This is because the model parameters required to give the same richness and evenness in the empirical data are themselves close to neutral, either because c is small or because the metacommunity follows a logseries distribution and m is close to 1 (in which case the local community strongly resembles a neutral-like metacommunity).

This section describes (i) our non-neutral alternative models, and methods for generating samples from them; (ii) our method for testing whether to reject the neutral null hypothesis for a particular data set; (iii) the method for combining (i) and (ii) to give a power calculation; (iv) the method for estimating model parameter values in order to estimate the statistical power of particular experiments.

Power calculation for fixed non-neutral model parameters

The two other model parameters (immigration rate and diversity of the metacommunity) also strongly affect the chance of rejecting the neutral hypothesis.

We did not find any simple way to summarise the dependence on model parameters evident in Figs.

We do not know a priori the appropriate non-neutral parameter values for these forests, but we can choose model parameters so that the model data match a number of features of the empirical data.

Specifically, we chose model parameters so that the community size, mean species richness,

The determination of appropriate model parameters , and the power calculation itself, is very computationally expensive, so we performed this for three candidate strengths of non-neutrali-ty, and for models PC and IF only.

Statistical power calculation for fixed non-neutral model parameters

Lists of the genes assigned to kinetic signatures and the corresponding model parameters are provided in Supporting File 1.

The inference of model parameters from CAGE data for the early peak and linear models using nested sampling and the 11 based likelihood is illustrated in Fig 1C.

Bayesian evidence values and model parameter estimates (and their standard deviations) are computed using nested sampling for all signatures for each time series.

Model parameters also give the timing of potentially important events such as transitions in eXpression levels within the time course.

Models are specified in advance, and selection is based on the integration of model parameters rather than from a point estimate of best values, an approach which can be sensitive to the optimisation procedure used.

Further exploration of model parameters yielded other insights.

Further details of the specification of priors for model parameters , and model selection are given in Materials and methods.

CAGE clusters and associated model parameters for all time courses.

This is a Bayesian estimation method which incorporates Gaussian priors over model parameters and uses a Gaussian approximation to the posterior density.

Thus, in the limit of the posterior equaling the prior, our beliefs about model parameters will not change and the penalty will be zero.

Only the formal model comparison presented above took into account additional model parameters .

The average model parameters were k = 10.49i4.28 and p = 0.70:0.09 for the sigmoidal model for effort, and k = 4.86:2.20 for the hyperbolic model for delay (see 81 Table).

Results are not trivially explained by a larger number of model parameters , the exerted force, or fatigue

But, for example, if the marginal distribution over one of the model parameters does not change as a result of model fitting, a penalty will not be paid for it.

The supplementary methods and results report an analysis of response time and choice based on simple regression analyses, and include additional tables reporting model parameter estimates, accuracy and complexity terms, and results of control analyses.

Note that the percentage of correctly predicted choices does not take into account the additional model parameter of the sigmoidal model, which importantly was considered in the formal model comparison results shown in Fig.

Sequential perturbation of Zipper model parameters shows that these changes can be mapped to changes in both power-law parameters (84C Fig).

(A) Mapping of 3-stage model parameters on power-law parameters.

Each set of markers shows the effect of increasing a zipper model parameter over two orders of magnitude centered on a base value.

This is reminiscent of modeling analysis showing that perturbation to Zipper model parameters modulates power-law parameter values along the same, restricted path (Fig 4A).

A power-law of the form P = RB/KDeff was fit to data for different values of each zipper model parameter .

The zipper model parameters are normalized with respect to their base values (S4 Table).

The fitting was performed using Markov Chain Monte Carlo (MCMC) methods, which find an ensemble of model parameters that fit the data and allow a credible interval for each of these parameters to be determined.

This LL sum can now be used as an objective function for our Markov Chain Monte Carlo scheme, to fit our model parameter values so that model outputs match the NNDSS data.

The black dots are US disease incidence data, and the shaded regions represent the credible intervals (50% and 95%) obtained through model parameter estimation of model 8.

State variables (population compartments) and model parameters for the model investigated.

In this study, we develop a new approach in which data are collected via a series of complex electrophysiology protocols from single cardiac myocytes and then used to tune model parameters via a parallel fitting method known as a genetic algorithm (GA).

