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The Acadian Forest of eastern Canada has shown a pervasive signal of forest degradation since 1985 (Fig. 1). Since 1985, >3 million ha have been clear-cut (Fig. 1d), with most of this area now occupied by either tree plantations and thinnings (Fig. 1c–e), which are dominated by single tree species20, or a mix of early successional tree species (Fig. 1a,d,e). Despite some ingrowth due to succession, old forest has declined by 39% during the period observed (Extended Data Fig. 1a,b; Supplementary Methods). The pattern of extensive harvest of old forest, followed by rapid regeneration of young forest appears to be common across many forest regions of North America (for example, central Canada, southeastern United States, western United States; Fig. 1b) (ref. 10) and can be considered ‘forest degradation’ in that these practices simplify forest structure, reduce tree species diversity and truncate old-forest age classes6. During the same 35-year time period, forest cover remained relatively stable, increasing by a net 6.5% (Fig. 3a, red line)21.Fig. 3: Forest degradation rather than loss drives habitat declines in old forest-associated bird species.a, Habitat trends (1985–2020) for the seven bird species exhibiting the greatest population declines according to SDMs; all of these species are old forest associated. During the same time interval, total forest cover did not decline (red line, right axis), indicating that habitat loss is a function of forest degradation rather than loss. b,c, Predicted habitat loss (pink) and gain (blue) between 1985 and 2020 for two example species: Blackburnian warbler (33% habitat loss; b) and golden-crowned kinglet (38% habitat loss; c). Habitat loss was quantified using SDMs with Landsat data as independent variables strongly predicted population trends for forest bird species.Full size imageOverall, SDMs using Landsat reflectance bands as predictors performed well for most forest bird species when tested on 50% spatially discrete hold-out data (Extended Data Fig. 2; (bar x) area under the curve (AUC) = 0.73 [range: 0.60–0.90]). SDMs therefore provided reliable estimates of habitat suitability and distribution for most of the 54 species. Species with lower model-prediction success tended to be associated with fine-scale forest structure (for example, individual tall trees, standing and fallen dead wood) which are poorly captured by satellite imagery.We back cast SDMs to quantify habitat change for all 54 forest bird species from 1985 to 2020. Habitat declines occurred for 66% of species during 1985–2020; 93% of species exhibited habitat reductions over the past decade (Fig. 3 and Extended Data Fig. 3). Species showing the greatest decreases in habitat were golden-crowned kinglet (Regulus satrapa; −38%) and Blackburnian warbler (Setophaga fusca; −33%; Supplementary Video 1) with seven species showing habitat declines >25% (Fig. 3). Most species with strongly declining habitat are associated with old forests22 (Fig. 4a,b), which is consistent with forest degradation due to harvesting of old forest. Indeed, clear-cut harvest alone was strongly associated with habitat declines for all old forest-associated species (Fig. 4c and Extended Data Figs. 4 and 5). Forest succession into old age classes was apparently insufficient to compensate for this rate of loss. Fifteen species exhibited habitat increases, but most (14 out of 15) of these tend to be associated with young or immature forests (Fig. 4a,b).Fig. 4: Evidence for the effect of forest degradation on mature-forest bird species.a, The relationship between habitat change, estimated from SDMs and independently derived population change estimates from the BBS for the Acadian forest. Bird species of mature (old) forests (M; dark green dots) exhibit the greatest habitat loss; this is generally reflected in strongly negative population trends. Bird species associated with regenerating forest (R; red dots) tend to have stable or increasing habitat but still show BBS population declines. b, The relationship between quantitatively derived estimates of mature-forest association and habitat change from 1985 to 2020. Mature forest-associated species tend to be losing the most habitat in relation to immature- (I; light-green dots) and regeneration-associated species. Successional stage categorizations (R, I, M) are from Birds of the World (BOW). The regression line was fit using a hierarchical Bayesian model (Supplementary Methods) and grey shading in b shows 95% credible intervals. Only a subset of species is shown in b (those with quantitative data for mature-forest associations; Supplementary Methods). c, The relationship between area clear-cut occurring from 1985 to 2020 in each species’ habitat within a 200 m-diameter buffer surrounding BBS routes (N = 90) and habitat loss (1985–2020) at the same scale for six mature forest-associated species. Black lines are regression lines and grey bands are 95% confidence intervals (regression estimates in Supplementary Table 3). As expected, clear-cutting is strongly associated with habitat loss, which indicates that ingrowth of new habitat is rarely compensated for by habitat loss (a signature of forest degradation via old age–class truncation).Full size imageSeveral lines of evidence support forest management as