Scottish Marine and Freshwater Science Volume 5 Number 13: Population consequences of displacement from proposed offshore wind energy developments for seabirds breeding at Scottish SPAs

2 Methodology

In this section we detail the development and validation of foraging model inputs (prey and bird density maps), the foraging model, and the subsequent translation of model output (adult body mass) into estimated population level adult survival.

2.1 Prey and bird density maps

A key aspect of the project involved the production of maps of expected bird and prey densities within the Forth/Tay area: bird density and prey density are key inputs to the foraging model, and it is therefore important that the spatial variations in these quantities represent, insofar as is practically possible, the actual characteristics of the Forth/Tay area.

2.1.1 Data on bird distributions

Data on bird distributions for the four species under initial consideration (kittiwake, guillemot, razorbill and puffin) were taken from GPS loggers that had been deployed on individual birds from the four SPAs of interest (Forth Islands, St. Abbs Head, Buchan Ness and Fowlsheugh) during the chick-rearing phases in 2010, 2011 and 2012. GPS tracking data enable us to estimate the relative spatial densities of birds that have come from a specific SPA; this would be difficult to do using at-sea or aerial transect data, because for transect data the origin of the bird is not known and non-breeding, as well as breeding, birds may be included in the counts. The initial intention had been to use at-sea, rather than GPS, data for puffins, because the GPS data for this species are limited. However, it was ultimately decided that GPS data would also be used for this species, since the at-sea data from outside the wind farm development areas but lying within the potential foraging range of the birds, available from the ESAS database, have poor coverage in recent years. Furthermore, the years for which coverage is good (the 1980s) represent periods when the population size and environmental conditions were very different to the present.

GPS data record the geographical location of each bird at specific points in time. The numbers of tracked birds for each species, SPA and year are shown in Table 2:1. Of the twelve species-by- SPA combinations that we consider, six have tracking data from more than 20 birds (all four SPAs for kittiwake, and Forth Islands for guillemot and razorbill), four have tracking data for less than 20 birds (guillemot for St. Abbs Head, Fowlsheugh and Buchan Ness, and puffin for Forth Islands), and two have no tracking data at all (razorbill for St. Abbs Head and Fowlsheugh).

Table 2:1: Availability of GPS tracking data for each species and SPA. Note that Buchan Ness is not an SPA for razorbill or puffin, and Fowlsheugh and St Abb's Head are not for puffin.

Species	SPA	Total number of tracked birds in
		2010	2011	2012
Kittiwake	Forth Islands	36	0	17
Kittiwake	St. Abbs Head	0	25	15
Kittiwake	Fowlsheugh	0	35	15
Kittiwake	Buchan Ness	0	0	25
Guillemot	Forth Islands	31	0	19
Guillemot	St. Abbs Head	0	8	1
Guillemot	Fowlsheugh	0	9	10
Guillemot	Buchan Ness	0	0	6
Razorbill	Forth Islands	18	0	15
Razorbill	St. Abbs Head	0	0	0
Razorbill	Fowlsheugh	0	0	0
Puffin	Forth Islands	0	0	7

GPS tracking locations are nominally obtained once every 100 seconds, but in reality the gaps between consecutive records are often much longer than this (because during the intervening period the logger has not been able to obtain signals from sufficient satellites to compute an accurate estimate of current location).

The raw data obtained from GPS loggers were processed and filtered in four ways:

1/ Spurious duplicate records that occur when the signal to the satellite is lost were removed;

2/ Records with obvious location errors (where distance from the colony is implausibly large) were removed;

3/ Records within 1km of the colony were filtered out in order to retain only locations at sea;

4/ Records for which speed exceeds 14km/h were filtered out in order to retain only locations at sea associated with foraging or resting behaviours. This is the point that lies at the bottom of the trough of the bimodal distribution of speeds, one peak corresponding to the bird in flight and one to the bird not in flight. The exact threshold speed varies between species, but 14km/h is a reasonable compromise.

The overall number of GPS location records, after filtering, is shown in Table 2:2.