Nine model parameters , describing maximal conductances of ionic currents [the sodium current (INa), the L-type calcium current (ICaL), the T-type calcium current (ICaT), the inwardly rectifying potassium (1K1), the rapid and slow delayed rectifier potassium currents (1Kr and IKS), the plateau potassium current (IKp), and the sarcolemmal calcium pump current (IpCa)] and the maximal flux of the sarcoplasmic reticulum Ca2+-ATPase (ISERCA) were estimated using a GA technique.

This step typically requires tuning of model parameters to reproduce Whole-cell behavior; this tuning is usually done manually in a laborious, iterative tweaking process, Which ends When the model output (e.g., an action potential) subjectively is deemed to adequately match the experimental counterparts.

The dissimilarities between the original FR model and the experimental data led to considerable changes in the estimated values for the model parameters for all four cells (Fig 6).

Considered together with the demonstration that the approach accurately identifies model parameters (Figs 2—4), these findings suggest that the approach significantly improves the fidelity of the model for cellular data, relative to the published generic model.

Empirical single-spike information is therefore equal to LNP model log-likelihood per spike, plus a constant that does not depend on model parameters .

Where 9 2 {Kg} are the model parameters , A is the time bin size, and 1 denotes a vector of ones.

With respect to the model parameters can be written: inverse-link function g at its input, and ‘0’ denotes Hadamard or component-Wise vector product.

The cbf- and rbf-LNP models were both fit by maximizing the likelihood for the model parameters 9 2 {Kg}.

Starting from all tensions set to zero, we optimized for the model parameter set With the best agreement of the two displacement fields.

With the cell and substrate models described above, we are now able to calculate a simulated displacement field for a given set of model parameters .

The intention of MBTFM is, however, to solve the inverse problem of finding the optimal set of model parameters (and thereby the reconstructed tractions) for a given cellular displacement field (Fig 2B).

To define optimality, we need to specify an error estimate for the deviation of the experimentally measured field and one that is simulated for a given set of model parameters .

The availability of such data is extremely important both for having a better set of model parameters and to validate new models.

Furthermore, our model shows that noise plays an important role in the onset of differentiation by enabling the development of the characteristic heterocyst patterns for a wide range of model parameters .

Heterocysts patterns develop for different levels of noise and diffusion constants, but the model parameters , which characterize cell response to nitrogen deprivation, should change accordingly.

This correlation between noise, diffusion and model parameters supports the idea that cyanobacteria have evolved towards a better response to the normal levels of noise in their environment.

In addition to comparing the estimated model parameters to the known PSC amplitudes and comparing components of the model to the injected current, we can also examine the detection of changes of synaptic inputs.

Thus, the model parameters are N (the number of presynaptic neurons), k and 6 (the shape and scale parameters for the homogeneous Gamma renewal processes), [,4 and o (the shape and log-scale parameters of the log-normal amplitude distribution), and T1 and 72 (the time constants of the artificial PSCs).

model parameters are able to accurately reproduce the relative amplitude of the presynaptic input (Fig.

For both the current-based and conductance-based inputs we then optimize model parameters to match the observed voltage fluctuations and spike timing using derivative-free search (Nelder-Mead) with random restarts.

Previous studies using total dl as the input to the gene expression model have revealed a high level of sensitivity of the Type III genes to changes in model parameters [10].

To determine the sensitivity of our results using free dl with respect to changes in model parameters , we took the best fit parameters for both free dl and total dl and varied them by i 10%.

The model with free dl is insensitive to 10% variations in the three model parameters (961;.

We examined spontaneous rates covering the entire range observed in our real neuronal population (0—40 spk/s) and found that the model parameters for generating synchronized and non-synchronized neurons were similar, albeit with a slight shift in the threshold I/E ratio for observing synchronized responses (Fig.

Model parameters underlying rate and temporal representations

We observed that synchronized, non-synchronized, and mixed responses were generated within three distinct regions of the model’s parameter space (Fig.

While some studies attempt to find values for these parameters that capture the tradeoff subjects make between cost and reward [72, 73], we set them empirically in order to allow the model to successfully perform the task (see 81 Table, 82 Table, S3 Table and S4 Table in the supporting information for the values of the model parameters used in the current study).

Model parameters .

The values of the model parameters used in the simulations.