the primary driver of forest degradation rather than alternative mechanisms (for example, climate-mediated forest decline, natural disturbance, permanent deforestation). First, our SDMs did not include climate data so the reflectance changes from satellite imagery used in our SDMs were predominantly due to forest compositional changes. Although climate (for example, inter-annual differences in precipitation) can cause subtle differences in reflectance (leaf colour) over time, most changes in the magnitude of reflectance are due to changes in forest composition or cover rather than effects of climate23 (Supplementary Figs. 1 and 2). Indeed, if the observed habitat declines were due to climate effects or natural disturbance, we would expect to see parallel habitat declines in protected areas, which we did not (Extended Data Figs. 6 and 7). Second, species exhibiting the greatest declines in habitat are those most strongly associated with old forest (Fig. 4a,b), which is the primary target of timber harvest. Indeed, the amount of area clear-cut was strongly associated with habitat loss for old forest-associated bird species (Fig. 4c and Extended Data Figs. 4 and 5). Third, deforestation (defined as permanent conversion to another land-cover type)24 was not a primary driver of habitat loss in our region; deforestation contributed 0.95, and 20 species had posterior probabilities >0.8. Importantly, most of the species showing an effect of habitat loss along routes on changes in population decline have lost substantial habitat over the time period and are associated with old forest (for example, Blackburnian warbler, northern parula [Setophaga americana], red-breasted nuthatch [Sitta canadensis], boreal chickadee [Poecile hudsonicus], dark-eyed junco [Junco hyemalis]; Extended Data Fig. 8), which would be expected with the harvest of old forest—a component of forest degradation. It is important to note that this test is highly challenging because many factors can drive annual fluctuations in bird abundance (for example, weather, phenology, conditions during migration or on the wintering grounds). Also, in any given year, habitat change along BBS routes can be quite small for some species; this low inter-annual variation in a predictor variable can preclude high statistical power to detect effects.We estimated the net number of breeding individuals that have probably disappeared due to habitat loss from 1985 to 2020 using published accounts of territory sizes for each species22 (Supplementary Table 5). This calculation assumes that available habitat is consistently occupied, which is supported by strong associations between habitat amount along BBS routes and bird abundance over the long term. Across all species, back-cast SDMs indicate that a net 28,215,247 ha (282,153 km2) of habitat has been lost, equating to a loss of between 16,779,704 and 52,243,938 breeding pairs (33,559,408–104,487,876 individuals; Supplementary Methods and Supplementary Table 5). One might expect that forest degradation, rather than resulting in broad-scale declines across species, is simply causing species turnover from old forest-associated bird species to young-forest associates. However, it is important to note that we quantified net bird decline from an unbiased list of the 54 most common forest bird species in eastern Canada. This list included both early and late successional species. Such net bird declines could be due to the fact that (1) even some early seral species are losing habitat (probably due to conversion from diverse early successional forest to species-poor plantations and thinnings)26 and (2) in this region, more species occupy older forests than regenerating forests27.We also quantified overall population trends for 54 species of forest birds using data from the BBS (Fig. 6). These estimates give the total magnitude of population changes which include, but are not limited to, habitat loss or gain effects. Thirty-nine of the 54 species examined (72%) are in population decline (defined as having 95% credible intervals that do not bound zero). The magnitude of the declines for 15 forest bird species is severe ( >5% per year). It is notable that most species exhibiting both habitat loss and population declines are old-forest associates (Fig. 4a; bottom left quadrant, dark green dots), with old-forest species exhibiting the greatest habitat losses (Fig. 4b and Supplementary Methods; hierarchical regression, (hat beta) = −16.66 [6.32 SE]).Fig. 6: Population trends for forest-associated birds in eastern Canada.a, Population trend parameter estimates and posterior distributions for 54 species of forest birds derived from Bayesian models. Seventy-two percent of species that are sufficiently common to model experienced population declines from 1985 to 2019. Colour key is provided in Fig. 5. The vertical green line indicates a population trend of zero. Dashed vertical lines coincide with trends of −15% (−0.15), −10% (−0.10) and −5% (−0.05) annual population trends. b, Predicted linear population trends for 1985–2019 (regression lines are mean trends derived from Bayesian Poisson models, Supplementary Methods) including annual variation estimated from BBS data. Shaded purple areas reflect 95% credible intervals and reflect the magnitude of species population declines shown in a. Populations of