Supplement 1. Calculations shown in Appendix C.

<h2>File List</h2><blockquote> <p><a href="Hobbs_Hilborn_supplement1.txt">Hobbs_Hilborn_supplement1.txt</a> -- Contains data collected at Isle Royal National Park (Michigan, USA) during the winter (January and February) from 1971–2001 and prey dependent model predictions and calculations.</p> <p><a href="Hobbs_Hilborn_supplement2.txt">Hobbs_Hilborn_supplement2.txt</a> -- Contains data collected at Isle Royal National Park (Michigan, USA) during the winter (January and February) from 1971–2001 and ratio dependent model predictions and calculations.</p> <p><a href="Hobbs_Hilborn_supplement3.txt">Hobbs_Hilborn_supplement3.txt</a> -- Contains data collected at Isle Royal National Park (Michigan, USA) during the winter (January and February)  from 1971–2001 and predator dependent model predictions and calculations.</p> <p><a href="Hobbs_Hilborn_supplement4.txt">Hobbs_Hilborn_supplement4.txt</a> -- Contains estimates of model selection statistics for the prey dependent, ratio dependent, and predator dependent models.</p> <p><a href="Hobbs_Hilborn_supplement.xls">Hobbs_Hilborn_supplement.xls</a> -- A spreadsheet showing details of the computation. The data files listed above can be downloaded into a spreadsheet of your choice.</p> <p> </p></blockquote><h2>Description</h2><blockquote> <p><b>Hobbs_Hilborn_supplement1.txt</b> contains data collected at Isle Royal National Park (Michigan, USA) during the winter (January and February) from 1971–2001 and prey dependent model predictions and calculations.</p> <p>The file is tab delimited and contains 8 columns and 94 rows.  The columns correspond to the variables listed below, and each row corresponds to a yearly observation, prey dependent model prediction, or calculation.</p> <p><b>Hobbs_Hilborn_supplement1</b></p> -- TABLE: Please see in attached file. -- <p>To make sure the file was downloaded properly, compare the column sums to the following figures: </p> -- TABLE: Please see in attached file. -- <p>There are also calculations based on the data that are indexed in a column to their left (2 columns, 7 rows).  These indices and the calculations they index are:</p> -- TABLE: Please see in attached file. -- <p> </p> <p><b>Hobbs_Hilborn_supplement2.txt</b> contains data collected at IsleRoyalNational Park (Michigan, USA) during the winter (January and February) from 1971–2001 and ratio dependent model predictions and calculations.</p> <p>The file is tab delimited and contains 9 columns and 94 rows.  The columns correspond to the variables listed below, and each row corresponds to a yearly observation, ratio dependent model prediction, or calculation.</p> <p><b>Hobbs_Hilborn_supplement2</b></p> -- TABLE: Please see in attached file. -- <p>To make sure the file was downloaded properly, compare the column sums to the following figures: </p> -- TABLE: Please see in attached file. -- <p>There are also calculations based on the data that are indexed in a column to their left (2 columns, 7 rows).  These indices and the calculations they index are:</p> -- TABLE: Please see in attached file. -- <p> </p> <p><b>Hobbs_Hilborn_supplement3.txt</b> contains data collected at IsleRoyalNational Park (Michigan, USA) during the winter (January and February)  from 1971–2001 and predator dependent model predictions or calculations.</p> <p>The file is tab delimited and contains 10 columns and 94 rows.  The columns correspond to the variables listed below, and each row corresponds to a yearly observation, predator dependent model prediction, or calculation.</p> <p><b>Hobbs_Hilborn_supplement3</b></p> -- TABLE: Please see in attached file. -- <p>To make sure the file was downloaded properly, compare the column sums to the following figures: </p> -- TABLE: Please see in attached file. -- <p>There are also calculations based on the data that are indexed in a column to their left (2 columns, 7 rows.  These indices and the calculations they index are:</p> -- TABLE: Please see in attached file. -- <p> </p> <p><b>Hobbs_Hilborn_supplement4.txt</b> contains estimates of model selection statistics for the prey dependent, ratio dependent, and predator dependent models.</p> <p>The file is tab delimited and contains 5 columns and 4 rows.  The columns correspond to the variables listed below, and each row corresponds to a model type.</p> <p> </p> <p><b>Hobbs_Hilborn_supplement4</b></p> -- TABLE: Please see in attached file. -- <p>To make sure the file was downloaded properly, compare the column sums to the following figures: </p> -- TABLE: Please see in attached file. -- <p> </p> <p><b>Instructions</b></p> <p>To reproduce the results presented in the paper, see the descriptions of the indexed calculations shown above.  To obtain the parameter estimates, use a nonlinear optimization routine to find the values of model parameters that maximize the sum of the log likelihoods.</p> </blockquote> <p> </p

Appendix B. A discussion regarding what likelihood to use.

A discussion regarding what likelihood to use

Appendix C. A discussion on how to use likelihood and information theoretics to evaluate support in data for competing models.

A discussion on how to use likelihood and information theoretics to evaluate support in data for competing models

Appendix D. A further discussion on the concept of likelihood.

A further discussion on the concept of likelihood

Appendix A. An example calculation of likelihood.

An example calculation of likelihood

Appendix A. Details of field sampling methods and the stage-structured model used in analyses.

Details of field sampling methods and the stage-structured model used in analyses

Birth phenology of feral horse (<i>Equus caballus</i>) untreated (○) and post-treated (• = first post-treatment birth, ▴ = birth subsequent to •) females.

<p>Births are shown as a function of temperature at approximate conception date for populations at Little Book Cliffs Wild Horse Range, CO (A), 2005–2011, and Pryor Mountain Wild Horse Range, MT (B), 2005–2011, and McCullough Peaks Herd Management Area, WY (C), 2007–2011. Post-treated females were previously inoculated with the immunocontraceptive porcine zona pellucida (PZP). Mean Normalized Difference Vegetation Index (green) represents temporal availability of forage. Mean daily surface temperature is shown in red.</p

The physiological pathway from photoperiod to reproductive cyclicity in the horse (<i>Equus caballus</i>).

<p>Increasing sunlight toward the long days of summer strikes the retina, which transmits a neural signal to the suprachiasmatic nuclei (A), across the hypothalamus, and ultimately synapses to the pineal gland to stimulate release of inhibitory neurotranmitters toward the pinealocytes (B). Melatonin production then diminishes, thus increasing release of gonadotropin releasing hormone (GnRH), which increases luteinizing hormone (LH) and follicle stimulating hormone (FSH), and ultimately induces reproductive cyclicity.</p

Appendix A. A table of regression parameters for equations used in calculating browsing intensity in Yellowstone National Park, USA.

A table of regression parameters for equations used in calculating browsing intensity in Yellowstone National Park, USA

Time between final contraceptive inoculation and first parturition from feral horse (<i>Equus caballus</i>) females.

<p>Births shown are from horses at Little Books Cliffs Wild Horse Range, CO, USA and Pryor Mountain Wild Horse Range, MT, USA as a function of consecutive annual porcine zona pellucida (PZP) inoculations, 2005–2011.</p