Table 2:2: Total number of GPS track locations and records, after filtering, for each species-by- SPA combination.

pecies	SPA	Total number of GPS records	GPS records per bird, mean and ( SD)
Kittiwake	Forth Islands	26325	497 (500)
Kittiwake	St. Abbs Head	19777	494 (265)
Kittiwake	Fowlsheugh	25253	505 (332)
Kittiwake	Buchan Ness	16352	654 (413)
Guillemot	Forth Islands	31899	638 (342)
Guillemot	St. Abbs Head	7411	823 (482)
Guillemot	Fowlsheugh	10280	541 (318)
Guillemot	Buchan Ness	3678	613 (136)
Razorbill	Forth Islands	16333	495 (390)
Razorbill	St. Abbs Head	0	-
Razorbill	Fowlsheugh	0	-
Puffin	Forth Islands	7465	1066 (681)

2.1.2 Estimation of bird densities

For each species, bird densities were estimated from the filtered GPS tracking data using a Binomial generalized additive model ( GAM). This model compares the characteristics of the GPS tracking locations against the characteristics of a set of 'control' points that represent the set of positions that birds could potentially have visited. We take the control points to be on a regular 0.5 x 0.5km grid; the grid only includes points that are within a certain pre-specified distance of the SPA. This distance is taken to be either the maximum distance from colony that is observed in our GPS data, or the mean foraging trip length that is reported in the literature - we select whichever of these two values is greater in order to avoid excluding potential foraging areas from the analysis (

Table 2:3). For kittiwake, the maximum distance from colony observed in the GPS data is much larger than the mean foraging trip length reported in the literature; in order to avoid the computational cost of using a very large grid of points, we take the maximum distance for this species to be 170km on the grounds that only a very small number of GPS records (28, or less than 0.04% of the entire dataset) occur beyond this distance (Figure 2:1).

The "foraging range" of the simulated birds was derived from the modelling of the GPS data, not from the specified 'maximum distance' value. The latter value is purely included for computational reasons, to ensure that we do not simulate birds in areas where they are very unlikely to occur (according to the GPS data) because (a) there is no point in doing so (birds wouldn't be sent there in practice because the probabilities associated with these areas are so low) and (b) it would substantially increase the computation to try to do so. This range is set to be sufficiently high that there would be a very low probability of birds travelling beyond it, according to the GPS data, but sufficiently low that computation is still feasible. The exact trade-off between the two things varies between species, but we have always tried to set the limit as high as we feasibly can - this is not conservative as such, because it simply ensures that the simulated distribution of foraging locations matches the observed distribution as closely as possible.

Table 2:3: Maximum distance to colony in GPS data, mean maximum distance from colony in literature (Thaxter et al. 2012) and maximum distance used in the analysis.

Species	Maximum distance from colony seen in GPS data	Mean maximum distance from colony (from literature)	Maximum distance used for our analysis
Kittiwake	246.1km	60km	170km
Guillemot	70.4km	84km	84km
Razorbill	70.0km	49km	71km
Puffin	66.1km	105km	105km

The GAMs are fitted simultaneously to data for all years and SPAs that have GPS tracking data. The models assume that the predicted density of birds can be decomposed into two parts: the first part captures the effects of distance to source SPA and distance to other nearest SPA (these are both assumed to have a linear relationship with log(density); the latter incorporates the potential effect of intraspecific competition) and a smooth term which represents spatial variations that cannot be attributed to distance to colony. These two components can be regarded as corresponding to "accessibility" and "suitability", respectively. The models are fitted in R using the bam function from the mgcv package. We had initially tried to fit models that described suitability in terms of environmental variables such as depth, sea surface temperature and sediment type ('habitat association models'), but this approach proved to be largely unsuccessful when it was applied to guillemots (see Appendix A) and was therefore abandoned. The GAM approach is somewhat similar to kernel density estimation, but it has the advantage that the smooth estimated density can be decomposed into components that relate to the characteristics of the location (suitability) and the availability of the location to birds from each SPA (accessibility).

