Annex A. Detailed descriptions of the assessment models examined in this project A1. DemCam Authors Bevacqua, D., Melia, P., Crivelli, A. J., Gatto, M. & De Leo, G. A. References Bevacqua, D., Melia, P., Crivelli, A. J., Gatto, M. & De Leo, G. A. (2007). Multi-objective assessment of conservation measures for the European eel (Anguilla anguilla): an application to the Camargue lagoons. ICES Journal of Marine Science 64, 1483-1490. Summary DemCam was developed specifically for the assessment of eel stock and catches in environments such as lagoons, low-lying water systems or uniform areas of rivers. A general formulation makes it suitable to describe the demography of different eel stocks, provided that sufficient data are available for the calibration of parameters. The model covers the continental phase of the life cycle, from the recruitment at the glass eel stage until the escapement of silver eels. It defines the eel stock and the harvest on an annual basis, structured by age, length, sex and stage (glass, yellow or silver eel). The model process The model specifically takes into account: • recruitment variability from year to year • carrying capacity of the system and density dependent survival of glass eels and adults • density dependent sex ratio • separate growth paths for undifferentiated, male and female eels • sex- and size-dependent natural mortality • sex- and size-dependent sexual maturation • fishing mortality depending on fishing effort and fish size, described in terms of gear selectivity and/or minimum landing size • possible extra mortality on silver eels during migration The model can be used to simulate the efficacy of different scenarios relevant to juvenile recruitment, fishing pressure and obstacles to migration. Detailed description of the model The model mimics the population dynamics of different cohorts of eels, with annual time step t. The population is structured in age and maturation stage, with the state variable given by N(t,x,s) indicating the abundance at time t of eels having age x and in maturation stage s (maturation stage can be undifferentiated, yellow males, yellow females, silver males, silver females). 1 Juvenile recruitment Any considered system is characterized by a settlement carrying capacity S , representing the MAX maximum number of settlers (recruits) that the system can sustain annually. This is a key parameter that determines density levels and consequent sex ratios (values of S usually range between 500- MAX 2000 elvers per hectare (ha) according to the system productivity). Every year, a glass eel recruitment (or stocking) of R individuals occurs in the system. Where elvers are stocked into the system, these are assumed to have ¼ of probability of surviving to become yellow eels, when compared against wild recruiting glass eels (Dekker, 2000). Whatever the value of glass eel recruitment R(t), no more than S elvers can enter the system and MAX contribute to cohort strength. In fact, the survival probability of recruited glass eels to the elver stage is computed as 1/(1+ R/S ) and consequently the effective number of settlers is computed as MAX S(t) =R(t)*1/(1+ R(t)/S ). MAX Sex ratio The fraction of males in the recruiting cohort is set as: • 0.25, if S(t)/S < 0.25; MAX • 0.75, if S(t)/S > 0.75; MAX • and S(t)/S otherwise. MAX Growth Growth has been estimated following the approach of Andrello et al. (2011) who adopted the eel growth model of Melià et al. (2006) to any other eel stock, providing that the age and length at silvering of males and females are known (See Andrello et al., 2011 for details). Individual weight w [g] is estimated from body length [cm] as w = a*l^b , where a = 8.34 10-4 and b = 3.17. These are the average parameters for weight/length relationships of A. anguilla from studies across Europe, as reviewed by Bevacqua et al. (2011). Natural mortality Natural mortality was estimated using the model of Bevacqua et al. (2011) that allows an estimate of mortality rates as a function of eel sex, size, mean annual water temperature and local densities of eel. The density level at time t is computed as a function of standing stock density N(t) and elver carrying capacity S Particularly, if N(t)/S < 1, density is assumed to be low, if 1< N(t)/S < 2, MAX . MAX MAX density is assumed to be average, and if N(t)/S >= 2 density is assumed to be high (see Bevacqua MAX et al. 2011 for details). Fishing mortality Fishing mortality rate is estimated as F = q*E(t)*φ , where q is catchability (a parameter representing eel susceptibility to the fishing gear), E is fishing effort (measured as number of gears per day per hectare) and φ is gear selectivity (ranging from 0 to 1) depending on mesh size and increases with fish size (see Bevacqua et al., 2009 for details). If a minimum landing size (MLS) is employed, φ is assumed equal to 0 for fish sizes < MLS. Note that if the data provider is able to provide a reliable assessment of fishing mortality rate F(t), data of E and q are not required. 