Comparing Inductive and Deductive Modeling of Land Use Decisions: Principles,a Model and an Illustration from the Philippines

Understanding the causes of land use change is of great importance for issues of tropical deforestation, agricultural development and biodiversity conservation. Many quantitative studies, therefore, aim to link land use change to its causal ‘driving forces.’ The epistemology of virtually all these studies is inductive, searching for correlations within relatively large, sometimes spatially explicit, datasets. This can be sound science but we here aim to exemplify that there is also scope for more deductive approaches that test a pre-defined explanatory theory. The paper first introduces the principles and merits of inductive and more deductive types of land use modeling. It then presents one integrated causal model that is subsequently specified to predict land use in an area in northeastern Philippines in a deductive manner, and tested against the observed land use in that area. The same set of land use data is also used in an inductive (multinomial regression) approach. With a goodness-of-prediction of 70% of the deductive model and a goodness-of-fit of 77% of the inductive model, both perform equally well, statistically. Because the deductive model explicitly contains not only the causal factors but also the causal mechanisms that explain land use, the deductive model then provides a more truly causal, as well as more theory-connected, understanding of land use. This provides land use scholarship with an invitation to add more deductive (theory-driven and theory-building) daring to its methodological repertoire.

Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations

When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input-output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input-output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel.     

Maximizing the Power of Genome-Wide Association Studies: A Novel Class of Powerful Family-Based Association Tests

For genome-wide association studies in family-based designs, a new, universally applicable approach is proposed. Using a modified Liptak’s method, we combine the p-value of the family-based association test (FBAT) statistic with the p-value for the Van Steen-statistic. The Van Steen-statistic is independent of the FBAT-statistic and utilizes information that is ignored by traditional FBAT-approaches. The new test statistic takes advantages of all available information about the genetic association, while, by virtue of its design, it achieves complete robustness against confounding due to population stratification. The approach is suitable for the analysis of almost any trait type for which FBATs are available, e.g. binary, continuous, time-to-onset, multivariate, etc. The efficiency and the validity of the new approach depend on the specification of a nuisance/tuning parameter and the weight parameters in the modified Liptak’s method. For different trait types and ascertainment conditions, we discuss general guidelines for the optimal specification of the tuning parameter and the weight parameters. Our simulation experiments and an application to an Alzheimer study show the validity and the efficiency of the new method, which achieves power levels that are comparable to those of population-based approaches.     

Quantitative analysis of the nanopore translocation dynamics of simple structured polynucleotides

Nanopore translocation experiments are increasingly applied to probe the secondary structures of RNA and DNA molecules. Here, we report two vital steps toward establishing nanopore translocation as a tool for the systematic and quantitative analysis of polynucleotide folding: 1), Using α-hemolysin pores and a diverse set of different DNA hairpins, we demonstrate that backward nanopore force spectroscopy is particularly well suited for quantitative analysis. In contrast to forward translocation from the vestibule side of the pore, backward translocation times do not appear to be significantly affected by pore-DNA interactions. 2), We develop and verify experimentally a versatile mesoscopic theoretical framework for the quantitative analysis of translocation experiments with structured polynucleotides. The underlying model is based on sequence-dependent free energy landscapes constructed using the known thermodynamic parameters for polynucleotide basepairing. This approach limits the adjustable parameters to a small set of sequence-independent parameters. After parameter calibration, the theoretical model predicts the translocation dynamics of new sequences. These predictions can be leveraged to generate a baseline expectation even for more complicated structures where the assumptions underlying the one-dimensional free energy landscape may no longer be satisfied. Taken together, backward translocation through α-hemolysin pores combined with mesoscopic theoretical modeling is a promising approach for label-free single-molecule analysis of DNA and RNA folding.     