The GAMs can be used to provide an estimate of the predicted bird density for each species-by- SPA combination. For species-by- SPA combinations without GPS tracking data (Razorbill at St. Abbs Head and Fowlsheugh) the model does not provide a meaningful estimate of suitability, and the predicted bird densities are therefore based solely on the estimated effects of distance to source SPA and distance to next nearest SPA.

Figure 2:1. Bird density map for Kittiwakes. GPS data were available for birds at all four SPAs. The greater densities with increasing latitude reflect the larger colony sizes in the north of the study area.

GPS data on guillemots at Buchan Ness are more limited than those for any other species-by- SPA combination, and expert judgement suggests that they may not be representative (with most points occurring very close to the colony); these data are therefore excluded from our analyses, and predicted bird densities for guillemots at Buchan Ness are based on the distance to source SPA and distance to next nearest SPA effects that have been estimated using data for the remaining guillemot colonies.

2.1.3 Estimation of prey densities

We consider two scenarios for estimating the relative density of prey at different locations:

a) we assume that the density of prey is proportional to the suitability values that were estimated from the bird GPS tracking data ("heterogeneous prey"); and

b) we assume that the density of prey is uniform across the entire Forth/Tay area ("homogeneous prey").

The heterogeneous prey scenario is based on the assumption that the distribution of foraging locations of birds across prey will, after accounting for the accessibility of locations to birds, be proportional to the distribution of prey across space. The homogeneous prey scenario assumes that prey densities are unrelated to the density of bird foraging locations. These represent two extreme scenarios, which form the ends of a continuum: it is likely, in reality, that bird foraging densities are related to prey densities but that they are not completely determined by prey densities. Comparing output from the two approaches therefore allows for a qualitative assessment of our uncertainty that is involved in accurately understanding the interaction between birds, wind farms and prey.

For the species-by- SPA combinations without adequate GPS tracking data (Razorbill at Fowlsheugh, Razorbill at St. Abbs, Guillemot at Buchan Ness) it is only possible to consider the uniform prey scenario. Therefore, prey density at colonies without GPS data was assumed to be uniform across the foraging range of the species. In areas of overlap between the foraging range of a colony without GPS data and a colony with GPS data, prey density was estimated from the GPS data.

2.2 The foraging model

We developed a model to simulate the feeding locations of multiple colonies over the chick-rearing period. The model simulated seabird foraging decisions assuming individuals were acting in concordance with optimal foraging theory. Each individual selected a suitable location for feeding during each foraging trip based on the spatial distribution of birds that was estimated from GPS tagging data using the approach of Section 2.1.2. Subsequent behaviour of birds was then simulated incorporating realistic assumptions and constraints derived from observed behaviour. The model simulated foraging behaviour for five species (note that exploratory analyses were carried out on four species excluding gannet, and final runs on all five species - see Section 2.6). The model was created and run using the statistical software R v 2.14.1(R Development Core Team 2012).

Fundamentally, we assumed that the foraging behaviour of individual seabirds was driven by prey availability, travel costs, provisioning requirements for offspring, and behaviour of con-specifics. Choice of foraging location was dependent upon prey density distribution maps produced using the GAM suitability models ( Section 2.1.3). Flight cost was determined using linear distances from the central foraging location ( SPA). We also obtained data on the bathymetry of the area from the British Geological Survey under licence ( http://www.bgs.ac.uk/products/offshore.html) to determine the maximum possible dive depth for a bird foraging at each location.

The values for parameters are given in Table 2:4 and the sources for these values in Appendix D.

2.2.1 Selection of foraging location

Foraging location was selected by an individual bird based on the estimated distribution of foraging locations (that was calculated empirically using GPS tracking data; Section 2.1.2). Birds were apportioned to foraging locations in proportion to the estimated probability density from the bird distribution model for each cell in the simulated seascape (cell size 1.67km x 1.67km). The selection process was done stochastically using random numbers and cumulative density distributions of the predicted probability of foraging per cell. The density estimation is specific to each colony, such that colony level effects such as distance from colony and inter-colony density-dependent competition are included within the foraging location choice of all simulated birds.

