If someone adds millions of small fish to a lake , how would the number of big fish change?

Lake is a type of natural ecosystem as it includes both biotic ( living components like plants, algae, micro-organism, and animals) and abiotic (nonliving components like water, light, temperature, oxygen, pH of water) factors.

Food chain is a linear network between organisms, representing energy transfer in the form of organic matter within this ecosystem.

The different living organisms within lake are related through the flow of energy ( in the form of organic matter) in the food chain.

For example-  

Phytoplanktons ( microscopic plants)  are autotrophic organisms that form the base of the food chain as they synthesize their own food through photosynthesis. They occupy the first trophic level and called producers.

Producers are eaten by primary consumers such as zooplankton and small fishes, which are eaten by secondary consumers ( such as large fishes in lake).

If someone adds millions of small fish to a lake, the food source of big fishes would increase tremendously, leading to increase in the number of big fishes initially.

After some time, small fishes (upon consuming primary producers like phytoplanktons) would decline the number of primary producers. This will lead to decrease in food source for small fishes, causing competition between them.

In due course of time, large fishes will decline eventually ( as their food source will become limited).

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