Marine ecosystem stability is maintained by applying an EBFM fishing mortality to the main prey species and at the same time supporting the biological production, P, of the dominant predator 6. That was based upon mimicking natural fish population processes that maintain the biological production transfer from prey to predator production between trophic levels, originally developed by 9. The necessary data to estimate the transfer is provided in Ecopath Models 10. The Ecopath model gives the biomass and production to biomass ratio, P/B, allowing estimation of the biological production of the species being fished and the predator species, P, by multiplying the biomass by P/B, so P = B x (P/B), where the P/B ratio is the rate of biomass regeneration 11. That is the basis for estimating the Trophic Transfer Efficiency, TTE, from the prey trophic level, TL, to the dominant predator in the next higher TL, provided in Ecopath Models. The TTE is estimated by the ratio of predator biological production to the prey production. The TL for a fish species is shown in EcoBase - Ecopath with Ecosim https://ecobase.ecopath.org/. The average TTE of biological production from prey to predator is estimated from the TL by 6:

TTE = 0.54 x TL_pred^-1.26 (1).

The aim is to estimate the EBFM fishing mortality of the prey, this case Krill, by first estimating the proportion of TTE allocated to maintain the dominant predator production so it is not affected by the fishery catch of its main prey. That proportion was estimated by √(TTE_pred) using the TL for baleen whales in equation 1.

The krill EBFM F_MSY was estimated by the method in 6, defined as MSY divided by fishery biomass. A precautionary factor is applied to adjust for uncertain recruitment allocated to the fishery 12. By supporting the main predator production, the EBFM F_MSY represents ecosystem stability of the krill to whale trophic transfer. Hence, the krill EBFM F_MSY is estimated by the method in 6 with the biological production allocated to the krill fishery reduced by 1 - √ (TTE_pred) to support the baleen whale predator production:

EBFM F_MSY (/year) = 0.67 x 0.5 x (1 - √(TTE_pred)(2).

The precautionary factor, Pa, of 2/3 (taken as 0.67), is typically applied to TL3 fisheries of small pelagic fish 7, 13 and 14. As the TTE equation 1 also applies to zooplankton in TL2, the Pa factor was assumed to apply to a Krill fishery, a large zooplankton in TL2. The factor 0.5 was applied because the optimum F_MSY occurs at half the carrying capacity of the 15 surplus production model. Therefore, the equivalent ecosystem-based krill catch was estimated by multiplying EBFM F_MSY by the krill biomass in the Ecopath Model.

The Full EBFM by 6 supports the biological production of predators as well as the prey production. The Full EBFM F_MSY is expected to have a low fishing mortality of about 0.1 1516. Accordingly, it is expected to support krill for effects of all the main predators and allow krill in the Antarctic fishery area to be sustained. The krill Full EBFM F_MSY was estimated by equation 3 by modification of the ecosystem stability EBFM F_MSY from Equation 2 with the TTE transfer to the krill prey:

Full EBFM F_MSY (/year) = √(0.54 x TL_prey^-1.26) x EBFM F_MSY(3).

Note that the TL is for the krill prey being consumed by the predator in equation 2.

The Ecopath Model by 5 shows the krill diet by predators in the Diet Matrix from their supplementary Table S4. The total consumption of krill biomass by the whales and other predators was estimated using the Ecopath Model results for the predator consumption to biomass ratio, Q/B, giving the total prey biomass consumption by the procedure of 10 as Q_prey = B_Pred x (Q/B)_Pred. Note that most of the consumption is lost by respiration and excretion to detritus 17, giving the TTE of about 10%. To make Q_prey specific for krill consumption, it is multiplied by the proportion of krill in the predator Diet Matrix from the Ecopath Model, giving Q_krill = B_Pred x (Q/B)_Pred x Diet_krill, which is called here the krill Crop_krill. As baleen whales feed on krill during the Antarctic summer of three months 18, Crop_krill is estimated for whales by multiplying by feeding time factor, F_time, 0.25 (3/12 months). Due to darkness and limited sunlight during the darker six months, feeding time by seals, penguins flying seabirds was expected to be reduced by about 1.5 months, so Crop_krill was reduced by F_time 0.875 (10.5/12 months) for those predators. Hence, Crop_krill was estimated by equation 4:

Crop_krill (t/Km²/year) = B_Pred x (Q/B)_Pred. x Diet_krill x F_time(4).

The Full EBFM F_MSY was estimated by reducing the krill biomass by the estimated amount of krill consumed by the predators.

