The question of how growth, dispersal, and environmental factors affect the persistence and spread of an invasive species is of great importance in spatial ecology. Motivated by the fact that in a species, different development stages may have different vital rates and dispersal characteristics, we propose and study a reaction-diffusion juvenile-adult model, which is a natural extension of the classical Fisher’s equation. We investigate the spread rates of the population if persistent. By comparing our juvenile-adult model with the physically unstructured Fisher model, we find that Fisher equation can be approximated by our juvenile-adult model in several ways. Accordingly, the spreading speed for Fisher’s model represents a special case of that for the juvenile-adult model. We analyze how the vital rates and different dispersal abilities between juveniles and adults influence the spreading spread of the structured population, the results indicate that the juvenile-adult model provides more insights into population spread than Fisher equation. We then study a reaction-diffusion juvenile-adult model with temporally periodic coefficients. We develop a novel numerical method to calculate the spreading speed under temporal variability. Finally, we utilize the time-periodic model to understand the spatial spread of a population with separate breeding and non-breeding seasons. In particular, we scrutinize how the seasonal variation in vital rates and dispersal rates, and the duration of the breeding season affect the spreading speed of the population. The theory developed here can provide effective strategies to control the spread of invasive species.

生长，扩散和环境因素如何影响入侵物种的持久性和扩散问题在空间生态学中非常重要。基于一个事实，即在一个物种中，不同的发育阶段可能具有不同的生命率和扩散特性，我们提出并研究了反应扩散青少年模型，这是经典费舍尔方程的自然扩展。如果持续存在，我们将调查人口的扩散率。通过将我们的青少年模型与非结构化的Fisher模型进行比较，我们发现Fisher方程可以通过几种方式近似于我们的青少年模型。因此，费舍尔模型的扩展速度代表了少年-成人模型的扩展速度。我们分析了生命率和青少年与成年人之间的不同分散能力如何影响结构化人口的扩散，结果表明，与费舍尔方程相比，青少年-成人模型提供了更多的人口扩散见解。然后，我们研究具有时间周期系数的反应扩散青少年模型。我们开发了一种新颖的数值方法来计算时间变化下的传播速度。最后，我们利用时间周期模型来了解具有不同繁殖季节和非繁殖季节的种群的空间分布。特别是，我们研究了生命率和传播率的季节性变化以及繁殖季节的持续时间如何影响种群的传播速度。