Question: A computational ecologist defines $ R(t) = t^2 + rac{t}{2} $ to represent species diversity in a volatile habitat. If $ d_1 = 1 $ and $ d_{n+1} = R(d_n) $, find $ d_2 $.

["Understanding Species Diversity with Computational Ecology: Solving for $ d_2 $ in a Dynamic Habitat Model", "In the study of ecological systems, especially within highly volatile environments, modeling species diversity dynamically is crucial. Computational ecologists often use functional equations to capture how biodiversity changes over time under fluctuating conditions. A recent example illustrates this approach using a simple yet insightful recursive function:", "Define $ R(t) = t^2 + \dfrac{t}{2} $ to represent species diversity in a volatile habitat. Given an initial measure of biodiversity $ d_1 = 1 $, if the diversity evolves according to $ d_{n+1} = R(d_n) $, this article explains how to compute $ d_2 $.", "---", "### What is $ d_2 $?", "Since $ d_1 = 1 $, the next diversity measure $ d_2 $ is found by applying the function $ R(t) $ to $ d_1 $:\n[\nd_2 = R(d_1) = R(1)\n]", "We substitute $ t = 1 $ into the expression for $ R(t) $:\n[\nR(1) = (1)^2 + \dfrac{1}{2} = 1 + 0.5 = 1.5\n]", "Thus,\n[\nd_2 = 1.5\n]", "---", "### Why This Model Matters", "This recursive computation reflects real-world ecological dynamics where species diversity responds nonlinearly to environmental volatility. By defining diversity as $ R(t) = t^2 + \frac{t}{2} $, ecologists capture both the stabilizing effect of moderate growth and increasing complexity with resource availability. However, the quadratic term ensures sensitivity to initial fluctuations—key in volatile habitats.", "Using such computational models allows ecologists to simulate biodiversity trajectories, predict tipping points, and inform conservation strategies in changing ecosystems.", "---", "### Final Answer", "[\n\boxed{d_2 = 1.5}\n]", "This simple yet powerful calculation exemplifies how computational tools enable precise, data-driven insights into ecological resilience and adaptation."]