2 Sexual maturation The probability that an eel will become sexual mature (silvering) at any length is computed according to the model of Bevacqua et al. (2006) with parameters modified according to the average maturation size and age of eel in the study system, as in Andrello et al. (2011). Migration mortality The model allows for an extra mortality on silver eel due to their susceptibility to obstacles during their downstream migration. In this case, an extra survival fraction for silver eels, σ , can be S considered before estimating the silver eel escapement. Data requirement The model requires time dependent data which might differ between years, and constant data which mainly reflects characteristics of the system and, for sake of simplicity and absence of reliable data, are erroneously considered as constant. The data requirements under these two classes are set out below: Time dependent data: • habitat availability at year t (ha) • glass eel recruitment + stocking at year t (kg) • elver recruitment + stocking at year t (kg) • fishing effort at year t (# gears per day) Constant data: • first year of simulation • last year of simulation • system carrying capacity (elvers per year per hectare) • survival probability from glass to elver stage (to convert elver to glass eel stocking) • annual average water temperature • average weight of a glass eel • average weight of an elver • parameters a and b used in the allometric relationship w=a*l^b • stretched mesh size (mm) • minimum landing size (mm) • yellow eel catchability q Y • silver eel catchability q S • average age for male silvering (yr) • average age for female silvering (yr) • average length for male silvering (mm) • average length for female silvering (mm) 3 Model Outputs The model assesses the stock abundance and population structure in terms of age, sex and maturation stage in every year of the simulation. The state variable is initially set equal to zero, hence all age classes are fully represented in the modelled stock when n years have passed, where n corresponds to the maximum eel age observed in the system. The results are saved in matrices having n rows and t columns, where t is the number of simulated years. The model produces matrices relevant to both abundance and biomass of standing stock, harvest and migrating stock (separately for males and females). The main results can be illustrated in figures. For example, Figures A1.1, A1.2 and A1.3, illustrate predicted time series of recruitment, yellow eel standing stock and silver eel production, respectively. Figure A1.1. DemCam simulation of glass eel recruitment and elver settlement over a 110 year time series. Note that the two y-axes show different scales, though both present individuals per hectare. 4 Figure A1.2. DemCam simulation of standing stock of yellow eel over a 110 year time series. The top chart shows yellow eel stock for males (blue) and females (red) measured in kg per hectare, while the lower chart shows the same time series but expressed as individuals per hectare. Figure A1.3. DemCam simulation of silver eel production over a 110 year time series. The top chart shows silver eel production for males (blue) and females (red) measured in kg per hectare, while the lower chart shows the same time series but expressed as individuals per hectare. 5 A2. Eel Density Analysis 2.0 (EDA) Authors Céline Jouanin(1), Cédric Briand(2), Laurent Beaulaton(3), Patrick Lambert(1) (1) Cemagref Bordeaux, 50 avenue de Verdun, 33612 Cestas cedex, (2) Institution d’Aménagement de la Vilaine, 8 rue Saint James, 56130 La Roche Bernard, (3) ONEMA, "Le Nadar" Hall C, 5 square Félix Nadar, 94300 Vincennes, France. References French Eel Management Plans. Summary EDA 2.0 (Eel Density Analysis) is a modelling tool which allows the prediction of yellow eel densities and silver eel escapement. The model is based on a geo-localized river network database, the CCM v2.1 (Catchment Characterisation and Modelling) (Vogt et al., 2007). The model is applied in France at the national level, and within the POSE project has been applied to 9 eel management units located in several European countries. The principle of the model is to extrapolate yellow eel densities from surveys to those in each reach of a river network, calculate the overall yellow eel stock abundance, convert these to silver eel equivalents and to estimate silver eel escapement by subtracting silver eel mortalities due to anthropogenic factors. It is also possible to give an estimate of the pristine escapement by running the EDA model with anthropogenic conditions artificially set to zero and time variable sets before 1980. Introduction EDA is a framework of eel density analyses rather than an end-user model. The basis of this methodology is that it is more efficient to calculate silver eel escapement with an indirect method based on yellow eel density, because direct estimations of silver eel densities are rare and difficult to extrapolate at the Eel Management Unit (EMU) scale. The modelling tool is based on a geo-localized river network database and designed to predict yellow eel densities and silver eel escapement. There are six main steps in the model application: 1. Relate observed yellow eel presence/absence and densities to habitat descriptors; 2. Extrapolate yellow eel densities from surveys to each river stretch by applying the statistical model calibrated in step 1; 3. Calculate the overall yellow eel stock abundance by multiplying these densities by the wetted area of each stretch; 4. Estimate a potential silver eel production from each stretch by converting yellow to silver eel abundance with a 5% rate of conversion; 5. Calculate the effective silver eel escapement by reducing production by mortalities during the downstream migration; and, 6. Sum the effective escapement from all the stretches to give an estimate at EMU scale. 