forecasting using models of ecological diffusion

Ecological diffusion is a theory that can be used to understand and forecast spatio‐temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white‐tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression‐based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.     

Temporal correlation based learning in neuron models

We study a learning rule based upon the temporal correlation (weighted by a learning kernel) between incoming spikes and the internal state of the postsynaptic neuron, building upon previous studies of spike timing dependent synaptic plasticity (Kempter, R., Gerstner, W., van Hemmen, J.L., Wagner, H., 1998. Extracting Oscillations: Neuronal coincidence detection with noisy periodic spike input. Neural computation 10, 1987–2017; Kempter, R., Gerstner, W., van Hemmen, J.L., 1999. Hebbian learning and spiking neurons. Physical Reviewm E59, 4498–4514; van Hemmen, J.L., 2001. Theory of synaptic plasticity. In: Moss, F., Gielen, S. (Eds.), Handbook of biological physics. vol. 4, Neuro Informatics, neural modelling, Elsevier, Amsterdam, pp. 771–823. Our learning rule for the synaptic weight w _ij is where the t _j,μ are the arrival times of spikes from the presynaptic neuron j and the function u(t) describes the state of the postsynaptic neuron i. Thus, the spike-triggered average contained in the inner integral is weighted by a kernel Γ(s), the learning window, positive for negative, negative for positive values of the time difference s between post- and presynaptic activity. An antisymmetry assumption for the learning window enables us to derive analytical expressions for a general class of neuron models and to study the changes in input-output relationships following from synaptic weight changes. This is a genuinely non-linear effect (Song, S., Miller, K., Abbott, L., 2000. Competitive Hebbian learning through spike timing dependent synaptic plasticity. Nature Neuroscience 3, 919–926).     

Pace of diffusion through membranes

Summary Although membranes are often viewed as barriers to diffusing particles, in many cases their presence does not slow down diffusion. Investigations of the transit time (mean diffusion time) for cases where the source and the target of diffusing particles are separated by various arrangements of membranes reveal the following facts: (i) The transit time is composed of the sum of the times to diffuse each of the membrane and aqueous regions separately and terms representing the time spent at the vicinity of the interfaces between these regions. (ii) In cases of one dimensional diffusion between aqueous and membranal phases, the transit time is governed by the parameter whereD _m andD _w are the diffusion coefficients in the membrane and water, respectively, and is the membrane/water partition coefficient of the particles. While the former ratio depends mostly on the viscosities of the two phases, the latter parameter is very strongly dependent on the identity of the particles. The diffusion from water to the membrane is faster than from the membrane to water whenever 1$$ " align="middle" border="0"> . The opposite is true when this parameter is smaller than 1. (iii) In case of one dimensional transmembranal diffusion, the transit time shows a minimum when wherel _w1 andl _w2 are the net diffusion distances in the aqueous phases on both sides of the membrane. In this case, if the diffusion proceeds through pores in the membrane, represents the fraction of membrane area that is occupied by the pores.The transit times for three dimensional diffusion into and from a spherical cell are also presented in a simple form. In addition, some of the relations between transit times and other measurable time parameters, such as the course of the decay of gradients and the time lag to establish steady states, are discussed briefly.The conclusions emerging from this analysis, together with the simple expressions for the transit times can make these investigation useful for the understanding of diffusion in systems containing natural or artificial membranes.     

Estimating Summer Nutrient Concentrations in Northeastern Lakes from SPARROW Load Predictions and Modeled Lake Depth and Volume

Global nutrient cycles have been altered by the use of fossil fuels and fertilizers resulting in increases in nutrient loads to aquatic systems. In the United States, excess nutrients have been repeatedly reported as the primary cause of lake water quality impairments. Setting nutrient criteria that are protective of a lakes ecological condition is one common solution; however, the data required to do this are not always easily available. A useful solution for this is to combine available field data (i.e., The United States Environmental Protection Agency (USEPA) National Lake Assessment (NLA)) with average annual nutrient load models (i.e., USGS SPARROW model) to estimate summer concentrations across a large number of lakes. In this paper we use this combined approach and compare the observed total nitrogen (TN) and total phosphorus (TN) concentrations in Northeastern lakes from the 2007 National Lake Assessment to those predicted by the Northeast SPARROW model. We successfully adjusted the SPARROW predictions to the NLA observations with the use of Vollenweider equations, simple input-output models that predict nutrient concentrations in lakes based on nutrient loads and hydraulic residence time. This allows us to better predict summer concentrations of TN and TP in Northeastern lakes and ponds. On average we improved our predicted concentrations of TN and TP with Vollenweider models by 18.7% for nitrogen and 19.0% for phosphorus. These improved predictions are being used in other studies to model ecosystem services (e.g., aesthetics) and dis-services (e.g. cyanobacterial blooms) for ~18,000 lakes in the Northeastern United States.     

