Philippa Kaur

Relevance for design of dFAD recovery programmesOur results provide guidance for implementing effective dFAD recovery programmes. More than 40% of dFAD trajectories in the Indian and Atlantic oceans drifted away from fishing grounds never to return, potentially later stranding in coastal areas (Imzilen et al.5 estimated that 10–20% of all French dFADs eventually strand, whereas 16.0% of our trajectories that definitively leave fishing zones strand). This loss represents at least 529 tonnes yr−1 of marine litter for the French fleet5,14 and probably 2–3 times that weight including all purse seiners in the two oceans28. More than 20% of dFAD trajectories that drifted away from fishing grounds passed within 50 km of a port (ranging from 3.3% to 31.6% for cut-off distances from 10 to 100 km; potentially underestimated due to remote deactivation of GPS buoys by purse seiners). This result suggests that coastal dFAD recovery programmes could be complementary to other mitigation measures, such as dFAD buoy limits already implemented by tRFMOs and spatio-temporal dFAD deployment closures proposed by Imzilen et al.5. Indeed, Imzilen et al.5 showed that prohibiting dFAD deployments in areas that would probably lead to strandings would principally protect coastal areas of the southwestern Indian Ocean and the eastern Gulf of Guinea, whereas we found that dFADs exiting fishing grounds from other areas, such as the northwestern Indian Ocean and the northern Gulf of Guinea, passed close to regional ports and could potentially be recovered at sea. Although our results are specific to the French and associated purse-seine fleet (representing ~1/3–1/2 of catch and dFAD deployments of all fleets28), available data indicate that other purse-seine fleets have similar spatio-temporal patterns of deployments28, suggesting that our results are applicable to the entire tropical tuna purse-seine fishery in the Indian and Atlantic oceans.These results contrast somewhat with existing analyses from the western and central Pacific Ocean, where it was estimated that 36% of dFADs ended up outside fishing grounds, but that the final recorded position of these abandoned dFADs were typically far from ports (502–952 km)29. Although these differences may be related to the larger spatial scales of the Pacific Ocean, additional analyses based on examinations of entire trajectories are needed to assess viability of recovery programmes based on ports.Consequences of spatial and temporal variation of dFAD lossHigh seas recovery could also be structured around our results on where important percentages of buoys exit fishing grounds towards the high seas. In the Indian Ocean, dFADs definitively leaving from the eastern border (70° E) end up stranded in or transiting through the Maldives and the eastern Indian Ocean. This happens relatively less frequently in the period from June to August and becomes much more frequent from October to December. Low loss rates during June to August are consistent with known seasonal patterns in dFAD deployment and fishing during this period4,25. At that time of the year, dFADs are deployed by fishers with the intent that they drift along the eastern African coast until they reach the main dFAD fishing grounds off Somalia, avoiding strong monsoon-driven currents favourable to eastward export of dFADs from July to December27. This is followed by a more intense dFAD fishing season during August–October. Finally, starting in October/November, a period of transition towards fishing further south in the Indian Ocean occurs, with relatively more focus on free-swimming school sets25,30, probably contributing to abandonment of dFADs in the northern Indian Ocean in the last quarter of the year.In the Atlantic Ocean, dFADs lost to the high seas exit fishing grounds mostly from the northwestern border (between 10° and 20° N) and southwestern border (2°–5° S), which is consistent with transport by the North Equatorial and South Equatorial Currents26. Although the seasonality of loss is less marked in the Atlantic Ocean than in the Indian Ocean, the peak months of July and December are associated with transitions in the spatio-temporal distribution of deployments from principally deploying just north of the equator off of West Africa to focusing on the Gulf of Guinea further east30. These transitions could lead to increased dFAD abandonment in areas highly susceptible to export of dFADs, although seasonality in currents may also play a role.Challenges facing recovery programmesWhile the information provided in this paper on spatio-temporal patterns of dFAD loss provides an essential foundation for implementing dFAD recovery strategies, there are several important practical challenges to the success of such efforts. Most efforts towards reducing or removing marine debris after it has been created have so far focused on beach clean-ups31,32. Such operations are costly, time-consuming and only capture a fraction of the overall debris18,33. Recovery at sea is a promising alternative solution34, but this requires consolidating systems to observe these debris35 and understanding their drift36, as well as putting in place appropriate incentives and socio-economic and political frameworks37. Broadly, data availability (for example, access to near-real-time location data from all fleets), equipment availability (for example, appropriately sized and equipped vessels for collecting large debris such as dFADs)32, recovery programme structure (for example, collaboration with local fishers, NGOs and/or nation-states; use of support vessels, and/or chartering of dFAD recovery vessels) and funding sources (for example, reuse of recovered tracking buoys or dFAD plastic floats, and/or polluter-payer systems collected at dFAD deployment or manufacturing) need to be optimized to recover a maximum number of dFADs while minimizing costs and fishing impacts. These considerations highlight the importance of identifying areas leading to losses and multiple ports of different sizes from which operations could potentially be conducted, as we have done above, as well as careful analysis of the possible impediments to implementation of recovery programmes.Some possible impediments to dFAD recovery programmes are environmental, strategic or geopolitical. For instance, although the Somali coast is identified as a dFADs stranding hotspot in winter5 and has potential for a port-based recovery programme as we show here, recovering dFADs along this coast is unlikely to be a priority due to the area’s relatively limited number of sensitive habitats, such as coral reefs, and because of the difficult and dangerous socio-political situation in the country and its adjacent waters. On the other hand, the Maldives archipelago is likely to be a priority given that it is an area with high dFAD stranding rates on coral reefs5 and also has many dFADs that leave fishing grounds and never return. Implementing a recovery programme in this area could be particularly valuable, especially given that the Maldives is