6 EMU descriptions EDA is designed to be applied at the Eel Management Unit. In the POSE project it has been applied to the French “Brittany” and “Rhone”, the Irish “Western”, the Spanish “Basque”, and the English “Anglian” River Basin Districts (Figure A2.1). It has not been applied to the following places: • German “Elbe” River Basin District where eel stock is mostly based on restocking. Though the number and places restocked were available, the large number of yellow eel electro- fishing data necessary to calibrate the model could not be gathered easily. • Swedish “Swedish West Coast” River Basin District which corresponds to open sea and for which there are no data on eel densities. • Italian “Sardinia” River Basin District where the only data available were for the lagoons and eel density data were not available. Figure A2.1. Map of Europe showing the locations and areas of the Eel Management Units which were considered for the application of EDA Data Requirements The model requires data describing the abundance of yellow eel. These data are typically represented as density (d), calculated for electro-fishing operations corresponding to catches during at least two electro-fishing passes, divided by the wetted surface area surveyed, and expressed as number eels per 100m². 7 These densities are analysed in relation to a series of habitat descriptors as potential explanatory variables. The descriptor parameters are related to the characteristics of the river basin and the anthropogenic conditions (obstacles and land use). Most of the data on habitat variables are taken from the CCM v2.1 (Catchment Characterisation and Modelling), a European hydrographical database based on a topographic model (Vogt et al., 2007, http://ccm.jrc.ec.europa.eu/). The CCM2 database includes a hierarchical set of river stretches and catchments based on the Strahler order, a lake layer and structured hydrological feature codes based on the Pfafstetter system (De Jager et al., 2010). The primary catchment unit is the drainage area – this is the smallest entity in this hierarchy and is drained by CCM river stretch. This system allows the identification of all upstream catchments and all river stretches downstream of a given point along the river network. All the river stretches are connected. Stretch characteristics All explanatory variables are calculated at the stretch level. The following variables are calculated from the river topology of the CCM: • Distance from the sea (km), calculated as the distance from the river mouth to the downstream node of the river stretch, plus half of the length of the river stretch; • Distance from the source (km), calculated as the distance from upper node of the river stretch to the upstream source of that river line, plus half of the length of the river stretch; • Relative distance (km), calculated as the distance from the sea / total distance (distance to sea + distance to source), after Imbert et al. (2010); • Strahler and Shreve stream orders; • Mean elevation (m), the average elevation in the primary catchment; • Mean slope (°), the average slope in the primary catchment; • Altitudinal gradient (%), the gradient calculated as [(elevation at the upstream node - elevation at the downstream node) / stretch length)*100]; • Area of drainage directly into the stretch (km²), excluding the drainage into the upper node; • Area of drainage upstream of the river stretch (km²). Temperature (°C) and rainfall (ml) statistics are extracted from the CRU (Mitchell et al., 2004), corresponding to the mean long-term average annual temperature and precipitations in the primary catchment. River width The CCM2 provides data on the length of each stretch, but not the wetted area, which is necessary in order to transform eel densities to estimates of standing stock. Typically, river width is linked to the river discharge with a square-root link (Leopold & Maddock, 1953; Andrews, 1984; Julien & Wargadalam, 1995; Jiongxin, 2004; Lee & Julien, 2006; Caissie, 2006). The river discharge is approximately proportional to the drainage area, though this allometric relationship shows some regional variations (Benyahya et al., 2009). Thornton et al. (2007) have found a direct square-root relation between the river width and the upstream drainage surface area (river width = 4.98 catchment area 0.47). However, the river width relationship tends to violate the linearity and homoscedasticity assumptions of simple linear regression. These characteristics suggest using a two-parameter power function with a multiplicative error term: W =aCAb e ∈i ⇔log(w )=log(a)+blog(CA )+∈ i i i i i 8 ∈ where W is the river width and CA is the cumulative streaming area, a and b are constants and iis the multiplicative error term for the ith river stretch. Anthropogenic conditions Obstacle pressure The obstacle pressure is characterised by the cumulative number of structures (dams and weirs) from the sea to the stretch, and the accumulation of scores for the passability of eel at each structure. These scores are based on the assessment criterion of the upstream passability from Steinbach (2009, modified from Steinbach, 2006), that weights different variables of dam construction (waterfall height, roughness, structure profile) using a scoring key that penalizes (+) or facilitates (-) an eel’s upstream passage. Land use Land use influences morphology, sediment transport and riparian vegetation, and therefore indirectly, fish populations. Catchment vegetation, especially riparian (streamside) vegetation, has been implicated as a major factor controlling fish populations in streams through its influence on availability of light, water temperature, and channel stability (Hicks et al., 1991). Hanchet (1990) recognised that in-stream habitat varied between land-use types and considered this the most likely explanation for the distribution of some fish species. Hicks & McCaughan (1997) observed a strong land-use effect on fish, such that pasture streams had the highest fish density, and biomass and eel production. Productive land uses (e.g. agriculture and forestry) have been shown to affect many of the characteristics of streams including fish (Hanchet, 1990; Jowett et al., 1996). Anthropogenic landscape disturbances such as row crop agriculture, deforestation and grazing shift the structural and functional relationships among the landscape elements and the stability of the physical environment. Consequently, land-use activities result in significant alterations in the population and community dynamics of stream fishes (Schlosser, 1991). For POSE, we used the pan-European land cover and land-use classification CORINE (Co-Ordination of Information on the Environment, CLC2006, 250m, version 12/2009) to provide land cover information in the analyses (European Commission, 1994). The data are obtained from the European Environment Agency website and are available at http://www.eea.europa.eu/data-and- maps/data/corine-land-cover-2000-clc2000-seamless-vector-database-1. For POSE, we grouped the 44 CORINE Land Cover classes into a simplified version with 3 groups (Table A2.1), to distinguish between low (no impact), medium (agricultural) and high (urban) impacts. 9 Table A2.1 Corine Land Cover grouped nomenclature. 3 groups Levels in CLC 1.1 Urban fabric 1.2 Industrial, commercial and transport units Urban 1.3 Mine, dump and construction sites 1.4 Artificial non-agricultural vegetated areas 2.1 Arable land Agricultural 2.2 Permanent crops 2.4 Heterogeneous agricultural areas 2.3 Pastures 3.1 Forests 3.2 Shrub and/or herbaceous 3.3 Open spaces with little or no vegetation No impact 4.1 Inland wetlands 4.2 Coastal wetlands 5.1 Inland waters 5.2 Marine waters The percentage of each land use category is calculated for each river stretch drainage area, as well as for the area of catchment upstream of each stretch. Detecting co-linearity Given the range of habitat descriptors and the possibility of complex links between, for example altitude and mean annual temperature, gradient and land-use, we first explore the datasets to test for any co-linear relationships between explanatory variables. High co-linearity can result in coefficient estimates that are difficult to interpret as independent effects and/or have high standard errors (Neter et al., 1990, Graham, 2003). We have decided to avoid using correlated variables in the model and therefore we tested each variable separately, as we didn’t know which variable was relevant, or might have the higher ecological meaning. We use the Spearman rank correlations coefficient rather than the Pearson correlation coefficient because the former makes no assumptions about the linearity in the relationship between the two variables (Zar, 1996). We also use the ‘varclus’ function in the library ‘Hmisc’ (Venables & Ripley, 2003; Harrell, 2002; Sarle, 1990). This function carries out a hierarchical cluster analysis, using the square of Spearman’s rank correlation (ρ2) as a similarity metric to obtain a more robust insight into the correlation structure of (possibly non linear) predictors. We use the rule of thumb from Booth et al. (1994) that suggests that a correlation between pairs of variables with magnitudes greater than ±0.5 indicate high co-linearity. To reduce the co-linearity, a set of candidate predictors are selected in the model in such a way that co-linearity problems are minimized (Draper & Smith, 1981; Alzola & Harrell 2002). To avoid spurious correlations, a separate entry is used for the set or pairs of variables tightly correlated. For the Corine Land Cover groups, we selected only a combination of two variables because the sum of ‘p_agricultural+p_urban+p_other’ and the sum of ‘p_up_agricultural+p_up_urban+p_up_other’ are equal to 1. 10