Baleen whales are a prominent group of sea mammals composed of 14 species, ranging from the blue whale (Balaenoptera musculus, 117 metric tons), to the pygmy right whale (Caperea marginata, 3-3.5 metric tons), Because they lack teeth, these whales filter-feed through fine, comb-like structures called baleen. During filter-feeding, a whale engulfs large volumes of sea water, closes its mouth, creates internal pressure by raising its tongue toward the top of the palate, pushes the water out through the slots in the baleen, traps small aquatic animals (especially krill) against the baleen, and swallows the animals.
Krill are shrimp-like marine invertebrates, animals lacking a backbone. Like the baleen whales that eat them, krill are filter feeders that comb through seawater for plankton, microscopic algae (phytoplankton) or animals (zooplankton) suspended in the water column.
Together, these organisms form a relatively simple food web.  Phytoplankton support zooplankton. Plankton support krill. Krill support many marine organisms, including baleen whales. Baleen whales are part of the diet for the Inuit, the indigenous people of the Arctic.
Oceans are generally nutrient poor. When marine organisms eliminate wastes or die, the nutrients in the wastes or remains eventually sink and collect in deep waters. Ocean currents at high latitudes bring deep waters and their nutrients to the surface. These upwellings promote algal blooms, noticeable increases in algal populations that support large swarms of krill. Baleen whales spend extended periods in the high-latitude oceans feeding on these swarms.
Global warming is decreasing the extent of sea ice near continents. Phytoplankton living on or near sea ice are a critical food source for krill. Sea ice also shields krill from predators. Accordingly, annual mean density of krill varies with the duration of sea ice during the preceding winter. This dependency is complex, however, because fluctuations in krill density derive from both changes in overall abundance and movements to other locations.  Moreover, exceptions to the correlation between krill density and sea ice duration occur from time to time and from region to region. 
Northern krill (Meganyctiphanes norvegica), a major food source for baleen whales, penguins, and seals. Narrow slots on the front legs filter plankton from the surrounding seawater. This example is about 3 cm in length.
Changes in the density of krill, given its key position in the food chain, should reverberate throughout the polar ecosystem, including baleen whales. , ,  Nonetheless, determining the relationships among declining sea ice, krill, and whales has proved elusive, given the impact of human activities such as hunting.
Commercial whaling in the 1800s decimated baleen whale populations. Finally, in 1946, an international agreement was forged to save the whales. Each country was allotted a maximum number of catches for different whale species. Some species (such as the southern right whales) have begun to recover in response to more limited hunting.
Unfortunately, illegal hunting has also hampered recovery efforts.
Restoration efforts for whales face other difficulties, including uncertainties about their population size and their low reproductive rates. Baleen whales travel far, wide, and deep. They are long-lived (some over 150 years), require 4 to 15 years to reach sexual maturity, and have only one or two calves every few years. Photo identification of markings on tail flukes has aided the tracking of individuals,  but sightings of various baleen whales remain intermittent. Estimates of whale population sizes, therefore, must rely heavily on theoretical models. , , 
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This is an excerpt from the book Global Climate Change: Convergence of Disciplines by Dr. Arnold J. Bloom and taken from UCVerse of the University of California.
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