A Global Sensitivity Test for Evaluating Statistical Hypotheses with Nonidentifiable Models

Summary We consider the problem of evaluating a statistical hypothesis when some model characteristics are nonidentifiable from observed data. Such a scenario is common in meta‐analysis for assessing publication bias and in longitudinal studies for evaluating a covariate effect when dropouts are likely to be nonignorable. One possible approach to this problem is to fix a minimal set of sensitivity parameters conditional upon which hypothesized parameters are identifiable. Here, we extend this idea and show how to evaluate the hypothesis of interest using an infimum statistic over the whole support of the sensitivity parameter. We characterize the limiting distribution of the statistic as a process in the sensitivity parameter, which involves a careful theoretical analysis of its behavior under model misspecification. In practice, we suggest a nonparametric bootstrap procedure to implement this infimum test as well as to construct confidence bands for simultaneous pointwise tests across all values of the sensitivity parameter, adjusting for multiple testing. The methodology's practical utility is illustrated in an analysis of a longitudinal psychiatric study.     

Uninformative Parameters and Model Selection Using Akaike's Information Criterion

Abstract: As use of Akaike's Information Criterion (AIC) for model selection has become increasingly common, so has a mistake involving interpretation of models that are within 2 AIC units (ΔAIC ≤ 2) of the top-supported model. Such models are <2 ΔAIC units because the penalty for one additional parameter is +2 AIC units, but model deviance is not reduced by an amount sufficient to overcome the 2-unit penalty and, hence, the additional parameter provides no net reduction in AIC. Simply put, the uninformative parameter does not explain enough variation to justify its inclusion in the model and it should not be interpreted as having any ecological effect. Models with uninformative parameters are frequently presented as being competitive in the Journal of Wildlife Management, including 72% of all AIC-based papers in 2008, and authors and readers need to be more aware of this problem and take appropriate steps to eliminate misinterpretation. I reviewed 5 potential solutions to this problem: 1) report all models but ignore or dismiss those with uninformative parameters, 2) use model averaging to ameliorate the effect of uninformative parameters, 3) use 95% confidence intervals to identify uninformative parameters, 4) perform all-possible subsets regression and use weight-of-evidence approaches to discriminate useful from uninformative parameters, or 5) adopt a methodological approach that allows models containing uninformative parameters to be culled from reported model sets. The first approach is preferable for small sets of a priori models, whereas the last 2 approaches should be used for large model sets or exploratory modeling.     

A PDMP model of the epithelial cell turn-over in the intestinal crypt including microbiota-derived regulations

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. That is, whether parameters can be uniquely determined from perfect or realistic data in theory and practice. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

     

Beyond the E-Value: Stratified Statistics for Protein Domain Prediction

E-values have been the dominant statistic for protein sequence analysis for the past two decades: from identifying statistically significant local sequence alignments to evaluating matches to hidden Markov models describing protein domain families. Here we formally show that for “stratified” multiple hypothesis testing problems—that is, those in which statistical tests can be partitioned naturally—controlling the local False Discovery Rate (lFDR) per stratum, or partition, yields the most predictions across the data at any given threshold on the FDR or E-value over all strata combined. For the important problem of protein domain prediction, a key step in characterizing protein structure, function and evolution, we show that stratifying statistical tests by domain family yields excellent results. We develop the first FDR-estimating algorithms for domain prediction, and evaluate how well thresholds based on q-values, E-values and lFDRs perform in domain prediction using five complementary approaches for estimating empirical FDRs in this context. We show that stratified q-value thresholds substantially outperform E-values. Contradicting our theoretical results, q-values also outperform lFDRs; however, our tests reveal a small but coherent subset of domain families, biased towards models for specific repetitive patterns, for which weaknesses in random sequence models yield notably inaccurate statistical significance measures. Usage of lFDR thresholds outperform q-values for the remaining families, which have as-expected noise, suggesting that further improvements in domain predictions can be achieved with improved modeling of random sequences. Overall, our theoretical and empirical findings suggest that the use of stratified q-values and lFDRs could result in improvements in a host of structured multiple hypothesis testing problems arising in bioinformatics, including genome-wide association studies, orthology prediction, and motif scanning.     