Modeling Allochthonous Dissolved Organic Carbon Mineralization Under Variable Hydrologic Regimes in Boreal Lakes

Here, we explore the interaction between hydrology and the reactivity of allochthonous dissolved organic carbon (DOC_alloch) in determining the potential of DOC_alloch to generate CO₂ through biological and photo-chemical mineralization in boreal lakes. We developed a mechanistic model that integrates the reactivity continuum (RC) concept to reconstruct in-lake mineralization of DOC_alloch under variable hydrologic conditions using empirical measurements of DOC_alloch concentrations and reactivity as model inputs. The model predicts lake DOC_alloch concentration (L-DOC_alloch) and its average overall reactivity \( \left( {\bar{K}_{\text{alloch}} } \right) \), which integrates the distribution of DOC_alloch ages within the lake as a function of the DOC loading (DOC_in), the initial reactivity of this DOC_in (k ₀), and the lake water residence time (WRT). The modeled DOC_alloch mineralization rates and concentrations were in agreement with expectations based on observed and published values of ambient lake DOC concentrations and reactivity. Results from this modeling exercise reveal that the interaction between WRT and k ₀ is a key determinant of the ambient concentration and reactivity of lake DOC_alloch, which represents the bulk of DOC in most of these lakes. The steady-state \( \left( {\bar{K}_{\text{alloch}} } \right) \) also represents the proportion of CO₂ that can be extracted from DOC_alloch during its transit through lakes, and partly explains the patterns in surface water pCO₂ oversaturation that have been observed across gradients of lake size and volume. We estimate that in-lake DOC_alloch mineralization could potentially contribute on average 30–40% of the observed surface carbon dioxide partial pressure (pCO₂) across northern lakes. Applying the RC framework to in-lake DOC_alloch dynamics improves our understanding of DOC_alloch transformation and fate along the aquatic network, and results in a predictable mosaic of DOC reactivity and potential CO₂ emissions across lakes within a landscape.     

Bifurcation analysis informs Bayesian inference in the Hes1 feedback loop

Background  

Ordinary differential equations (ODEs) are an important tool for describing the dynamics of biological systems. However, for ODE models to be useful, their parameters must first be calibrated. Parameter estimation, that is, finding parameter values given experimental data, is an inference problem that can be treated systematically through a Bayesian framework.     

Convergence to genetically uniform state in stepping stone models of population genetics

We investigate continuous time stepping stone models. Extending the models treated in population genetics, we consider the system described by the following infinite dimensional stochastic differential equation, $$dx_k (t) = a_k (x_k )dB_k + \left\{ {\sum\limits_{j \in S} {q_{k,jXj} } } \right\}dt, k \in S$$ which contains the effects of random sampling drift and a kind of stochastic fluctuation in selection. We obtain a necessary and sufficient condition for the system to converge to a genetically uniform state.     

Influence of internal loading on phosphorus concentration in shallow lakes before and after reduction of the external loading

An analysis of data from 49 shallow lakes showed, that the parameters of empirical models between phosphorus loading and concentration in the lake (e.g. Vollenweider type of relations) differ significantly for lakes without or with a reduced external loading. For lakes without a reduction of the external loading the summer phosphorus concentration is determined by the external phosphorus loading and the hydraulic loading. For these lakes the classical models suffice; deviations between calculations and measurements are partly due to errors made in the determination of the loading.In contrast, for lakes where the external loading was reduced, the measured internal loading explains most of the variation in the summer lake concentration. The external loading is of minor importance and the classical models cannot be applied. The internal loading measured before reduction of the external loading is not useful in predicting the concentration afterwards. Instead of the internal loading, the sediment composition can be used. The advantage of using sediment composition is that these variables are easier to determine and vary less in time. The most promising variable is the ratio between total P and total Fe in the sediment.Abbreviations: Q_s hydraulic loading (m y^-1) - hydraulic retention time (y) - L_ext external phosphorus loading (gP m^-2 y^-1) - L_int internal phosphorus loading (gP m^-2 y^-1) - P_lake phosphorus concentration in the lake (gP m^-3) - P_inlet phosphorus concentration in the inlet water (gP m^-3) - P_sed phosphorus content on the sediment (gP kg^-1 d.w.) - Fe_sed iron content of the sediment (gFe kg^-1 d.w.) - Y dependent variable multiple regression calculations - X1, X2 independent variables multiple regressions calculations - a, a1 constants - a2, b constants     