It is assumed the Ecopath Model errors measured by 19 (see their Table 2) in the California Current apply to the similarly phytoplankton productive Southern Ocean 5, where the California Current phytoplankton production was measured by 20. The above equations are expected to give reliable estimates because they provide relatively errors measured by coefficients of variation, CV. The results were relatively low: Euphausiids P/B 0.2 but did not provide the B CV which is expected similar to that for small pelagic fish at typically 0.25. Other CVs are: the humpback whale B 0.15, P/B 0.15, Harbor seals B 0.15, P/B 0.10 and flying seabirds typically B 0.10, P/B 0.15. Although CV values are not provided for penguins or TL, 21 noted changes in Ecopath model values average 0.20, which is assumed to apply for penguins, TL and diet estimates.

The estimated Krill EBFM F_MSY and Full EBFM F_MSY for baleen whales and other predators, as well as the predator diet and krill cropping compared with the fishery catch is shown in Table 1.

Table 1 shows the estimated TTE for predators ranged from 0.085 for seals to 0.110 for baleen whales. The Krill EBFM F_MSY for ecosystem stability of whales and other predators averaged 0.233, and the Full Krill EBFM F_MSY averaged 0.097/year. The total predator cropping of krill 13.583 t/Km²/year, mostly by penguins, is equivalent to 54% of the krill biomass. That is similar to the average of 46% predation loss for marine fisheries estimated by 22, higher than the average of 30% for five small pelagic TL3 predation mortalities, M2, by 23 (see their Table 2) and similar to the 58% for Horse Mackerel, Mackerel and other small pelagic fish. Hence, the Krill predation was subtracted from the fishery biomass to estimate the ecosystem-based fishing mortality in the next Section 3.2. Note that the krill consumption is about 50 mt/year in the fishery area, 9-fold higher than the 5.61 mt/year catch estimated by 3, indicating the possible reason for reduction in the fishing limit by a similar proportion to 0.62 mt/year. Consequently, the commercial fishery catch at the upper limit of 0.168 t/Km²/year is equivalent to a fishing mortality of 0.0067/year (see note b in Table 1, 0.168/krill biomass 25), an order of magnitude lower than the average Full EBFM F_MSY. Given that finding, the expected fishing mortality by applying the Full Krill EBFM F_MSY to the krill biomass with reduction by predator consumption is examined below.

The Antarctic krill had a high biomass of 25 t/Km² at the time of Ecopath Modelling, giving a total biomass in the fishery area of 92.5 m. tonnes (25 x 3.7 mKm²) and high biological production of 62.5 t/Km²/year (P = B 25 x P/B 2.5). The findings by 17 Christensen and Pauly (1995) show predator predation reduces the fishery biological production because P equals biomass accumulation plus predation plus catch plus other mortality and losses, so the total predation was subtracted from the biomass to estimate the ecosystem-based catch. That gives a remaining biomass 11.417 (25.0 -13.583) t/Km²/year and subtracting the existing fishery catch of 0.168, gives an available biomass 11.249 t/Km²/year. Applying to the average krill Full EBFM F_MSY of 0.097/year in Table 1 gives an estimated catch 1.091 t/Km²/year, a total krill fishery catch of about 4.04 million tonne in the fishery area, which is similar to that estimated by 3 at 5.61 mt/year, but about 28% lower.

Information on climate change effects in the Arctic Ocean are used to provide some perspective on likely effects in the Antarctic Ocean.

Phytoplankton diatoms in the Southern Ocean are indicated as the main food for Antarctic krill 28, so significant changes could affect krill production. However, they found the net effect of temperature related climate change is uncertain, but suggested deep water circulation changes may eventually affect nutrient inputs and alter food web flows and biogeochemistry. The early study by 29 see Figure 2 on low temperature effects on diatom growth showed a mounded curvilinear relationship for the diatom Detonulaconfervacea. The curve is indicated as beginning at about 2.2^oC, peaking at about 11.9^oC doublings/day and decreased at higher temperatures. That species has been reported as occurring in the Arctic Ocean in Baffin Bay, further south in Davis Strait and in the Bay of Fundy (see World Register of Marine Species https://www.marinespecies.org/aphia.php?p=taxdetails&id=149286, so a similar response to water temperatures may occur for diatoms in the Southern Ocean. At the Antarctic Peninsula, 30 measured the grow rates in container bags of the diatoms Thalassiosirasp., Nitzschla sp., and Chaetocerossp. at the typical water temperature of 1.5^oC, having an average growth rate of 0.39/day, which was suggested by published models to be about 30% of the rate at 20°C. On the other hand, in situ measurements showed no net growth, apparently due to losses such as sinking and predation 31. However, 32 found climate change reduced cloud cover over the northern Antarctic Peninsula. The increased exposure to sunlight increased water temperature and stratification, and hence phytoplankton growth rates and abundance in the upper euphotic zone.