Model‐based identifiable parameter determination applied to a simultaneous saccharification and fermentation process model for bio‐ethanol production

In this work, a methodology for the model‐based identifiable parameter determination (MBIPD) is presented. This systematic approach is proposed to be used for structure and parameter identification of nonlinear models of biological reaction networks. Usually, this kind of problems are over‐parameterized with large correlations between parameters. Hence, the related inverse problems for parameter determination and analysis are mathematically ill‐posed and numerically difficult to solve. The proposed MBIPD methodology comprises several tasks: (i) model selection, (ii) tracking of an adequate initial guess, and (iii) an iterative parameter estimation step which includes an identifiable parameter subset selection (SsS) algorithm and accuracy analysis of the estimated parameters. The SsS algorithm is based on the analysis of the sensitivity matrix by rank revealing factorization methods. Using this, a reduction of the parameter search space to a reasonable subset, which can be reliably and efficiently estimated from available measurements, is achieved. The simultaneous saccharification and fermentation (SSF) process for bio‐ethanol production from cellulosic material is used as case study for testing the methodology. The successful application of MBIPD to the SSF process demonstrates a relatively large reduction in the identified parameter space. It is shown by a cross‐validation that using the identified parameters (even though the reduction of the search space), the model is still able to predict the experimental data properly. Moreover, it is shown that the model is easily and efficiently adapted to new process conditions by solving reduced and well conditioned problems. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29:1064–1082, 2013     

Estimating negative binomial parameters from occurrence data with detection times

The negative binomial distribution is a common model for the analysis of count data in biology and ecology. In many applications, we may not observe the complete frequency count in a quadrat but only that a species occurred in the quadrat. If only occurrence data are available then the two parameters of the negative binomial distribution, the aggregation index and the mean, are not identifiable. This can be overcome by data augmentation or through modeling the dependence between quadrat occupancies. Here, we propose to record the (first) detection time while collecting occurrence data in a quadrat. We show that under what we call proportionate sampling, where the time to survey a region is proportional to the area of the region, that both negative binomial parameters are estimable. When the mean parameter is larger than two, our proposed approach is more efficient than the data augmentation method developed by Solow and Smith ( 2010 , Am. Nat. 176 , 96–98), and in general is cheaper to conduct. We also investigate the effect of misidentification when collecting negative binomially distributed data, and conclude that, in general, the effect can be simply adjusted for provided that the mean and variance of misidentification probabilities are known. The results are demonstrated in a simulation study and illustrated in several real examples.     

Validation of potential inhibitors for SrtA against Bacillus anthracis by combined approach of ligand-based and molecular dynamics simulation

The development of SrtA inhibitors targeting the biothreat organism namely Bacillus anthracis was achieved by the combined approach of pharmacophore modeling, binding interactions, electron transferring capacity, ADME, and Molecular dynamics studies. In this study, experimentally reported Ba-SrtA inhibitors (pyridazinone and pyrazolethione derivatives) were considered for the development of enhanced pharmacophoric model. The obtained AAAHR hypothesis was a pure theoretical concept that accounts for common molecular interaction network present in experimentally active pyridazinone and pyrazolethione derivatives. Pharmacophore-based screening of AAAHR hypothesis provides several new compounds, and those compounds were treated with four phases of docking protocols with combined Glide-QPLD docking approach. In this approach, scoring and charge accuracy variations were seen to be dominated by QM/MM approach through the allocation of partial charges. Finally, we reported the best compounds from binding db, Chembridge db, and Toslab based on scoring values, energy parameters, electron transfer reaction, ADME, and cell adhesion inhibition activity. The dynamic state of interaction and binding energy assess that new compounds are more active inside the binding pocket and these compounds on experimental validations will survive as better inhibitors for targeting the cell adhesion mechanism of Ba-SrtA.     

An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases

The parameter identifiability problem for dynamic system ODE models has been extensively studied. Nevertheless, except for linear ODE models, the question of establishing identifiable combinations of parameters when the model is unidentifiable has not received as much attention and the problem is not fully resolved for nonlinear ODEs. Identifiable combinations are useful, for example, for the reparameterization of an unidentifiable ODE model into an identifiable one. We extend an existing algorithm for finding globally identifiable parameters of nonlinear ODE models to generate the ‘simplest’ globally identifiable parameter combinations using Gröbner Bases. We also provide sufficient conditions for the method to work, demonstrate our algorithm and find associated identifiable reparameterizations for several linear and nonlinear unidentifiable biomodels.     

