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

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

Abstract

Background

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 – _{0}(_{0}(_{1} describes the probability of a newly founded population to reach the established phase, whereas _{1} describes the population’s probability of extinction per short time interval once established.

Results

For illustration, we applied the method to a previously developed stochastic population model of the endangered African wild dog (_{1}), 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.

Conclusions

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.

Background

Trying to (re)establish populations by releasing individuals into suitable habitat is an important element of modern conservation practice. The success of such release attempts depends largely on two factors, namely the newly founded population reaching the established phase and, once this stage is reached, maintaining itself in the release area (on the importance of this distinction, see

In a previous study

Two important questions arising in any release attempt

Modelling approach

To tackle these questions, we used our previously developed individual-based model for wild dogs

In short, the model was designed to predict the probability of small, reintroduced populations of wild dogs establishing themselves and persisting in the release area under various levels of reintroduction effort (for details, see

Our validation procedure ensured that the model correctly captures internal relationships between variables and to some degree the internal organization of the real system (see

The robustness of the model was evaluated by conventional local sensitivity analysis of all model parameters, where each parameter was varied separately by ±10% of its mean value (rounded to integer if required). The analysis showed a moderate sensitivity _{m} to the relative change in parameter value) (Table

Parameter

Reference value

Sensitivity

+10% of parameter value

–10%of parameter value

_{m} to the relative change in parameter value.

Reproduction in newly formed packs (

0.33

2.07

–0.22

Reproduction in established packs (

0.66

7.62

–4.24

Pack size (

8.1 ± 1.1

0.20

–0.37

Litter size (

7.9 ± 0.8

3.63

–3.16

Primary sex ratio (

0.55 ± 0.06

–0.62

2.11

Ecological capacity (

62

1.76

–0.16

Density dependence threshold (

31*

3.23

–2.82

Dispersal in males (

0.80*

–0.96

1.52

Dispersal in females (

0.90*

–1.08

2.48

Disperser group size threshold (

2*

0.27

–0.14

Pack formation (

0.64

0.50

–0.12

Dominant displacement (

0.20

0.46

–0.12

Mortality in male pups (

0.07 ± 0.06

–0.53

0.96

Mortality in female pups (

0.16 ± 0.14

–0.37

0.34

Mortality in yearling males (

0.29 ± 0.14

–0.53

1.67

Mortality in yearling females (

0.20 ± 0.20

–0.46

0.00

Mortality in young adult males (

0.17 ± 0.08

–1.39

1.83

Mortality in young adult females (

0.01 ± 0.01

–0.90

1.30

Mortality in old adult males (

0.30 ± 0.16

–0.19

2.23

Mortality in old adult females (

0.22 ± 0.16

–0.56

0.80

Dispersal mortality in males (

0.45

–1.67

1.61

Dispersal mortality in females (

0.43

–1.42

1.33

Longevity (

9

1.73

–2.12

Catastrophe occurrence (

0.04

–0.84

1.05

Catastrophe severity (

0.42

–1.89

3.28

Our model thus appears to capture the essential characteristics of a real wild dog population and to be relatively robust to parameter uncertainty (see

Quantifying establishment probability

To determine a critical initial number of packs (consisting of eight individuals each; _{0}) plot”; _{0}(_{1} and _{1}. The former, _{1}, reflects the initial state of a population at time _{1} is equal to one; if a population initially is so small that it does not necessarily reach the established phase but might go extinct beforehand, _{1} is smaller than one _{1}, is independent of the initial state of a population and describes the probability of extinction per short time interval in the established phase, which is constant. The inverse of this risk, _{m} = 1/_{1}, can be defined as the “intrinsic mean time to extinction” _{1} = 1, _{m} is equal to the arithmetic mean time to extinction that can be determined from repeated simulations starting from the same initial population

The two constants _{1} and _{1} can easily be determined by running, say, 1000 simulations, determining _{0}(_{0}(_{1} and _{m} as output is available from the authors upon request.) The slope of the linear parts of all “Wissel plots” shown in Figure _{m}, is about 320 years in this case (Figure _{m} is only about 30 years.)

“Wissel plots” (–ln(1 – _{0}(

**“Wissel plots” (–ln(1 –**_{0}**(****))****time****), each produced from 1000 simulations of a wild dog population model.** For parameters, see Table _{m}, is independent of _{1})

Intrinsic mean time to extinction _{m} of a reintroduced wild dog population (dots) and intercept of the “Wissel plots” with the

**Intrinsic mean time to extinction**_{m}**of a reintroduced wild dog population (dots) and intercept of the “Wissel plots” with the****-axis (squares).** For parameters, see Table _{m} and the

If the initial number of packs is larger than one but still too small, _{1} is smaller than one and thus the intercept of the (extrapolated) linear parts of the “Wissel plot” with the _{1}), is positive (Figure _{m} of 10,000 years corresponds to an extinction risk of 1% in 100 years _{m} obtained in our case results in an extinction risk exceeding 10%.

In wild dogs, new packs typically form when two unrelated opposite sex disperser groups meet and bond

Intrinsic mean time to extinction _{m} of an established wild dog population

**Intrinsic mean time to extinction**_{m}**of an established wild dog population.** For parameters, see Table

The asymptotic nature of our results for establishment (Figure

Sensitivity analysis (Table

Conclusions

Release strategies are often based on intuition and trial-and-error rather than a critical appraisal of the available evidence

Therefore, reintroduction biology and related disciplines (e.g. invasion and restoration ecology as well as the emerging field of assisted colonization) would likely benefit from using structurally realistic models as well as adopting the plot and concepts proposed by _{1}) in Figure

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

All authors contributed to the design of the study, acquisition and interpretation of data, and writing of the manuscript. All authors read and approved the final manuscript.