The current water temperatures in the Southern Ocean are reported by 33 as ranging from -2.62^oC to 5.2^oC. As the lower -2.62^oC temperature is about 4.8^oC lower than the minimum 2.2^oC in the diatom curve in the Arctic Ocean by 29, and assuming a similar response curve for diatoms in the Southern Ocean, a peak production at around 7.1^oC (Arctic peak 11.9 – 4.8) may occur. That suggests a further temperature increase by climate change to higher than only about 1.9^oC (7.1 - Southern Ocean upper temperature 5.2^oC) could cause a reduction in phytoplankton production. Although the recent water temperature increase in the Southern Ocean in 2023 has not been published, the sea ice area decreased by about 20% in 2023 since the area in 1979 34, their Figure 3b, indicating a significant temperature increase. Furthermore, 35 measured a 1.4^oC increase in the Arctic Ocean due to global temperature increases. By comparison, 36 reported the overall Southern Ocean temperature trend in the upper 800m as +0.29 ± 0.09 °C per decade from 1993 to 2017, giving a 0.7^oC increase in 2017, or 0.9^oC extrapolated to 2024. If the dominant diatoms of Rhizosoleniasp. and Thalassiothrixsp in the Southern Ocean 28 have a similar curvilinear relationship with temperature as shown by 29, the reduction of phytoplankton production, and associated krill production in the near future is a possibility. However, 32 found a recent increase in production with climate change. Hence, further research on the effects of water temperature on phytoplankton growth rates in the Southern Ocean is suggested.

In the summary of climate change effects on phytoplankton in the Southern Ocean, 28 noted the oceans have taken up 25 to 30% of annual atmospheric CO₂, with about 40% in the Southern Ocean and sea ice uptake about 58% of that uptake. However, sea ice extent around the West Antarctic Peninsula was indicated as declined by up to 40% over the past 26 years. Importantly, 37 noted ice sheet tipping points at about +1.5 to 2.0^oC, similar to the above suggested increase that may adversely affect phytoplankton production. Conversely, spring melt water in the Southern Ocean with released high iron, which was indicated by 28 to contribute 40-50% of the productivity in the entire ocean. Furthermore, 38, see their Figure 2 found increased phytoplankton production from 1998 to 2018 in the Arctic Ocean due to increased water temperature, reduced sea ice area causing greater exposure to light, and likely increase in nutrients from deep ocean waters. Therefore, the various interrelationships of climate change effects on phytoplankton indicate ongoing monitoring and assessments need to be undertaken.

The natural temperature range of krill was suggested to lie between -1.8 and 5.5 ◦C by 39. They found smaller size and higher oxygen demand at > 3.5◦C. The findings where similar to those by 40 who noted from the literature that the krill growth optimum temperature was 0.5 ◦C to 1◦C and growth rates decreased between 3◦C and 4 ◦C and found effects on lengths at ≥ 3.5◦C, potentially affecting the South Georgia krill fishery. However, according to the rate of overall temperature increase by 36, a constant increase of 3.5^oC in the Southern Ocean may not occur in the near term, consistent with their rate of water temperature increase.

A reduction in krill fishing intensity in the Antarctic Peninsula area was suggested by 8 to protect the krill egg and larvae recruitment to krill production because the area has a high proportion of the current krill catch. That was supported by 41 who suggested the area be made into a marine protected area. The study by 42 suggested krill fishing by new countries and climate change caused decreasing recruitment of krill near the Antarctic Peninsula by reduction in sea ice coverage, and a larger average body length being fished. It was also suggested the existing level of fishing is poorly quantified and controlled. Earlier, 43 suggested krill fishing should be stopped in existing protection zones of the South Georgia and Antarctic Peninsula fishery areas due to the high proportion of krill consumed by predators, particularly land based seabirds. For those reasons, a reduction of the current krill catch in the Peninsula area is suggested, which may also give some precaution for near-term climate change effects on the whole krill fishing area.

The Antarctic Peninsula fishing area 48.1 to the 1000m bathymetry is shown in 8 see their Figure 1. If fishing was stopped in the Peninsula area, the reduction in fishing for the area indicated in 8 was estimated to be about 10.3%. Assuming the Peninsula area has a similar catch per krill biomass as in the whole Antarctic fishing area, the 10.3% reduction is expected to be equivalent to reducing the fishery area upper limit of 0.62 mt/year to 0.556 mt/year (0.62 x (1 – 0.103)), which is still higher than the highest reported catch of 0.45 mt/year in 2021/22. The reduced catch is suggested because climate change effects, particularly for the Southern Ocean, indicated by 27 for the importance to carbon uptake, 44 for expected phytoplankton changes and 37 on marine ecosystem effects cannot be disregarded. Obviously, such a change requires further investigation and research on environmental change effects on larvae recruitment to krill production due to climate change, and the fishery manager and stakeholder approval for the final fishing level decision.