Once all simulated birds had been assigned to a foraging location, the estimated prey density at each location ( Section 2.1.3) was multiplied by total overall prey abundance to find the prey abundance associated with each grid cell in the simulation. No observational data were available on prey abundance; an overall prey abundance value for each species was therefore determined by running the foraging model using a range of possible values for total prey abundance (without any wind farms present) and choosing the value that gave the best match to empirical data on key bird traits (adult mass and survival, chick mass and survival, nest attendance rates, foraging hours and flight hours) during the breeding season (see Appendix F, section F1).

The daily energy requirement ( DER) of each bird was then determined (see sections 2.2 & 2.3), and a calculation was made for each cell to determine if all birds that chose to forage there were able to meet their DER. This was done by comparing the total prey abundance within each cell to that required by summing the DER of all birds that have chosen to forage within that cell. Any resulting energy deficit was then averaged across all birds within the focal cell to determine the proportion of each bird's DER that they were able to meet at that location. These deficits were recorded and used to update the bird's body mass and that of its chick, and its subsequent behaviour at the next time step.

The total prey abundance per cell was then combined with the DER of each bird in the focal cell (via the functional response, see Section 2.2.2.1) and the total number of birds that chose to forage within the focal cell (via the interference competition equation, see Section 2.2.3) to determine the time each bird must spend foraging to meet its DER (or proportion thereof) in each cell. As a result, for each day and simulated bird, the model simulated the total time spent foraging, the total time spent in flight, and the proportion of the DER of the bird and chick that it was able to meet.

This process is summarised in Figure 2:2.

Figure 2:2: Diagram of foraging model structure and relationships between variables. Input data are in green boxes and model output used to estimate bird energy budgets are in pink boxes. All boxes contained within the dotted box represent the core of the foraging model functions, and are stochastic variables estimated for each simulated bird.

2.2.2 Intake rate and intra-specific interference competition

Two of the most important behavioural mechanisms governing the acquisition of energy in seabirds are the functional response (how intake rate varies with prey density) and intra-specific competition (how intake rate of an individual is affected by the density of other birds foraging in the same location). We created a set of rules determined from optimal foraging theory assuming that birds would employ behaviours to maximise daily energy gain up to an upper limit set from observational data on the DER of each species.

2.2.2.1 Functional response and achieved intake rate

Prey availability is the principal determinant of the amount of time an animal must spend foraging to meet its DER. Typically this relationship is modelled using a functional response equation that relates prey intake rate to the density of available prey at a particular foraging location. Empirical functional response estimates for seabirds are lacking, however using empirical data on the time spent foraging by 18 guillemots (Wanless et al. 2005) we estimated the key components of the functional response assuming a Type III response (Enstipp et al. 2007). We set a maximum prey intake rate per minute for each species based on available data (see Table 2:4). Our approach was to take the maximum mass of single prey and the mean prey capture rate to obtain an estimate of the maximum prey capture rate, based on empirical data (Birt-Friesen et al. 1989; Humphreys 2002; Lewis et al. 2003; Daunt et al. 2006; Harris & Wanless 2011; Thaxter et al. 2013, unpublished data). We obtained plausible values for all species except gannet. For this species, we set the maximum single prey recorded (559.4g, Lewis et al. 2003) as the maximum prey intake rate per minute, on the assumption that a second prey could not be obtained in that time period. We estimated that intake rate would not increase significantly until a certain prey density of prey per km ² was exceeded. The parameters controlling the shape of the functional response (rate of increase in intake rate with increasing prey, and density of prey at which intake rate starts to increase) were set using expert opinion such that resulting intake rates achieved by simulated birds matched with knowledge regarding each species. Having defined the form of the functional response, we then calculated the prey capture rate for each individual foraging at its chosen location by multiplying the prey intake rate by the diving efficiency. The diving efficiency was included to account for the extra energy cost incurred with increasing dive depth (Daunt & Wanless 2008). Unlike razorbills, puffins and gannets, which are pelagic feeders, guillemots feed both benthically and pelagically, with a bimodal distribution of foraging depth (Daunt et al. 2006; Thaxter et al. 2010). To allow for this, 50% of guillemots were assumed to dive to the seafloor or the maximum dive depth recorded for the species, whilst the remaining 50% of guillemots selected a dive depth from a normal distribution with a mean of 11.71m and a standard deviation of 8.07m derived from empirical data (Daunt & Wanless 2008). Kittiwakes do not dive, therefore the diving efficiency adjustment was not used for this species. For all species, the resulting prey capture rate was used to determine the foraging time required by each bird to meet its DER for each time step.