well integrated into regional maritime transport and tuna fisheries. However, implementing such a programme for a large island chain composed of >1,000 individual islands will probably be complex. Extensive collaboration with regional stakeholders, such as research institutes, fisher associations and NGOs, as well as buoy manufacturers, would be essential to operationalize a recovery programme in the Maldives and elsewhere.Another major challenge for at-sea dFAD recovery is availability of appropriate vessels to remove dFADs from the water. The vertical subsurface structure of dFADs generally stretches from 50 to 80 m below the surface. The weight of the materials used to build dFADs and the numerous sessile organisms that attach to the ‘dFAD tail’ eventually make dFADs very heavy (up to hundreds of kilograms) and therefore difficult to remove from the water. Complete removal is probably only possible for medium to large vessels with an appropriate crane or winch for hauling heavy material. Purse-seine vessels themselves could participate in dFAD recovery efforts, but this would be costly and disruptive to fishing. For smaller vessels, it may only be possible to remove some parts of the dFAD, potentially aided by natural breakdown of the object or acoustic release systems, such as the GPS buoy, plastic flotation devices and/or surface raft metallic or plastic structural elements. However, this could still be extremely useful as the remaining material will normally sink before reaching coastal environments, thereby potentially avoiding the most important environmental impacts. This strategy would be particularly valuable if the subsurface structure can be made of biodegradable materials9,23,38. Imzilen et al.5 suggested that the removal of GPS buoys by artisanal fishers is already occurring in coastal areas. Therefore, if dFAD tracking information can be made accessible and appropriate incentive mechanisms are put in place to encourage recovery of dFAD elements, this strategy could substantially reduce marine debris from dFADs. Other practical considerations should be taken into account once at port, such as the availability of infrastructure for shipping, disposing of, recycling and/or reusing tracking buoys and other dFAD components. All of these potential impediments can be addressed, but they will require active engagement from fishers, tRFMOs, NGOs and coastal nations.Complementary measuresIn addition to such recovery programmes, existing complementary measures controlling the numbers of dFADs present at sea (for example, limits on the number of operational GPS-tracking buoys and limits on the use of support vessels) may need to be strengthened, as a higher number of dFADs obviously contributes to higher risks of marine debris and stranding. Lowering limits on the number of dFADs may also encourage vessels to increase sharing of buoy information, thereby maximizing use of dFADs and potentially reducing dFAD loss. However, oddly enough, such measures may aggravate problems of ALD dFADs if their consequences are not accurately anticipated. For example, limits on the number of tracked dFADs implemented by tRFMOs have modified the strategy of some components of the purse-seine fishery, encouraging them to remotely deactivate satellite-transmitting GPS-tracking buoys when dFADs leave fishing grounds to maintain the number of operational buoys below authorized limits. The loss of position information prevents the tracking of dFADs outside fishing grounds and may result in under-estimation and spatial bias in estimates of the risks of stranding and loss5,39. A potential solution would be to consider ALD dFADs as part of a stock of ‘recoverable dFADs’ that are not counted as part of the individual vessel’s quota of operational buoys, but for which position information is transmitted and made available to partners involved in recovery programmes39. Other useful options to facilitate the recovery of buoys include limiting the per vessel number of deployments instead of limiting the number of tracked dFADs and/or making new deployments contingent on recovery of an equivalent number of already deployed dFADs. The current tRFMO-implemented reduction in the number of support vessels in the Indian Ocean is also likely to increase the loss of dFADs because these vessels may be used to recover dFADs before they leave fishing grounds, highlighting the urgent need for complementary dFAD management and recovery approaches.Financial considerationsA final question about dFAD recovery programmes is how they could be financed. The logistical challenges described above, such as chartering appropriate recovery vessels, involve substantial costs that cannot be ignored. The most simple and logical financing scheme would be a polluter-payer programme whereby vessels, dFAD manufacturers and/or fishing nations pay some monetary amount per ALD dFAD, potentially in proportion to its expected negative impacts, into an independently run and verified clean-up fund. The basic elements for identifying which vessels, fishing companies and/or nations are deploying dFADs are largely in place via tRFMO reporting requirements, dFAD vessel logbooks and purse-seine observer programmes. The detailed spatio-temporal maps provided here and in Imzilen et al.5 identify where the losses and impacts are occurring, thereby providing a blueprint for apportioning such funds geographically.Missing elementsThe missing elements for reducing dFAD loss are mostly political: facilitating access to tracking and activation-deactivation information for all ALD dFADs (for example, the EU recently objected at the 2nd Indian Ocean Tuna Commission (IOTC) ad hoc working group on dFADs to making dFAD data publicly available for scientific purposes); implementing requirements for appropriate disposal of ALD dFADs; and improving collaboration between industry and regional stakeholders concerned with clean-up programmes. Although these missing elements may seem formidable, there are very promising precedents for rapidly addressing these types of issues. Throughout the 2010s, various initiatives of purse-seine fleets, national scientists, tRFMOs and organizations such as the International Sustainable Seafood Foundation (ISSF) have allowed the rapid adoption of mitigation measures. This was the case for non-entangling dFADs40, best practices guidelines for the release of sensitive species41,42,43, exhaustive observer coverage44,45 and dFAD management plans46, which are all required for ISSF-participating fishing companies if they wish tuna from their fishing vessels to be accepted by ISSF member canneries. A similar approach could be used to address dFAD loss, using the fulcrums of the ISSF, Marine Stewardship Council certification and European Union (EU) environmental regulations to extend the commitments already made by some of the fleets (for example regarding data availability and tests of recovery mechanisms) to other fleets and other areas, and therefore rapidly transform industry behaviour for the benefit of all. More

