Phytoplankton is the staple upon which the entire marine food chain is built. Phytoplankton is the main source of food for zooplankton, which in turn is the staple for many small fish and other sea creatures, which are then eaten by the bigger fish and large mammals such as seals and whales. A decline of phytoplankton harms the entire food chain, and is contributing mightily to the decline of all life in the ocean.
The role of phytoplankton goes well beyond the marine environment. Like terrestrial vegetation, phytoplankton photosynthesizes and in doing so consumes carbon dioxide and produces about half of the world’s oxygen supply – equalling that of trees and plants on land.
The phytoplankton of the seas provide an enormous carbon sink, one essential for absorbing the huge volumes of carbon we have and increasingly release through fossil fuel consumption. As such Phytoplankton plays an enormous role in the world’s carbon cycle and therefore the stability of the global climate. 
Researchers at two UK universities have found that rising temperatures in the world’s oceans will affect the development of the plankton. 
The loss of phytoplankton … seems to be part of a very troublesome feedback loop. Rising ocean temperatures are driving a decline the Earth’s natural ability to absorb carbon dioxide, which is in turn leading to a greater abundance of greenhouse gasses, which leads to warmer oceans. 
The increasing warmth caused by a changing climate will upset the natural cycles of carbon dioxide, nitrogen and phosphorous. This will affect the plankton, making it scarcer but temperature (also) plays a critical role in driving the cycling of chemicals in marine micro-algae. It affects these reactions as much as nutrients and light.
As temperatures warm, marine micro-algae appear not to produce as many ribosomes as they do in cooler water (ribosomes join up the building blocks of proteins in cells and are rich in phosphorous).
If their numbers fall this will produce higher ratios of nitrogen compared with phosphorous. The result, would be lower plankton productivity, with implications for the marine carbon cycle. There will be consequences both for climate change and for marine food webs. 
The effect on the marine food chain is quite obvious as less plankton will be available for higher species, hence the many communities dependent on protein from the sea will be in serious trouble (but the effect on climate) is really difficult to predict. There may not be as much plankton in the oceans to absorb carbon dioxide but warmer seas, with higher nitrogen content, may store more carbon dioxide than they do now.
The corals that form the structure of the great reef ecosystems of tropical seas depend upon a symbiotic relationship with algae-like unicellular flagellate protozoa that are photosynthetic and live within their tissues. Zooxanthellae give coral its coloration, with the specific color depending on the particular clade. 
Sometimes when corals become physically stressed, the polyps expel their algal cells and the colony takes on a stark white appearance. This is commonly described as “coral bleaching” (Barnes, R.S.K. and Hughes, 1999; Lalli and Parsons, 1995). If the polyps go for too long without zooxanthellae, coral bleaching can result in the coral’s death. 
Most evidence indicates that elevated temperature is the cause of mass bleaching events.
The IPCC’s moderate warming scenarios (B1 to A1T, 2 °C by 2100, IPCC, 2007, Table SPM.3, p. 13) forecast that corals on the Great Barrier Reef are very likely to regularly experience summer temperatures high enough to induce bleaching
Since countless sea life depends on the reefs for shelter and protection from predators, the extinction of the reefs would ultimately create a domino effect that would trickle down to the many human societies that depend on those fish for food and livelihood. 
References: 1. https://bloomfieldmichael.wordpress.com/2010/09/28/phytoplankton-vanishing-from-warming-oceans-world%E2%80%99s-oxygen-supply-threatened/ (September 28, 2010)
2. http://www.climatenewsnetwork.net/plankton-will-suffer-as-oceans-warm/ (September 8, 2013)
3. http://en.wikipedia.org/wiki/Coral_bleaching (December, 2003
4. http://oceanservice.noaa.gov/education/kits/corals/coral02_zooxanthellae.html (September 24, 2007
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