$$ extbf{Explanation:}$$ $$ullet$$ Primary productivity depends on the plant species inhabiting a particular area and also on a variety of environmental factors, availability of nutrients and photosynthetic capacity of the plants.  $$ullet$$ A young forest has not yet reached the climax and has low density of trees which accounts for its low primary productivity. $$ullet$$ A natural old forest is supposed to have reached its climax as it comprises of big trees with thick foliage which is responsible for its high primary productivity.  $$ullet$$ A shallow polluted lake is devoid of producers as a consequence of pollution and accounts to a very low primary productivity.  $$ullet$$ An alpine meadow is full of grasses with little or no tree which confers a low primary productivity.  $$ullet$$ Thus, it can be concluded from the above discussion that a natural old forest ecosystem will be more productive in terms of primary productivity in comparison the above mentioned different ecosystems.