these eight old forest-associated species have declined 60–90% over the period observed.Full size imageBBS declines are not restricted to old-forest species; several species in rapid population decline are early seral species (for example, Lincoln’s sparrow [Melospiza lincolnii], mourning warbler [Geothlypis philadelphia]; Fig. 4a, bottom right quadrant). Despite the fact that these species have gained habitat over 35 years, their populations continue to decline. Only three species (black-capped chickadee [Poecile atricapillus], hairy woodpecker [Leuconotopicus villosus] and ruby-throated hummingbird [Archilochus colubris]) are increasing in abundance. Populations of these species increased despite evidence of habitat decline (Fig. 4a, top left quadrant)—perhaps because each benefit from anthropogenic habitats and supplemental food. Importantly, habitat changes from 1985 to 2019 along BBS routes were representative of changes at the scale of the entire region for most species (Extended Data Fig. 9), so BBS population trends are highly likely to reflect population trends at the regional scale. This contrasts to the 1965–1985 period when mature-forest loss along routes was slower than in the broader region28.We also modelled BBS population trends over the past ten years, as this is the period of importance for informing listing decisions under the Committee on the Status of Endangered Wildlife in Canada (COSEWIC). Nine species have exhibited population declines >30% over ten years (Supplementary Fig. 3), which meets the criterion for consideration as ‘threatened’ under COSEWIC Criterion A (ref. 29). More

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

This first national descriptive study used an indicator, which comprehensively reflects incident all-type hospitalized cases coded endometriosis in the French territory up to the municipality scale. We observed an increase in the risk of being hospitalized from 2011 to 2017 and spatial heterogeneity with the identification of 20 scattered hotspots in Metropolitan France as well as in 2 overseas departments.Descriptive resultsThe annual incidence rate (12.9/10,000 PYs) of all-type hospitalized cases coded endometriosis in France in females aged 10–49 years was of the same order of magnitude as the rates observed in other countries (Italy, Iceland) using similar methods29,30. Moreover, a recent meta-analysis2 estimated the pooled incidence rate of endometriosis based on hospital data to be 13.6/10,000 PYs (95% CI: 10.9; 16.3), which situates the French estimation within the confidence interval and close to the pooled value.In our study, 68.3% of all-type cases and 83.2% of non-adenomyosis cases were aged 25–49 years, and only 3.6% (8.5% for non-adenomyosis cases) were under 24 years. In young females, this low percentage could reflect underdiagnosis or delayed diagnosis, because histologic evidence may occur after an interval of 5–10 years following the first signs of endometriosis31. Moreover, many cases are fortuitously diagnosed during fertility check-ups, which rarely take place before 25 years of age. This age distribution in France is close to the distribution observed in a recent Italian study (3.6%  50 years) carried out using similar methods in the population of the Friuli Venezia Giulia region from 2011 to 201330. The Italian authors remarked a noticeable percentage of incident cases over 50 years of age for non-adenomyosis cases (11.5%), close to our results (8.3%), even though endometriosis is expected to attenuate after menopause. They suggested that endometriosis deposits could still be potentially active in older patients and be reactivated in the presence of certain hormones30. This hypothesis seems quite relevant regarding the potential link with EDC exposure. Indeed, the developmental hypothesis supposes that reproductive disorders at adult age could result from early (i.e., prenatal, perinatal, or pubertal) exposure to EDCs in specific exposure windows. In males, this hypothesis has been especially developed according to the so-called “testicular dysgenesis syndrome (TDS)”32. The disruption of fetal androgen action with EDCs, specifically in the “masculinization programming window” (MPW), induces a shorter anogenital distance that is supposed to provide a life-long readout of the level of androgen exposure in the MPW33 and is consistently associated in animals and humans with TDS troubles (cryptorchidism, hypospadias, poor sperm quality)34.In females, the mirror concept of “ovarian dysgenesis syndrome” has been proposed, including a higher risk to develop endometriosis35. Interestingly, endometriosis has recently been associated with a shorter anogenital distance in women36, and this anthropological indicator, measurable using MRI, could be useful for a non-invasive diagnosis of the disease37.In addition, some authors suggest that endometriosis onset could occur in two steps: an early hormonal-developmental step and a second hormonal step at adult age38,39, or a first initiation step with a second promotion step based on experimental tumor production40. Overall, these hypotheses could contribute to the unexpected proportion of hospitalized endometriosis cases identified after menopause. Another explanation could be the large number of fortuitous diagnoses of endometriosis at the same time as hysterectomies