Predicting the Risk of Extinction of Species: Impact of Negative Growth Rate and Allee Effect

  • Bapi Saha
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 335)


Predicting the risk of extinction of species is an important aspect in conservation biology. Mathematical models describing the density dependent per capita growth rates play a predominating role in quantifying the risk of extinction. We used population time series data from global population dynamics database (GPDD) to predict the threat status of the species using three commonly used growth models, allowing demographic disturbances. The best fitted model from a set of candidate models is used to evaluate the extinction measures. We observed that there are instances where the intrinsic growth rate is negative, which has not been reported earlier. We show that, in such cases, the extinction probability is high, but the species may adopt some strategy that saves them from extinction. The mathematical implications are described in light of ecological concepts.


Intrinsic growth rate Allee effect Extinction probability Global population dynamics database Per capita growth rate 



Author is thankful to Amiya Ranjan Bhowmick for valuable discussions and editing help in the final version of the manuscript. The author is also thankful to Prof. Joydev Chattopadhay and Dr. Sabyasachi Bhattacharya, Indian Statistical Institute, Kolkata for giving valuable insights of the ecological and mathematical context of the problem.


  1. 1.
    Saha, B., Bhowmick, A.R., Chattopadhyay, J., Bhattacharya, S.: On the evidence of an Allee effect in herring populations and consequences for population survival: a model-based study. Ecol. Model. 250, 72–80 (2013)CrossRefGoogle Scholar
  2. 2.
    Saha, B., Bhowmick, A.R.: Predicting the extinction vulnerability of species: stochastic approach to deterministic population dynamic models. Bull. Cal. Math. Soc. 105(3), 191–210 (2013)MathSciNetGoogle Scholar
  3. 3.
    Sibly, R.M., Barker, D., Denham, M.C., Hone, J., Pagel, M.: On the regulation of populations of mammals, birds, fish, and insects. Science 309, 607–610 (2005)CrossRefGoogle Scholar
  4. 4.
    Ross, J.V.: Comment on “on the regulation of populations of mammals, birds, fish and insects” II. Science 311, 1100b (2006)CrossRefGoogle Scholar
  5. 5.
    Allee, W.C., Emerson, A., Park, O., Park, T., Schmidt, K.: Principles of Animal Ecology. W.B. Saunders Co., Philadelphia (1949)Google Scholar
  6. 6.
    Dennis, B.: Allee effects: population growth, critical density, and the chance of extinction. Nat. Resour. Model. 3, 481–538 (1989)MATHMathSciNetGoogle Scholar
  7. 7.
    Fowler, C.W., Baker, J.D.: A review of animal populations dynamics at extremely reduced population levels. Ann. Rep. Int. Whaling Comm. 41, 545–554 (1991)Google Scholar
  8. 8.
    Courchamp, F., Berce, L., Gascoigne, J.: Allee Effects in Ecology and Conservation. Oxford University Press, Oxford (2008)CrossRefGoogle Scholar
  9. 9.
    Hilborn, R., Walters, C.: Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. Chapman and Hall, New York (1992)CrossRefGoogle Scholar
  10. 10.
    Lande, R.: Demographic stochasticity and Allee effect on a scale with isotropic noise. Oikos 85, 353–358 (1998)CrossRefGoogle Scholar
  11. 11.
    Dennis, B.: Allee effects in stochastic populations. Oikos 96, 389–401 (2002)CrossRefGoogle Scholar
  12. 12.
    Courchamp, F., Clutton-Brock, T.H., Grenfell, B.T.: Inverse density dependence and the Allee effect. Trends Ecol. Evol. 14, 405–410 (1999)CrossRefGoogle Scholar
  13. 13.
    Engen, S., Bakke, O., Islam, A.: Demographic and environmental stochasticity—concepts and definitions. Biometrics 54, 39–45 (1998)CrossRefGoogle Scholar
  14. 14.
    Drake, J.M., Lodge, D.M.: Allee effects, propagule pressure and the probability of establishment: risk analysis for biological invasions. Biol. Invasions 8(2), 365–375 (2006)CrossRefGoogle Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Government College of Engineering and Textile TechnologyBerhamporeIndia

Personalised recommendations