Population explosion in 'developing' countries may not contribute to global warming/climate change as much as 'developed' countries, but they are and will be putting serious pressure on the existence of rainforests, critical biodiversity habitats and other sensitive ecosystems, simply due to the need for food and space. Endemic species are being wiped out by habitat loss and land use change to feed more and more number of people, due to the dual pressures of population growth and economic movement. The idea that the western concept of 'development' is a good model for the rest of the world is highly debatable.
The sort of birth rates we are seeing in certain regions spells is simply not sustainable for the future of earth as we know it. I do not buy into the idea that somehow humans are entitled to wipe out forests and entire species for their 'development'. The rate of population growth will lead to the 'development' of areas so far untouched by humans (As quickly diminishing as they are..) and further pressures on natural resources and deleterious impacts on forests and biodiversity levels.
Even talking about emissions, the LULUCF sector is the 2nd largest contributor to net carbon levels on earth, pretty much exclusively driven by the demand for more space , food and money for humans. The rampant deforestation happening in Indonesia is due to the exponential growth of industries like Palm Oil, Timber, Rubber, coal and minerals, for meeting demand from rapidly developing countries like India, Brazil and China as well as 'developed' regions like North America and Europe. It is easy to predict the consequences of population growth as more of everything will be needed to accommodate rising consumption.
It is not about 'blaming the poor' as someone mentioned, it is about anticipating the future consequences of unsustainable population growth rates in certain parts of the world and addressing it through workable interventions.
High levels of consumption from 'developed countries' is a massive problem as well and needs to be addressed as a priority. If you look at per capita consumption, Europe and North America are much higher than any developing country and the adverse environmental impact this has had on areas producing the necessary commodities are well documented. Which is why the economically 'developed' countries need to invest heavily in sustainable development of high population risk regions, including education for sensible family planning and building frameworks for incentivizing people to have fewer children with better prospects for the future. At the same time, these countries should take concrete steps extremely high consumption rates of commodities with a high environmental footprint like beef and palm oil internally and promote a shift to more sustainable alternatives.
Unfortunately reducing the demand for fossil fuels, livestock and agricultural commodities significantly in Europe and North America will help the present and near future, but the impacts of 50 billion people on the earth in a thousand years is scary thing to contemplate.
Here is a heartwarming stat for you, at current growth rates, Africa will have a population of 355 billion people by 2200.. yay!