Animals such as this orangutan in Indonesia are endangered because of illegal deforestation.Credit: Jami Tarris/Future Publishing via Getty

Funding battles stymie plan to protect global biodiversityScientists are frustrated with slow progress towards a new deal to protect the natural world. Government officials from around the globe met in Geneva, Switzerland, on 14–29 March to find common ground on a draft of the deal, known as the post-2020 global biodiversity framework, but discussions stalled.The framework so far sets out 4 broad goals, including slowing species extinction, and 21 mostly quantitative targets, such as protecting at least 30% of the world’s land and seas. It is part of an international treaty known as the United Nations Convention on Biological Diversity, and aims to address the global biodiversity crisis, which could see one million plant and animal species go extinct in the next few decades.Many who were at the meeting say that disagreements over funding for biodiversity conservation were the main hold-up in negotiations. For example, the draft deal proposed that US$10 billion of funding per year should flow from developed nations to low- and middle-income countries to help them to implement the biodiversity framework. But many think this is not enough.Negotiators say they will now have to meet again before a highly anticipated UN biodiversity summit later this year, where the deal was to be signed.‘Collegiality’ influences researchers’ promotion prospectsUniversities in North America often consider how well researchers interact with each other when making decisions about who gets promoted, a study has found, even though these factors are not formally acknowledged in review guidelines.A researcher’s performance is usually assessed according to three pillars: research, teaching and service. But in recent years, there has been a push from some academics to add another pillar: collegiality. Many say that the concepts of cooperation, collaboration and respect, which broadly fall under the definition of collegiality, are important to the functioning of laboratories and research teams.DeDe Dawson, an academic librarian at the University of Saskatchewan in Saskatoon, Canada, and colleagues analysed more than 860 review, promotion and tenure documents from different departments at 129 universities in the United States and Canada to get a sense of how often collegiality is taken into account.The study, published on 6 April (D. Dawson et al. PLoS ONE 17, e0265506; 2022), found that the concept of collegiality was widespread: the word ‘collegiality’ and related terms, such as ‘citizenship’ or ‘professionalism’, appeared 507 times in 213 of the documents, suggesting that it was often taken into account in evaluations. But just 85 documents included a definition of the term, and fewer still explained how it was measured or used in assessments.

Source: D. Dawson et al. PLoS ONE 17, e0265506 (2022)

Collegiality was mentioned most often in research-intensive institutions (see ‘Academia’s fourth pillar’). The authors say that this could be because the behaviour involved is valued in research groups.Dawson and her colleagues warn that relying on collegiality in performance reviews without adequate guidance could introduce bias, as those in charge fill in the blanks with their own definitions.“We need to make sure that we don’t use collegiality to exclude others that may communicate or interact differently,” says Sujay Kaushal, a geologist at the University of Maryland in College Park, who has previously studied collegiality. More

