The gut microbiota represent a highly complex ecosystem comprised of approximately 1000 species that forms a mutualistic relationship with the human host. A critical attribute of the microbiota is high species diversity, which provides system robustness through overlapping and redundant metabolic capabilities. The gradual loss of bacterial diversity has been associated with a broad array of gut pathologies and diseases including malnutrition, obesity, diabetes and inflammatory bowel disease. We formulated an in silico community model of the gut microbiota by combining genome-scale metabolic reconstructions of 28 representative species to explore the relationship between species diversity and community growth. While the individual species offered a broad range of metabolic capabilities, communities optimized for maximal growth on simulated Western and high-fiber diets had low diversities and imbalances in short-chain fatty acid (SCFA) synthesis characterized by acetate overproduction. Community flux variability analysis performed with the 28-species model and a reduced 20-species model suggested that enhanced species diversity and more balanced SCFA production were achievable at suboptimal growth rates. We developed a simple method for constraining species abundances to sample the growth-diversity tradeoff and used the 20-species model to show that tradeoff curves for Western and high-fiber diets resembled Pareto-optimal surfaces. Compared to maximal growth solutions, suboptimal growth solutions were characterized by higher species diversity, more balanced SCFA synthesis and lower exchange rates of crossfed metabolites between more species. We hypothesized that modulation of crossfeeding relationships through host-microbiota interactions could be an important means for maintaining species diversity and suggest that community metabolic modeling approaches that allow multiobjective optimization of growth and diversity are needed for more realistic simulation of complex communities.