Improved identifiability of myocardial material parameters by an energy-based cost function

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were \(C_1=3000\pm 1700\,\hbox {Pa}\) and \(\alpha =45\pm 25\) (\(b_f=25\pm 14\), \(b_{ft}=11\pm 6\), \(b_{t}=9\pm 5\)) for the HF cases and \(C_1=1700\,\hbox {Pa}\) and \(\alpha =15\) (\(b_f=8\), \(b_{ft}=4\), \(b_{t}=3\)) for the healthy case.     

Biological kinetic behaviors and operational performances in aerated and oxygenated systems

Biological kinetic behaviors of the oxygenated and aerated activated sludge process were studied and compared in both once-through and constant sludge recycle systems. The models derived by Herbert, Elsworth, and Telling [J. Gen. Microbiol., 14 , 601 (1956)] and Ramanathan and Gaudy [Biotechnol. Bioeng., 11 , 207 (1969)] were used for the studies of once-through and constant sludge recycle systems, respectively. Soft drink waste water was used for the growth limiting substrate. Temperature was controlled within 30 ± 2°C. The influent substrate concentration was maintained at 1,000 mg/liter. The experiments were conducted at various dilution rates (from \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{9} $\end{document} to 1/1.0 hr^?1), and recycle solids concentration values (from 5,000 to 10,000 mg/liter), with hydraulic recycle ratio, α, at 0.3. Biological kinetic constants were evaluated and compared. It was found that these constants were different for the aerated and oxygenated systems within a certain range of dilution rates studied. The critical dilution rates for diluting out effluent chemical oxygen demand (COD) occurred at 0.1 and 0.2 hr^?1in the once-through operation, and 0.2 and 0.4 hr^?1in the sludge recycle operation for aerated and oxygenated systems, respectively. Observed sludge yield values and specific growth rate were varied with the type of aeration and with and without constant sludge recycle concentration applied. Sludge carbohydrates and proteins content in the oxygenation system (cell recycle) were 10.1–21.6% and 35.6–52.2%. Sludge volume index in the air and oxygenation systems varied from 41.4 to 354 and 31.9 to 58.5, respectively.     

Graph hierarchies for phylogeography

Bayesian phylogeographic methods simultaneously integrate geographical and evolutionary modelling, and have demonstrated value in assessing spatial spread patterns of measurably evolving organisms. We improve on existing phylogeographic methods by combining information from multiple phylogeographic datasets in a hierarchical setting. Consider N exchangeable datasets or strata consisting of viral sequences and locations, each evolving along its own phylogenetic tree and according to a conditionally independent geographical process. At the hierarchical level, a random graph summarizes the overall dispersion process by informing which migration rates between sampling locations are likely to be relevant in the strata. This approach provides an efficient and improved framework for analysing inherently hierarchical datasets. We first examine the evolutionary history of multiple serotypes of dengue virus in the Americas to showcase our method. Additionally, we explore an application to intrahost HIV evolution across multiple patients.     

Modelling the Dynamics of an Experimental Host-Pathogen Microcosm within a Hierarchical Bayesian Framework

The advantages of Bayesian statistical approaches, such as flexibility and the ability to acknowledge uncertainty in all parameters, have made them the prevailing method for analysing the spread of infectious diseases in human or animal populations. We introduce a Bayesian approach to experimental host-pathogen systems that shares these attractive features. Since uncertainty in all parameters is acknowledged, existing information can be accounted for through prior distributions, rather than through fixing some parameter values. The non-linear dynamics, multi-factorial design, multiple measurements of responses over time and sampling error that are typical features of experimental host-pathogen systems can also be naturally incorporated. We analyse the dynamics of the free-living protozoan Paramecium caudatum and its specialist bacterial parasite Holospora undulata. Our analysis provides strong evidence for a saturable infection function, and we were able to reproduce the two waves of infection apparent in the data by separating the initial inoculum from the parasites released after the first cycle of infection. In addition, the parameter estimates from the hierarchical model can be combined to infer variations in the parasite''s basic reproductive ratio across experimental groups, enabling us to make predictions about the effect of resources and host genotype on the ability of the parasite to spread. Even though the high level of variability between replicates limited the resolution of the results, this Bayesian framework has strong potential to be used more widely in experimental ecology.     