Minimum distance to weak efficient frontierBriec and Charnes et al. first proposed the Minimum distance to weak efficient frontier (MinDW) model39,40, which can be expressed as (m + n) linear programming ((m) is the number of input indicators and (n) is the number of output indicators), assuming that the input variable is (x) and the output variable is (y). The specific formula is shown in Eq. (1):$$ begin{aligned} & max beta_{z} ,z = 1,2, ldots ,m + n \ & s.t.left{ begin{gathered} sumnolimits_{j = 1}^{q} {alpha_{j} x_{rj} + beta_{z} e_{r} le x_{rk} ,r = 1,2, ldots ,m} hfill \ sumnolimits_{j = 1}^{q} {alpha_{j} x_{ij} + beta_{z} e_{i} ge y_{ik} ,i = 1,2, ldots ,n} hfill \ alpha_{j} ge 0 hfill \ end{gathered} right. \ end{aligned} $$
(1)
(e_{r}) and (e_{i}) are constants. In the programming formula, only one (e) is equal to 1, and the others are 0, that is shown in Eq. (2):$$ begin{aligned} & e_{r} = 1;{text{ if}}; , r = z; , e_{r} = 0 , ;{text{if}}; , r ne z \ & e_{i} = 1 , ;{text{if}}; , i = z – m; , e_{r} = 0 , ;{text{if}}; , i ne z – m \ end{aligned} $$
(2)
The efficiency value of model is expressed as Eq. (3):$$ theta_{z}^{*} = frac{{1 – frac{1}{m}sumnolimits_{r = 1}^{m} {frac{{beta_{z}^{*} e_{r} }}{{x_{rk} }}} }}{{1 + frac{1}{n}sumnolimits_{i = 1}^{n} {frac{{beta_{z}^{*} e_{i} }}{{y_{ik} }}} }} $$
(3)
The efficiency value of MinDW model is expressed as (theta_{max }^{*} = max (theta_{z}^{*} ,z = 1,2, cdots ,m + n)), and the maximum efficiency value corresponds to the minimum (beta^{*}), that is the nearest distance to the frontier.This paper uses the MinDW model with negative output to conduct empirical analysis. The method can be expressed as (m + n + d) linear programming ((m) is the number of inputs, (n) is the number of desirable output, (d) is the number of unexpected output), assuming that the input variable is (x), the desirable output variable is (y), and the undesirable output variable is (f). The specific formula is shown in Eq. (4):$$ begin{aligned} & max beta_{z} ,z = 1,2, ldots ,m + n + d \ & s.t.left{ begin{gathered} sumnolimits_{j = 1}^{q} {alpha_{j} x_{rj} + beta_{z} e_{r} le x_{rk} ,r = 1,2, ldots ,m} hfill \ sumnolimits_{j = 1}^{q} {alpha_{j} x_{ij} – beta_{z} e_{i} ge y_{ik} ,i = 1,2, ldots ,n} hfill \ sumnolimits_{j = 1}^{q} {alpha_{j} x_{lj} + beta_{z} e_{l} le f_{lk} ,l = 1,2, ldots ,d} hfill \ alpha_{j} ge 0 hfill \ end{gathered} right. \ end{aligned} $$
(4)
(e_{r}), (e_{i}) and (e_{l}) are constants. In the programming formula, only one (e) is equal to 1, and the others are 0, that is shown in Eq. (5):$$ begin{aligned} & e_{r} = 1;{text{ if}}; , r = z; , e_{r} = 0 , ;{text{if}}; , r ne z \ & e_{i} = 1 , ;{text{if }};i = z – m; , e_{r} = 0 , ;{text{if}}; , i ne z – m \ & e_{l} = 1 , ;{text{if}}; , l = z – m – n; , e_{l} = 0 , ;{text{if}}; , l ne z – m – n \ end{aligned} $$
(5)
The efficiency value of model is expressed as Eq. (6):$$ theta_{z}^{*} = frac{{1 – frac{1}{m}sumnolimits_{r = 1}^{m} {frac{{beta_{z}^{*} e_{r} }}{{x_{rk} }}} }}{{1 + frac{1}{n + d}left( {sumnolimits_{i = 1}^{n} {frac{{beta_{z}^{*} e_{i} }}{{y_{ik} }}} + sumnolimits_{l = 1}^{d} {frac{{beta_{z}^{*} e_{l} }}{{f_{lk} }}} } right)}} $$
(6)
