## Supplement 1. Matlab software used in this study.

## File List

**Folder lists:**

Data

GP(the linear model)

GP(the constant model)

GP(the S model)

GP(the lnS model)

Ricker(integral)

BH(integral)

**Download all files at once --**AllFilesAtOnce.zip (md5: b667a9b12b231ebbb2d06da38f6b117a)

## Description

'Data' contains a script file used for generating simulated data sets.

'GP(the linear model)' contains functions used for running the semiparametric Bayesian model with the linear mean function) to estimate log(alpha). The outputs of this model is mean ('mloga') and variance ('vloga)' of the posterior distribution of 'log(alpha)', where 'alpha' is reproductive rate estimated at S=0.

'GP(the constant model)' contains functions used for running the semiparametric Bayesian model (with the constant mean function) to estimate log(alpha). The outputs of this model is mean ('mloga') and variance ('vloga)' of the posterior distribution of 'log(alpha)', where 'alpha' is reproductive rate estimated at S=0.

'GP(the S model)' contains functions used for running the semiparametric Bayesian model (un-conditional model) to estimate log(alpha). The outputs of this model is mean ('mloga') and variance ('vloga)' of the posterior distribution of 'log(alpha)', where 'alpha' is reproductive rate estimated at S=0.

'GP(GP(the lnS model))' contains functions used for running the semiparametric Bayesian model (un-conditional model) to estimate log(alpha) (developed in Munch et al. 2005). The outputs of this model is mean ('mloga') and variance ('vloga)' of the posterior distribution of 'log(alpha)', where 'alpha' is reproductive rate estimated at S=0.

'Ricker(integral)' contains functions used for estimating log(alpha) using the Ricker model. The outputs of this model is mean ('mloga') and variance ('vloga)' of the posterior distribution of 'log(alpha)', where 'alpha' is reproductive rate estimated at S=0.

'BH(integral)' contains functions used for estimating log(alpha) using the Beverton-Holt model. The outputs of this model is mean ('mloga') and variance ('vloga)' of the posterior distribution of 'log(alpha)', where 'alpha' is reproductive rate estimated at S=0.