Interviews with Faculty Researchers

– Interview with Prof. Wang Zhian
Professor, Department of Applied Mathematics

Prof. Wang Zhian’s mathematical research on density-dependent dispersal offers novel insights into the dynamics of species movement, presenting a significant deviation from traditional random diffusion models. His work primarily explores how dispersal is influenced by the density of other species, a phenomenon observed across biological systems.

Conventional random diffusion models, which depict movement as an undirected, scattered process, often has a limitation to account for the interactions and directional flows commonly seen in nature. In contrast, density-dependent dispersal introduces a more complex layer, incorporating both random movement and convective, or directed motion. Prof. Wang emphasizes that convective movement involves organisms responding to external signals or environmental factors, which drives them toward or away from particular regions. This is especially relevant in scenarios where species move in response to specific attractants or repellents, contributing to aggregation or segregation patterns.

One of his key innovations is the study of cross-diffusion structures, where the movement of one species is influenced by the density of another. This concept plays a critical role in understanding the interactions between species, such as predator-prey dynamics or microbial competition. Cross-diffusion results in more organized and sometimes extreme outcomes, such as the clustering of populations or their segregation into distinct ecological niches. In natural settings, examples like animals flocking towards food sources or repelling due to threats are instances of these density-driven dispersal mechanisms.

Importantly, Prof. Wang’s work transcends traditional statistical research and empirical data collection. By constructing and analysing reaction-diffusion models with density-dependent dispersal, he identifies key factors that drive distinct outcomes, emphasizing the global dynamics of these systems. This analytical approach enhances our understanding of how species interactions shape movement patterns over time. In addition, to make his findings more accessible to the general public, Prof. Wang employs graphical representations and numerical simulations to effectively demonstrate how his mathematical results align with observable phenomena from experiments.

His research has practical implications in fields such as ecology, microbiology and epidemic modelling, shedding light on how population waves propagate through environments and influence species interactions. While the mathematical framework for analysing density-dependent processes is still evolving, it provides essential tools for a deeper understanding of our biological world.

密度依賴性擴散研究：分析與應用

– 王治安教授專訪
應用數學系教授

與傳統隨機擴散模型不同，王治安教授通過對密度依賴擴散的數學模型的研究，為物種運動的動態模式提供了新的見解。他的研究主要探討物種的分佈以及生存滅絕如何受到其他物種密度的影響，而這種現象在生態系統裡一直存在。

傳統的隨機擴散模型認為物種的移動並無方向性，因此難以解釋自然界中常見的相互作用和具方向性的流動。相比之下，密度依賴擴散的理論考慮了更複雜的因素，包含隨機移動和對流或定向運動。當中，對流運動涉及物種對外間信號或環境因素作出反應，令它們傾向往特定方向移動或反向移動。這種吸引及排斥反應導致物種出現聚集或分離情況。在自然環境中，動物湧向食物源或因威脅而排斥等例子都是密度驅動擴散的例子。

交叉擴散結構研究論述了物種的移動受到另一個物種密度的影響。這概念對理解物種之間的相互作用，如捕食者與獵物的動態或微生物間的競爭，具有重要意義。他認為，吸引及排斥效應有時會導致更加有序甚或極端的結果，例如族群聚集或被隔離到不同的生態位，這樣可能導致物種滅絕危機。

王教授的研究與傳統統計學研究和收集實證數據有所不同。透過建立和分析具有密度依賴性擴散模型，他希望能找出驅動不同生態模式和結果的主要因素，並理解這些模式背後的共同規律。這種分析方法讓我們對物種間的相互作用，以及物種如何隨時間而產生不同分佈現象有更深入的理解。為讓公眾更容易理解他的理論，王教授採用了圖形和數值模擬來展示其理論如何解釋所觀察的現象。

他的研究在生態學、微生物學和流行病模型等領域具有實質貢獻，解釋了物種如何因應環境而移動並揭示了物種如何互相影響。雖然這些理論仍在改良，但已讓我們對一些生態現象有了更深入的理解。