The efficiency value of MinDW model is expressed as (theta_{max }^{*} = max (theta_{z}^{*} ,z = 1,2, cdots ,m + n + d)), and the maximum efficiency value corresponds to the minimum (beta^{*}), which means the nearest distance to the frontier.The efficiency value of MinDW model will not be less than the efficiency value of directional distance function model with any direction vector or other distance types (such as radial model and SBM model). In other words, the efficiency value of MinDW model is the largest. Combined with the above process, we can define the common boundary ((beta^{meta*})) and the model is as Eq. (7):$$ begin{aligned} & beta^{meta*} = max frac{{1 – frac{1}{m}sumnolimits_{r = 1}^{m} {frac{{beta_{z} e_{r} }}{{x_{rk} }}} }}{{1 + frac{1}{n + d}left( {sumnolimits_{i = 1}^{n} {frac{{beta_{z} e_{i} }}{{y_{ik} }}} + sumnolimits_{l = 1}^{d} {frac{{beta_{z} e_{l} }}{{f_{lk} }}} } right)}} \ & s.t.left{ begin{gathered} sumnolimits_{j = 1}^{{q_{m} }} {alpha_{j} x_{rj} + beta_{z} e_{r} le x_{rk} ,r = 1,2, cdots ,m} hfill \ sumnolimits_{j = 1}^{{q_{m} }} {alpha_{j} x_{ij} – beta_{z} e_{i} ge y_{ik} ,i = 1,2, cdots ,n} hfill \ sumnolimits_{j = 1}^{{q_{m} }} {alpha_{j} x_{lj} + beta_{z} e_{l} le f_{lk} ,l = 1,2, cdots ,d} hfill \ alpha_{j} ge 0 hfill \ end{gathered} right. \ end{aligned} $$
(7)
Similarly, the efficiency value of DMU relative to the scale frontier ((beta^{scale*})) can be obtained by the Eq. (8):$$ begin{aligned} & beta^{scale*} = max frac{{1 – frac{1}{m}sumnolimits_{r = 1}^{m} {frac{{beta_{z} e_{r} }}{{x_{rk} }}} }}{{1 + frac{1}{n + d}left( {sumnolimits_{i = 1}^{n} {frac{{beta_{z} e_{i} }}{{y_{ik} }}} + sumnolimits_{l = 1}^{d} {frac{{beta_{z} e_{l} }}{{f_{lk} }}} } right)}} \ & s.t.left{ begin{gathered} sumnolimits_{j = 1}^{{q_{s} }} {alpha_{j} x_{rj} + beta_{z} e_{r} le x_{rk} ,r = 1,2, ldots ,m} hfill \ sumnolimits_{j = 1}^{{q_{s} }} {alpha_{j} x_{ij} – beta_{z} e_{i} ge y_{ik} ,i = 1,2, ldots ,n} hfill \ sumnolimits_{j = 1}^{{q_{s} }} {alpha_{j} x_{lj} + beta_{z} e_{l} le f_{lk} ,l = 1,2, ldots ,d} hfill \ alpha_{j} ge 0 hfill \ end{gathered} right. \ end{aligned} $$
(8)
Finally, in the common frontier model, the technology gap ratio (TGR) is equal to the ratio of the efficiency value of the common frontier to the scale frontier41. The formula is as Eq. (9):$$ TGR^{MinDW} = frac{{beta^{meta*} }}{{beta^{scale*} }} $$
(9)
(beta^{meta*}) and (beta^{scale*}) represent the optimal solution of formula (7) and formula (8), respectively. Obviously, (0 le TGR le 1). TGR is used to measure the distance between the optimal production technology and the potential optimal technology of a group, and identify whether there are any differences in LHG under different groups. The closer the TGR is to 1, the closer the technology level is to the optimal potential technology level. Conversely, it shows the larger gap between the technology level and the potential optimal technology level.Metafrontier-Malmquist–Luenberger indexMalmquist productivity index is widely used in the study of dynamic efficiency change trend, and has good adaptability to multiple input–output data and panel data analysis. The actual production process often contains unexpected output. After Chung et al. proposed Malmquist–Luenberger (ML) index, any Malmquist index with undesired output can be called ML index42. Oh constructed the Global-Malmquist–Luenberger index43. All the evaluated DMUs are included in the global reference set, which avoids the phenomenon of infeasible solution in VRS. The global reference set constructed in this paper is as Eqs. (10)–(11):$$ Q^{G} left( x right) = Q^{1} left( {x^{1} } right) cup Q^{2} left( {x^{2} } right) cup cdots cup Q^{T} left( {x^{T} } right) $$