Changes in transorgan electric potential inChenopodium rubrum during the course of photoperiodic flower induction

Electrophysiological processes were investigated in reception organs of photoperiodism in a model short-day plant,Chenopodium rubrum L. (selection 374), within the inductive cycle for flowering. Transorgan (surface) electric potential (E_tr) was measured as a potential difference between the first leaf surface and the roots of an intact plant, and between the surface of an excised leaf and the petiole base. The time-course of E_tr in intact plants showed irregular, or partially regular, oscillations within both phases of the inductive cycle and under continuous light. The highest amplitudes were during the postinductive light period. E_tr in excised leaves behaved practically in the same way as in intact plants. The E_tr oscillations were localized in leaves. In general, no electrophysiological changes were found in the reception organs within the inductive cycle which could be correlated with the formation and transport of floral stimulus, or with the attainment of an induced state. The results indirectly support the idea that the floral stimulus is chemical in nature.     

On the identifiability of metabolic network models

A major problem for the identification of metabolic network models is parameter identifiability, that is, the possibility to unambiguously infer the parameter values from the data. Identifiability problems may be due to the structure of the model, in particular implicit dependencies between the parameters, or to limitations in the quantity and quality of the available data. We address the detection and resolution of identifiability problems for a class of pseudo-linear models of metabolism, so-called linlog models. Linlog models have the advantage that parameter estimation reduces to linear or orthogonal regression, which facilitates the analysis of identifiability. We develop precise definitions of structural and practical identifiability, and clarify the fundamental relations between these concepts. In addition, we use singular value decomposition to detect identifiability problems and reduce the model to an identifiable approximation by a principal component analysis approach. The criterion is adapted to real data, which are frequently scarce, incomplete, and noisy. The test of the criterion on a model with simulated data shows that it is capable of correctly identifying the principal components of the data vector. The application to a state-of-the-art dataset on central carbon metabolism in Escherichia coli yields the surprising result that only $4$ out of $31$ reactions, and $37$ out of $100$ parameters, are identifiable. This underlines the practical importance of identifiability analysis and model reduction in the modeling of large-scale metabolic networks. Although our approach has been developed in the context of linlog models, it carries over to other pseudo-linear models, such as generalized mass-action (power-law) models. Moreover, it provides useful hints for the identifiability analysis of more general classes of nonlinear models of metabolism.     

Modeling aerobic carbon oxidation and storage by integrating respirometric, titrimetric, and off-gas CO2 measurements

A method for detailed investigation of aerobic carbon degradation processes by microorganisms is presented. The method relies on an integrated use of the respirometric, titrimetric, and off-gas CO(2) measurements. The oxygen uptake rate (OUR), hydrogen ion production rate (HPR), and the carbon dioxide transfer rate (CTR) resulting from the biological as well as physicochemical processes, coupled with a metabolic model characterizing both the growth and carbon storage processes, enables the comprehensive study of the carbon degradation processes. The method allows the formation of carbon storage products and the biomass growth rates to be estimated without requiring any off-line biomass or liquid-phase measurements, although the practical identifiability of the system could be improved with additional measurements. Furthermore, the combined yield for biomass growth and carbon storage is identifiable, along with the affinity constant with respect to the carbon substrate. However, the individual yields for growth and carbon storage are not identifiable without further knowledge about the metabolic pathways employed by the microorganisms in the carbon conversion. This is true even when more process variables are measured. The method is applied to the aerobic carbon substrate degradation by a full-scale sludge using acetate as an example carbon source. The sludge was able to quickly take up the substrate and store it as poly-beta-hydroxybutyrate (PHB). The PHB formation rate was a few times faster than the biomass growth rate, which was confirmed by off-line liquid- and solid-phase analysis. The estimated combined yield for biomass growth and carbon storage compared closely to that determined from the theoretical yields reported in literature based on thermodynamics. This suggests that the theoretical yields may be used as default parameters for modeling purposes.     

