In ecology, a nonconstant functional relationship between per capita growth rate and population size is referred as density dependence and mathematical models are utilized to detect its presence in natural populations. The theta-logistic model (parameterized by r_m: intrinsic growth rate; θ: shape parameter; and K: carrying capacity) has been extensively discussed through various generalizations in the literature due to its flexibility and sound ecological interpretations which can be generalized for many natural populations. In this article, we show that nonlinear least squares approach is not an appropriate choice for estimating the model using real data. Using simulation, we show that the unknown parameters are better estimated under a Bayesian framework. We utilize the Gibbs algorithm for simulating samples from the posterior density, which is approximated by grid approximation and Bayesian credible intervals are obtained. Reliability of the estimation process is shown by using simulated data sets. Rules for choosing the prior distributions are discussed. We also apply the proposed strategy to estimate parameters using real data sets from the global population dynamics database. The robustness of the method with respect to prior distribution of the parameters is investigated by taking different choice of priors. We also establish its effectiveness in estimating parameters in a predator-prey system. The discussed method is computationally intensive, but its simple implementation will be useful for fitting complex models to study growth patterns of natural populations.

在生态学中，人均增长率与种群数量之间的非恒定函数关系称为密度依赖性，并且利用数学模型来检测其在自然种群中的存在。Theta-logistic模型（参数由r _m表示：内在增长率；θ表示：形状参数；以及K：承载能力）由于其灵活性和合理的生态学解释而可以广泛应用于许多自然种群，因此在文献中已通过各种概括性地进行了广泛讨论。在这篇文章中，我们表明，非线性最小二乘法并不是估计使用真实数据模型中的一个合适的选择。通过仿真，我们表明在贝叶斯框架下可以更好地估计未知参数。我们利用吉布斯算法从后验密度模拟样本，该算法通过网格逼近近似并获得贝叶斯可信区间。通过使用模拟数据集可以显示估计过程的可靠性。讨论了选择先验分布的规则。我们还将应用建议的策略，使用来自全球人口动态数据库的真实数据集来估计参数。通过采用不同的先验选择，研究了该方法相对于先验参数的鲁棒性。我们还建立了其在估计捕食者－猎物系统中的参数方面的有效性。所讨论的方法计算量大，但是其简单的实现将对拟合复杂模型以研究自然种群的增长模式很有用。