You should have a look on Raup, D. M. (1981): Extintion: bad genes or bad luck? Acta geológica hispánica 16(1): 25-33. He stated, that the typical time a species survives is about 10 million years.

Please see Ignoring Nature No More http://press.uchicago.edu/ucp/books/book/chicago/I/bo14398472.html

Morris and Doak 2002 "Quantitative Conservation Biology" is a good intro to pop. viability analysis, goes through non-demographic and deterministic models through demographic and environmental stochastic PVA's, and comes with Matlab scripts you can get started with.

http://www.sinauer.com/quantitative-conservation-biology-theory-and-practice-of-population-viability-analysis.html

I suggest VORTEX software

http://vortex10.org/Vortex10.aspx

http://www.cbsg.org/download-vortex 

Scott Mills has a good book entitled Conservation of Wildlife Populations: Demography, Genetics, and Management, 2nd Edition.  This gives a nice easy to read overview of population modeling. 'Although targeting primarily undergraduates and beginning graduate students with some basic training in basic ecology and statistics (in majors that could include wildlife biology, conservation biology, ecology, environmental studies, and biology), the book will also be useful for practitioners in the field who want to find - in one place and with plenty of applied examples - the latest advances in the genetic and demographic aspects of population ecology.'  Hope this is helpful.  All the best with your research.

I second Aaron's above suggestion for Scott Mills book. It sounds like you're interested in a population viability analysis (PVA). Mill's book covers PVA and references Caswell's Matrix population models: construction, analysis, and interpretation book, which would also be helpful to you. To implement these types of matrix models (easily done in R packages like "popbio") you'll need to have (or be able to estimate) parameters like age-specific survival, age-specific reproductive contribution, and an estimate of population size for each age class. Best of luck.

Hi Alain,

I think that it could also be good to have a look to a demographical textbook such as Williams, Nichols & Conroy (2002) Analysis and Management of Animal Population. 

It provides a lot of basic concept in population analysis that you may need before going further in PVA. 

More recently, there is also another book by Conroy about decision making: Conroy & Peterson 2013 Decision Making in Natural Resource Management: A Structured, Adaptive Approach 

Good luck for your research !

http://onlinelibrary.wiley.com/book/10.1002/9781118506196

https://www.elsevier.com/books/analysis-and-management-of-animal-populations/williams/978-0-12-754406-9

I recommend you "A Practical Handbook for Population Viability Analysis", by Morris et al (1999). Probably you can find it in the web

Dear Alain,

Aside Vortex, I would suggest you this book:

http://www.ramas.com/apppopn.htm

Most of exercises are made using the software RAMAS EcoLab

Best

The Gibbon, 2009

"Species Conservation and Management: Case Studies" ed. by Akcakaya et al. 2004.  Though this book is geared toward the use of the RAMAS suite of modeling programs, it provides a good overview of the work other groups have done with it and may help you to define your question based on what others have done with different types of datasets and species systems.

Case "An illustrated guide to theoretical ecology" 

You could begin with the Vortex Manual for the basic steps of PVA http://vortex10.org/Vortex10.aspx