The WWF thinks so.. Saying that we are running out of resources is nothing new. It comes up fairly often. The Club of Rome long ago predicted this would happen.. There are really three issues here.
1. The Environment
2. Natural Resources
3. Species going extinct.
1. Pollution that causes damage to other human beings can be controlled by taxing the polluting activites. This reduces those activities and therefore the pollution. So the right taxes can control this (my students might recall the class discussion of negative externalities)
2. Natural Resources. The Club of Rome predicted we would run out some time ago. This has not happened. The reason is that as the price of resources go up due to increased demand, it creates incentives for alternative sources. People also switch to things like more fuel efficient cars. It takes alot less energy to produce $1 of GDP in the USA than it did in 1980. Higher resource prices cause people to act more efficiently. Even if supply decreased, then the price would rise which would encourage conservation. So we don't need to worry about running out of resources.
3. Should humans cut back on the production of some goods and services if that is the only way to keep some life forms from going extinct? This might be necessary if humans are destroying the habitats of some animals or our pollution is killing them.As an economist, I don't think I can offer any insights. I think that is a moral question and I don't think my opinion on this would be very insightful.
Richard Posner and Nobel Prize winning economist Gary Becker have some interestng views on whether or not we should worry about over population.