Authors: Bente Philippsen (corresponding author) 
Throughout the entire history of radiocarbon dating, new sources of error have appeared, have been examined, and corrections have been found. Of particular interest and complexity are the so-called reservoir effects, which result in apparent ages that are too old.
One of the basic assumptions in radiocarbon dating is that a sample incorporates carbon in equilibrium with the atmosphere. This can be directly, e.g. in a plant via photosynthesis, or indirectly, e.g. when an animal feeds on plants. This type of sample is called terrestrial. If a sample obtains its carbon from another reservoir with a lower [sup.14]C level than the atmosphere, the basic assumption is no longer valid. The measured ages can be too old. This is typically the case for aquatic samples, originating in the sea (marine samples) or in freshwater systems such as lakes and rivers. This is of particular concern to archaeologists, as aquatic resources were an important contribution to human nutrition in Northern Europe, from Mesolithic hunter-gatherer-fishers to medieval Christians.
The marine reservoir effect is well-acknowledged among archaeologists, although the knee-jerk subtraction of 400 years from radiocarbon dates of marine samples might be too simplistic in some cases.
At least theoretically, the freshwater reservoir effect (FRE) has been known for a longer time than the marine reservoir effect. The most common cause of high apparent ages in freshwater systems is the presence of dissolved ancient carbonates, leading to the so-called hardwater effect. Under closed system conditions, calcite dissolution by carbonic acid leads to a 50% dilution of the [sup.14]C concentration [1, 2], causing a maximum FRE of one half-life of [sup.14]C, about 5,370 years. Under open system conditions, water DIC is continuously exchanging with the infinite reservoir of [sup.14]C-active soil CO[sub.2], causing no reservoir offset. In reality, freshwater systems have intermediate conditions, and a FRE between 0 and almost 6,000 years is possible .
The hardwater effect was already predicted by J. Iversen in a private communication to E. S. Deevey, October 5, 1949 . The effect was considered by Godwin in 1951  when discussing radiocarbon dates from the British Isles, and measured for the first time in 1954 on aquatic plants . The marine reservoir effect was observed and discussed slightly later in the 1950s [6, 7, 8].
However, it took several decades before the FRE was measured and discussed in archaeologically relevant sample types, such as human bones [9, 10, 11, 12, 13, 14] or food crusts on pottery [15, 16, 17, 18]. In these cases, the consumption or preparation of large amounts of freshwater fish lead to spurious apparent ages of the bones and pottery.
Also aquatic plants which are incapable of assimilating carbonates, and rely on CO[sub.2], such as aquatic mosses, can show a substantial FRE . High apparent ages can also be measured in carbonate-free groundwater and surface water , and apparent ages of up to 20,000 BP were reported from an Icelandic geothermal area .
In softwater lakes, the FRE can be caused by slow CO[sub.2] exchange between the atmosphere and the lake water due to a large depth-to-surface ratio, good wind protection or extended periods of lake ice cover [22, 23]. Other causes for a soft-water FRE are the inflow of old groundwater , the oxidisation of old organic matter , the inflow of water from a glacier containing old CO[sub.2], or old CO[sub.2] from volcanic activity .
Freshwater reservoir effects can vary significantly within one lake or river [18, 25, 26], even when only regarding submerged plants , or a single fish species from one lake . Furthermore, the FRE influences radiocarbon dating in fjords and estuaries and can lead to site and time specific reservoir ages [28, 29, 30]. …