Ecosystem fragmentation is one of the main threats to species persistence via habitat reduction and isolation which often lead to species extinctions. A question that has long been of interest is the minimum habitat size that can sustain viable populations in fragmented landscape. Despite numerous empirical and theoretical efforts on this topic, most studies fail to address this central question, and our mechanistic understanding of and capacity to predict the effects and outcomes associated with fragmentation stressor is still illusive. We develop an ordinary differential equation (ODE) based framework that incorporates the effect of the patch area on the net population growth rate for a plant species in fragmented ecosystem via a general net growth function. We investigate the minimum patch area needed to sustain a given plant species. We use data from the Amazonian herb Heliconia acuminata to test our model. Furthermore, we compare the performance ODE model and a linear matrix model to predict the observed data. We provide a general formula for a threshold value for the fragment area, below which a plant population is not viable. For Heliconia acuminata, our ODE-based model predicts a value for the minimum fragment area of $\approx 0.7ha$, which reflects the observed data and is smaller than the value obtained using the matrix projection model. Our findings suggest that the Heliconia’s mortality rate responds more negatively to fragmentation. Furthermore, we found that the ODE-based model can serve as an alternative to the linear demographic model.

生态系统破碎化是通过栖息地减少和隔离对物种持久性的主要威胁之一，这通常会导致物种灭绝。长期以来，人们一直感兴趣的一个问题是能够在支离破碎的景观中维持可行种群的最小栖息地大小。尽管在这个主题上进行了大量的实证和理论努力，但大多数研究未能解决这个核心问题，我们对与碎片压力源相关的影响和结果的机械理解和预测能力仍然是虚幻的。我们开发了一个基于常微分方程 (ODE) 的框架，该框架通过一般净增长函数结合了斑块面积对破碎生态系统中植物物种净种群增长率的影响。我们调查维持给定植物物种所需的最小斑块面积。Heliconia acuminata来测试我们的模型。此外，我们比较了性能 ODE 模型和线性矩阵模型来预测观察到的数据。我们为碎片面积的阈值提供了一个通用公式，低于该阈值植物种群是不可行的。对于Heliconia acuminata，我们基于 ODE 的模型预测了最小碎片面积的值$\approx 0.7H\mathrm{一种}$，它反映了观察到的数据，小于使用矩阵投影模型获得的值。我们的研究结果表明，Heliconia 的死亡率对碎片的反应更为消极。此外，我们发现基于 ODE 的模型可以作为线性人口统计模型的替代方案。