(10)
$$ Q^{t} left( {x^{t} } right) = left{ {left( {y^{t} ,f^{t} } right)left| {x^{t} ;can;produce} right.;left( {y^{t} ,f^{t} } right)} right} $$
(11)
This paper takes MML index as the LHG.$$ begin{aligned} MML_{t – 1}^{t} & = sqrt {frac{{1 – D_{t – 1} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{t – 1} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}} times frac{{1 – D_{t} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{t} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}}} \ & = sqrt {frac{{1 – D_{t – 1} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}}{{1 – D_{t} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}} times frac{{1 – D_{t – 1} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{t} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}} \ & ;;;;; times frac{{1 – D_{t} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{t – 1} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}} \ end{aligned} $$
(12)
Next, it further decompose the MML index into efficiency change (EC) and technology change (TC). The specific formula is shown in Eqs. (13)–(14):$$ TC_{t – 1}^{t} = sqrt {frac{{1 – D_{t – 1} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}}{{1 – D_{t} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}} times frac{{1 – D_{t – 1} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{t} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}} $$
(13)
$$ EC_{t – 1}^{t} = frac{{1 – D_{t} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{t – 1} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}} $$
(14)
where (left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} } right)) and (left( {x^{t} ,y^{t} ,f^{t} } right)) represent the input, expected output and unexpected output of t-1 and t, respectively. (TC_{t – 1}^{t}) is the devotion to LHG raise of DMU’s technical progress from (t – 1) to (t). And (EC_{t – 1}^{t}) represents the devotion to LHG raise of DMU’s efficiency improvement from (t – 1) to (t). The higher the value is, the larger the devotion is. The (MML) index is recorded as (MI). The value of (MI) is the LHG. The green total factor productivity index of laying hens breeding under the common frontier and scale frontier are as Eqs. (15)–(16):$$ metaMI_{t – 1}^{t} = sqrt {frac{{1 – D_{{_{t – 1} }}^{m} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{{_{t – 1} }}^{m} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}} times frac{{1 – D_{{_{t} }}^{m} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{{_{t} }}^{m} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}}} $$
(15)
$$ groupMI_{t – 1}^{t} = sqrt {frac{{1 – D_{{_{t – 1} }}^{g} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{{_{t – 1} }}^{g} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}} times frac{{1 – D_{{_{t} }}^{g} left( {x^{t} ,y^{t} ,f^{t} ;y^{t} , – f^{t} } right)}}{{1 – D_{{_{t} }}^{g} left( {x^{t – 1} ,y^{t – 1} ,f^{t – 1} ;y^{t – 1} , – f^{t – 1} } right)}}} $$
(16)
For the DMUs with scale heterogeneity, we can measure the technology gap between the group frontier and the common frontier, which is caused by the specific group structure.Data and variablesBased on the research of the existing literature36, this paper selects five indexes to build the input–output indicator system. Details are as below:

