The landscape of retail has seen a seismic shift with the advent and subsequent proliferation of e-commerce. This transformational change has been more pronounced in certain sectors, one of which is the cosmetics industry. The digitalization of cosmetics retail presents a new arena of possibilities, challenges, and forecasts. The forecast for the future, as any economist would tell you, is a blend of data-driven insights and informed speculations. The following article seeks to illuminate the future trajectories of online makeup stores by exploring their underpinning dynamics, emerging trends, and potential game-changers.

E-commerce in the makeup industry isn’t merely an online extension of brick-and-mortar stores; it is an expansive and dynamic ecosystem with unique spheres of interaction. The underlying theory of "Long Tail Economics" by Chris Anderson comes into play here. The theory postulates that businesses, by serving a large number of niche markets online, can achieve as much profit as by catering to a mainstream market. Online makeup stores offer a vast array of brands and products that physical stores often cannot provide due to limited shelf space, thereby capturing a wider consumer base with diverse needs and preferences.

The field of Predictive Analytics is playing an increasingly significant role in the future of online makeup stores. This sophisticated branch of data analytics employs statistical algorithms and machine learning techniques to predict future outcomes based on historical data. In the context of online cosmetics retail, predictive analytics can be used to forecast buying patterns, predict trends in consumer behavior, and tailor personalized marketing strategies, thus enhancing consumer engagement and retention.

Furthermore, the integration of Augmented Reality (AR) in online makeup stores has revolutionized the shopping experience. AR, a technology that superimposes a computer-generated image on a user's view of the real world, provides an interactive experience of an enhanced reality. Online makeup stores are leveraging AR to allow consumers to virtually 'try on' makeup, which was once a significant limitation of online cosmetics shopping. The application of AR has seen a positive correlation with increased sales, a trend expected to continue and evolve. For example, companies like Sephora and Ulta have already embraced this technology, offering virtual try-ons and tutorials.

The concept of Omnichannel Retailing, which utilizes multiple channels to provide an integrated shopping experience, is another key trend shaping the future of online cosmetics retail. This strategy amalgamates the advantages of online and offline channels, offering a seamless and flexible shopping experience to consumers. For instance, consumers might explore products online and subsequently purchase them in-store, or vice versa. This approach essentially blurs the lines between different retail channels, fostering a holistic retail ecosystem.

Evidently, the consumer is at the epicenter of these emergent trends and innovations, a reflection of the shift from product-centric to customer-centric strategies in recent years. The extensive application of data analytics corresponds with the concept of "Consumer Sovereignty" in economics, which underscores the power of consumers in driving market trends.

However, these technological advancements and strategies come with their own sets of challenges and tradeoffs. For instance, data privacy concerns are a significant drawback of the increased reliance on data analytics, necessitating stringent data protection regulations and consumer consent. Similarly, while AR enhances the virtual shopping experience, it cannot entirely replicate the tactile experience of in-store shopping.

To conclude, the future landscape of online makeup stores is set to be shaped by a blend of technological innovations, strategic shifts, and consumer-oriented approaches. However, as with any prediction, these trends are subject to change influenced by various variables such as technological advancements, regulatory changes, and shifts in consumer behavior. What remains constant is the continual evolution of online cosmetics retail, a testament to the transformative power of digitalization.