The application of meteorology in medical sciences

After a brief mention of the distinct features of human biometeorology as compared with the other fields of biometeorology methods of approach are reviewed. The main aim of research is to establish a ranking order for the impact of the factors of the atmospheric environment within general biometeorology and within ecology as a whole. Both deductive and inductive methods reveal that all ranking is relative and dependent on the particular purpose served and the special limitations introduced through control of the ecosystem. The application of meteorology in the medical sciences requires a basic understanding of human biometeorology. It can only be fruitful if the various specialists define their purpose clearly so that meteorologists can arrange their recording scheme and data evaluation accordingly.     

Minimal output sets for identifiability

Ordinary differential equation models in biology often contain a large number of parameters that must be determined from measurements by parameter estimation. For a parameter estimation procedure to be successful, there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not uniquely structurally identifiable with the given set of outputs selected as measurements. In designing an experiment for the purpose of parameter estimation, given a set of feasible but resource-consuming measurements, it is useful to know which ones must be included in order to obtain an identifiable system, or whether the system is unidentifiable from the feasible measurement set. We have developed an algorithm that, from a user-provided set of variables and parameters or functions of them assumed to be measurable or known, determines all subsets that when used as outputs give a locally structurally identifiable system and are such that any output set for which the system is structurally identifiable must contain at least one of the calculated subsets. The algorithm has been implemented in Mathematica and shown to be feasible and efficient. We have successfully applied it in the analysis of large signalling pathway models from the literature.     

Hybrid modeling of xanthan gum bioproduction in batch bioreactor

This work is focused on hybrid modeling of xanthan gum bioproduction process by Xanthomonas campestris pv. mangiferaeindicae. Experiments were carried out to evaluate the effects of stirred speed and superficial gas velocity on the kinetics of cell growth, lactose consumption and xanthan gum production in a batch bioreactor using cheese whey as substrate. A hybrid model was employed to simulate the bio-process making use of an artificial neural network (ANN) as a kinetic parameter estimator for the phenomenological model. The hybrid modeling of the process provided a satisfactory fitting quality of the experimental data, since this approach makes possible the incorporation of the effects of operational variables on model parameters. The applicability of the validated model was investigated, using the model as a process simulator to evaluate the effects of initial cell and lactose concentration in the xanthan gum production.     

Permeability study of vertebral cancellous bone using micro-computational fluid dynamics

Understanding of cancellous bone permeability is lacking despite its importance in designing tissue engineering scaffolds for bone regeneration and orthopaedic surgery that relies on infiltration of bone cement into porous cancellous bone. We employed micro-computational fluid dynamics to investigate permeability for 37 cancellous bone specimens, eliminating stringent technical requirements of bench-top testing. Microarchitectural parameters were also determined for the specimens and correlated, using uni-variate and multi-variate regression analyses, against permeability. We determined that bone surface density, trabecular pattern factor, structure model index and trabecular number are other possible predictors of permeability (with R values of 0.47, 0.44, 0.40 and 0.33), in addition to the commonly used porosity parameter (R value of 0.38). Pooling these parameters and performing multi-variate linear regression analysis improved yield the R-value of 0.50, indicating that porosity alone is a poor predictor of cancellous bone permeability and, therefore, other parameters should be included for a better and improved linear model.     

Data-based identifiability analysis of non-linear dynamical models

MOTIVATION: Mathematical modelling of biological systems is becoming a standard approach to investigate complex dynamic, non-linear interaction mechanisms in cellular processes. However, models may comprise non-identifiable parameters which cannot be unambiguously determined. Non-identifiability manifests itself in functionally related parameters, which are difficult to detect. RESULTS: We present the method of mean optimal transformations, a non-parametric bootstrap-based algorithm for identifiability testing, capable of identifying linear and non-linear relations of arbitrarily many parameters, regardless of model size or complexity. This is performed with use of optimal transformations, estimated using the alternating conditional expectation algorithm (ACE). An initial guess or prior knowledge concerning the underlying relation of the parameters is not required. Independent, and hence identifiable parameters are determined as well. The quality of data at disposal is included in our approach, i.e. the non-linear model is fitted to data and estimated parameter values are investigated with respect to functional relations. We exemplify our approach on a realistic dynamical model and demonstrate that the variability of estimated parameter values decreases from 81 to 1% after detection and fixation of structural non-identifiabilities.