performed for diverse indications in women at an older age.Temporal trendsStudies on the temporal trends of endometriosis incidence used diverse methods and delivered differing results according to the country as reviewed in a recent study1. Only three studies carried out with hospital data in the general population are available. A Finnish study showed a decrease in incidence from 1987 to 201241. An Icelandic study did not conclude to any trend from 1981 to 200029, and a recent Korean study only showed an incidence increase in young women aged 15–19 and 20–24 years, but not in other age groups42.In France, the increase in the risk of being hospitalized, observed for both adenomyosis and non-adenomyosis cases, could reflect a real increase in the incidence of endometriosis, consistent with the perception of numerous clinicians. We did not observe an upward trend in females under the age of 25 years, which could reflect the underdiagnosis of this population. The global increase could also relate to the increasing use of non-invasive examinations, like ultrasounds or pelvic MRI during the study period. Pelvic MRI was only recommended by the French Health Authority at the end of the study period43, although clinicians would have anticipated this recommendation, which is supported by the results of the additional analyses (Supplementary Material). In the study period, there was a 69% increase in cases who underwent this examination concurrently with hospitalization, which accounted for around a third of cases. The increasing use of MRI (or ultrasounds) would result in more and more cases treated without hospitalization and could explain the apparent increase of hospitalized incidence at later ages and less at younger ages.Regarding the secondary indicator, the incidence rate in the whole of France during the study period remained steady. However, the trends differed according to each type (Table 4). The risk did not increase for endometrioma, a type of endometriosis that is not expected to depend on the use of pelvic MRI, but it did increase for intestinal endometriosis, expected to be strongly influenced by pelvic MRI. Therefore, these results also support the role of pelvic MRI. As for the divergent evolution of specific types of endometriosis, experts believe that it could depend on shifting practice patterns such as the more frequent tendency to medically treat endometrioma.Table 4 Number of incident cases of hospitalized endometriosis and crude incident rate for specific types of endometriosis for the study period in the whole of France, in females aged 10 years and above.Full size tableAnother factor could also contribute to the global increase in hospitalized endometriosis. Several patient societies (EndoFrance, Endomind, Info-endometriose) have strongly advocated for better detection and care of this disease and provided targeted information, which may have resulted in increased awareness of patients and clinicians regarding the disease during the study period.These factors are likely interlinked with a possible real increase in endometriosis incidence, which could be confirmed by a longer monitoring period.Spatiotemporal and spatial trendsThe spatiotemporal and spatial heterogeneity of the risk of hospitalized endometriosis that we observed in France during the study period could be related to spatial disparities and different evolutions in terms of detection and hospital care. In half of the 20 hotspots in Metropolitan France, we identified a town where an expert clinic for endometriosis was operational during the study period (Fig. 4). In the overseas departments, we identified an expert clinic in the Reunion Island, where we also observed a high incidence. However, we identified expert clinics in areas with a low or moderate risk of hospitalized endometriosis, especially in Paris (four expert clinics), Lyon (two expert clinics), Rennes, Brest, and Angers. Adjusting the spatial model at the department scale with the density of gynecologists and obstetricians using the available data provided by the shared inventory of health professionals from 2011 to 2016 did not change the geographic distribution (data not shown). Adjusting for incident cases of non-endometriotic ovarian cysts only brought about some changes in several departments in the north where the risk attenuated, even though it stayed above 1 (data not shown).Taken together, these results indicate that the activity of local expert clinics could only partially explain the spatial and spatiotemporal heterogeneity of the risk of hospitalized endometriosis. The contribution of environmental factors remains possible and plausible, as we argued above.The results of the exploratory cluster detection performed in Metropolitan France showed a negative relation with the socioeconomic deprivation index. Indeed, a high socioeconomic status (SES) or education level has been associated with a higher frequency of endometriosis44,45, which probably reflects the better detection and patient care of women with high SES. However, this relation was inverted in a recent Swedish study, although the authors partly attribute this inconsistent finding to egalitarian health care in Sweden46.Among the 40 detected clusters (p  More

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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