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

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.

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.

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.