1.

Input variables:

(1)

Quantity of concentrated forage. Mainly includes seeds of crops and their by-products.

(2)

Quantity of grain consumption. Quantity of grain consumed is the quantity of grain consumed by laying hens when they are raised. For example: corn, sorghum, broken rice, wheat, barley, wheat bran, etc.

(3)

Material expenses. The sum of water and fuel power costs, labor costs, and medical epidemic prevention fees. Water and fuel power costs include water, electricity, coal and other fuel power costs; labor costs mean the human management cost of each laying hen from the brood stage to the laying stage; medical and epidemic prevention costs include the cost of disease prevention and control.

2.

Positive output Main product production, which is the egg production per layer.

3.

Negative output Total discharge. According to the calculation method of The Manual of Pollutant Discharge Coefficient, Eq. (17) is used to calculate the COD, TN, and the TP of each layer. Then, according to the calculation method of class GB3838-2002 water quality standard in V, Eq. (18) is used to calculate the total discharge.

$$ POLLUTANTS = FP(FD) times Days $$
(17)
$$ TOTAL , POLLUTANTS = frac{COD}{{40}} + frac{TN}{2} + frac{TP}{{0.4}} $$
(18)
where, (FP(FD)) is the pollution discharge coefficient and the (Days) is the average raising days. Descriptive statistics of input and output indicators are shown in Table 1.Table 1 Descriptive statistics of input and output indicators.Full size tableThe quantity of concentrate, the quantity of food consumed, the cost of labor, the cost of medical treatment all come from “National Agricultural Product Cost and Benefit Data Compilation”. The pollutant discharge coefficient of laying hens is derived from “The Manual of Pollutant Discharge Coefficient”. According to the definition of scale in above two materials, a small scale 300–1000 laying hens, a medium scale 1000–10,000 laying hens, and a large scale greater than 10,000 laying hens are grouped to calculate cost efficiency.From 2004 to 2018, this paper selects 24 major egg-producing provinces (municipalities) in China as samples, after eliminating singular data in the three scales and averaging the missing data, the final small-scale group is left with 7 provinces including Liaoning, Shandong, Henan, Heilongjiang, Jilin, Shanxi, and Shaanxi; the medium-scale group is the remaining 21 provinces of Beijing, Hebei, Jiangsu, Liaoning, Shandong, Tianjin, Zhejiang, Anhui, Henan, Heilongjiang, Jilin, Hubei, Inner Mongolia, Shanxi, Yunnan, Gansu, Ningxia, Shaanxi, Sichuan, Xinjiang, Chongqing; the large-scale group has 18 provinces, including Beijing, Fujian, Guangdong, Henan, Jiangsu, Liaoning, Shandong, Tianjin, Anhui, Henan, Heilongjiang, Hubei, Jilin, Shanxi, Yunnan, Gansu, Sichuan and Chongqing.As is shown in Table 2, after dividing the provinces by region, the eastern region has 10 provinces (municipalities): Liaoning, Shandong, Beijing, Hebei, Jiangsu, Tianjin, Zhejiang, Fujian, Guangdong, Henan. The central region has 7 provinces (autonomous region): Henan, Heilongjiang, Jilin, Shanxi, Anhui, Hubei, Inner Mongolia. The western region has 7 provinces (municipalities): Shaanxi, Gansu, Ningxia, Sichuan, Xinjiang, Chongqing, Yunnan.Table 2 Samples selected from 2004–2018.Full size table More

