Mathematical/statistical models for forecasting population distributions of age, sex, weight, and height I come from a mathematical background but I have no experience with the topic of mathematical biology. Are there well established mathematical/statistical models for forecasting the evolution of population distributions of biometric parameter such as age, sex, weight, and height? For instance, I have often heard that the proportion of elderly people in the population is projected to increase. What models are being used to generate forecasts such as these?

The term you are looking for is demography \- there are literally thousands of papers published on this topic.

Each of your topics mentioned has its own models and prevailing theories, so without an exact question it is very hard to answer as to which model you might find best.

Having said that there are well established models of things like geometric growth of populations (proposed by Thomas Malthus in 1798). The United Nations does a lot of modeling of populations and the like. You might be interested in their freely available publications and information here.