A Comparison of Bimolecular Reaction Models for Stochastic Reaction–Diffusion Systems

Stochastic reaction–diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary spatially-continuous models that have been used in recent studies: the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. Both models treat molecules as points undergoing Brownian motion. The former represents chemical reactions between two reactants through the use of reactive boundary conditions, with two molecules reacting instantly upon reaching a fixed separation (called the reaction-radius). The Doi model uses reaction potentials, whereby two molecules react with a fixed probability per unit time, λ, when separated by less than the reaction radius. In this work, we study the rigorous relationship between the two models. For the special case of a protein diffusing to a fixed DNA binding site, we prove that the solution to the Doi model converges to the solution of the Smoluchowski model as λ→∞, with a rigorous $O(\lambda^{-\frac{1}{2} + \epsilon})$ error bound (for any fixed ?>0). We investigate by numerical simulation, for biologically relevant parameter values, the difference between the solutions and associated reaction time statistics of the two models. As the reaction-radius is decreased, for sufficiently large but fixed values of λ, these differences are found to increase like the inverse of the binding radius.     

Nonparametric approaches for estimating regional lake nutrient thresholds

Nonparametric approaches including a classification and regression tree (CART), a nonparametric changepoint analysis (nCPA) and a Bayesian hierarchical modeling (BHM) method were developed to determine ecoregional nutrient response thresholds. A CART analysis revealed that hierarchical structure was important for predicting Chl a concentrations from total nitrogen (TN) and total phosphorus (TP). The nCPA and BHM methods confirmed the CART results for each node in the tree, and the 90% confidence interval for each threshold was calculated to quantify uncertainty. The CART, nCPA, and BHM methods suggested that the nutrient criteria differed significantly within certain nutrient ecoregions and that numerical nutrient criteria of 0.0150–0.222 mg/L TP and 0.300–1.766 mg/L TN may control Chl a concentrations in the various lake ecoregions. The results of this analysis suggest that the integration of CART, nCPA and BHM might be useful for determining nutrient thresholds.     

Nested Sampling for Bayesian Model Comparison in the Context of Salmonella Disease Dynamics

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike''s Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered.     

Bayesian model selection for spatial capture–recapture models

A vast amount of ecological knowledge generated over the past two decades has hinged upon the ability of model selection methods to discriminate among various ecological hypotheses. The last decade has seen the rise of Bayesian hierarchical models in ecology. Consequently, commonly used tools, such as the AIC, become largely inapplicable and there appears to be no consensus about a particular model selection tool that can be universally applied. We focus on a specific class of competing Bayesian spatial capture–recapture (SCR) models and apply and evaluate some of the recommended Bayesian model selection tools: (1) Bayes Factor—using (a) Gelfand‐Dey and (b) harmonic mean methods, (2) Deviance Information Criterion (DIC), (3) Watanabe‐Akaike's Information Criterion (WAIC) and (4) posterior predictive loss criterion. In all, we evaluate 25 variants of model selection tools in our study. We evaluate these model selection tools from the standpoint of selecting the “true” model and parameter estimation. In all, we generate 120 simulated data sets using the true model and assess the frequency with which the true model is selected and how well the tool estimates N (population size), a parameter of much importance to ecologists. We find that when information content is low in the data, no particular model selection tool can be recommended to help realize, simultaneously, both the goals of model selection and parameter estimation. But, in general (when we consider both the objectives together), we recommend the use of our application of the Bayes Factor (Gelfand‐Dey with MAP approximation) for Bayesian SCR models. Our study highlights the point that although new model selection tools are emerging (e.g., WAIC) in the applied statistics literature, those tools based on sound theory even under approximation may still perform much better.