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We used the IUCN Red List criteria34,35 and methods developed in other global status-assessment efforts36,37 to assess 10,078 reptile species for extinction risk. We additionally include recommended Red List categories for 118 turtle species38, for a total of 10,196 species covered, representing 89% of the 11,341 described reptile species as of August 202039.Data compilationWe compiled assessment data primarily through regional in-person and remote (that is, through phone and email) workshops with species experts (9,536 species) and consultation with IUCN Species Survival Commission Specialist Groups and stand-alone Red List Authorities (442 species, primarily marine turtles, terrestrial and freshwater turtles, iguanas, sea snakes, mainland African chameleons and crocodiles). We conducted 48 workshops between 2004 and 2019 (Supplementary Table 1). Workshop participants provided information to complete the required species assessment fields (geographical distribution, population abundance and trends, habitat and ecological requirements, threats, use and trade, literature) and draw a distribution map. We then applied the Red List criteria34 to this information to assign a Red List category: extinct, extinct in the wild, critically endangered, endangered, vulnerable, near threatened, least concern and data deficient. Threatened species are those categorized as critically endangered, endangered and vulnerable.TaxonomyWe used The Reptile Database39 as a taxonomic standard, diverging only to follow well-justified taxonomic standards from the IUCN Species Survival Commission40. We could not revisit new descriptions for most regions after the end of the original assessment, so the final species list is not fully consistent with any single release of The Reptile Database.Distribution mapsWhere data allowed, we developed distribution maps in Esri shapefile format using the IUCN mapping guidelines41 (1,003 species). These maps are typically broad polygons that encompass all known localities, with provisions made to show obvious discontinuity in areas of unsuitable habitat. Each polygon is coded according to species’ presence (extant, possibly extant or extinct) and origin (native, introduced or reintroduced)41. For some regions covered in workshops (Caucasus, Southeast Asia, much of Africa, Australia and western South America), we collaborated with the Global Assessment of Reptile Distributions (GARD) (http://www.gardinitiative.org/) to provide contributing experts with a baseline species distribution map for review. Although refined maps were returned to the GARD team, not all of these maps have been incorporated into the GARD.Habitat preferencesWhere known, species habitats were coded using the IUCN Habitat Classification Scheme (v.3.1) (https://www.iucnredlist.org/resources/habitat-classification-scheme). Species were assigned to all habitat classes in which they are known to occur. Where possible, habitat suitability (suitable, marginal or unknown) and major importance (yes or no) was recorded. Habitat data were available for 9,484 reptile species.ThreatsAll known historical, current and projected (within 10 years or 3 generations, whichever is the longest; generation time estimated, when not available, from related species for which it is known; generation time recorded for 76.3% of the 186 species categorized as threatened under Red List criteria A and C1, the only criteria using generation length) threats were coded using the IUCN Threats Classification Scheme v.3.2 (https://www.iucnredlist.org/resources/threat-classification-scheme), which follows a previously published study42. Where possible, the scope (whole ( >90%), majority (50–90%), minority (30%), rapid ( >20%), slow but notable ( More

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