Pre-trained Vision Transformer (ViT) models have achieved impressive performance across various computer vision tasks. However, most existing pre-trained models are built on fixed datasets and lack the flexibility to incorporate new pre-training data. When additional data becomes available, previous models must typically be retrained on both old and new data, which is costly and impractical, especially in privacy-sensitive or resource-constrained environments. Moreover, direct fine-tuning on downstream tasks does not provide mechanisms to adapt to the specific data distributions of those tasks, and it only supports fixed model sizes. To address these challenges, we propose \textbf{Adaptive-Learngene}, a novel framework in which the ancestry model is trained solely on newly available data, and a new component, termed a learngene, is extracted and added to a global learngene pool that expands incrementally. This design enables a dynamically evolving pool of learngenes without requiring access to previous data. For each new downstream task, the Task-Adaptive Learngene Selector (TALS) retrieves a sparse combination of learngenes that best match to the data distribution of the target task. TALS requires only a small amount of downstream data for this selection, enabling descendant models of different sizes to be efficiently initialized and tailored to specific data distributions and resource constraints. Extensive experiments on diverse downstream tasks demonstrate that our method matches or outperforms existing approaches while offering superior scalability, adaptability, and efficiency in dynamic learning environments.