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Open Access Open Badges Research article

Establishment probability in newly founded populations

Markus Gusset1*, Michael S Müller2 and Volker Grimm2

Author affiliations

1 Wildlife Conservation Research Unit, Department of Zoology, University of Oxford, Abingdon, OX13 5QL, UK

2 Department of Ecological Modelling, UFZ, Helmholtz Centre for Environmental Research – UFZ, 04318, Leipzig, Germany

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Citation and License

BMC Research Notes 2012, 5:313  doi:10.1186/1756-0500-5-313

Published: 20 June 2012



Establishment success in newly founded populations relies on reaching the established phase, which is defined by characteristic fluctuations of the population’s state variables. Stochastic population models can be used to quantify the establishment probability of newly founded populations; however, so far no simple but robust method for doing so existed. To determine a critical initial number of individuals that need to be released to reach the established phase, we used a novel application of the “Wissel plot”, where –ln(1 – P0(t)) is plotted against time t. This plot is based on the equation <a onClick="popup('','MathML',630,470);return false;" target="_blank" href="">View MathML</a>, which relates the probability of extinction by time t, P0(t), to two constants: c1 describes the probability of a newly founded population to reach the established phase, whereas ω1 describes the population’s probability of extinction per short time interval once established.


For illustration, we applied the method to a previously developed stochastic population model of the endangered African wild dog (Lycaon pictus). A newly founded population reaches the established phase if the intercept of the (extrapolated) linear parts of the “Wissel plot” with the y-axis, which is –ln(c1), is negative. For wild dogs in our model, this is the case if a critical initial number of four packs, consisting of eight individuals each, are released.


The method we present to quantify the establishment probability of newly founded populations is generic and inferences thus are transferable to other systems across the field of conservation biology. In contrast to other methods, our approach disaggregates the components of a population’s viability by distinguishing establishment from persistence.

Allee effect; Establishment probability; Extinction risk; Lycaon pictus; Population viability; Reintroduction effort; Wissel plot