Independent intake rate was defined using a sigmoidal function (Type III functional response) with three estimated parameters ( IR.max, IR.mu and IR.lambda) and prey density (x):

Independent intake rate: IR.max * exp(-exp(( IR.mu * exp(1) / IR.max) * ( IR.lambda - x) + 1)) * diving efficiency

Intra-specific interference competition

Intra-specific interference competition was included in the foraging simulation model using the model of Hassell & Varley (1969):

a _i = Q* P ^{- m}

where a _i is the intake rate of an individual bird, Q is the intake rate achieved by a single bird foraging alone (derived from the equation above in section 2.2.2.1), P is the density of other individuals foraging at the location and m is the interference coefficient. The interference coefficient determines the strength of the density dependent reduction in intake rate due to conspecific foragers sharing the same location. The intake rate achieved by a single forager, Q, was determined by the prey availability and functional response curve for each species, P was the number of simulated seabirds choosing to forage at each location, and the level of interference, m, was set at a realistic value for each species based on previous observations and expert opinion (Ens and Goss-Custard 1984, Dolman et al. 1995, Goss-Custard et al. 1995), and by matching model output (adult intake rates, adult body mass change, foraging time) to observed values for each species.

2.2.3 Cost model

We developed a cost model to accrue the amount of time and energy birds expended in reaching and foraging within their chosen location. This model was an expanded version of that used in Daunt & Wanless (2008) and Wanless et al. (1997) and separated the flight cost and foraging cost for each seabird to derive total energy expenditure.

2.2.3.1 Activity costs

Foraging cost for each bird was defined as the amount of time an individual was required to spend foraging to meet both its own DER and 50% of the DER of its offspring. On the first time step of the simulation, adult Daily Energy Expenditure ( DEE) was drawn from a normal distribution parameterised using the mean and standard deviation of adult DEE from empirical data. On all subsequent days adult DEE was set to match the energy expended by each bird in the previous time step. Chick DEE remained constant throughout the simulation. We chose not to model increases in chick DEE with growth in order to constrain model processing time to reasonable limits. The species-specific mean daily energy requirement of chicks was based on provisioning rates recorded at colonies for each species (see Table 2:4). This calculation implies both parents share the costs of provisioning equally. The resulting required daily energy expenditure ( DEE) was divided by an assimilation efficiency (0.78, Hilton et al. 2000) to obtain the total DER of the birds.

Daily time budgets of birds during chick-rearing demonstrate that adults divide their activities into four categories of behaviour - foraging, flight, time spent at the colony, and time spent resting on the sea surface (Daunt et al. 2002). For each bird, the foraging model returns the simulated flight time for each bird spent travelling to its chosen foraging location, and the simulated foraging time required to meet its required DEE. The remaining time during each model time period was split into time spent at the colony and time spent resting at sea. A minimum of one hour spent resting at sea was required for each bird (Daunt et al. 2002), and each bird attempted to spend half of each time step at the colony thereby preventing unattendance of its chick at the nest. Any remaining time was split evenly between time at the colony and time resting at sea. If a bird could not meet its DEE in the time available without unattending its nest, a set of decision rules were implemented based on the energy state of the adult. If an adult had a body mass that exceeded 90% of the mean body mass of an adult for that species at the start of the breeding season (based on empirical data; Appendix D) then it would return to its nest regardless of its achieved DEE for that day to prevent leaving its chick unattended. However, if its body mass was between 80-90% of mean initial mass then it would continue to forage to meet its required DEE for that time step, thereby leaving its chick unattended if its partner was not at the nest at that time.

We derived the flight cost incurred by each seabird by calculating the time taken to travel the distance both to and from the chosen foraging location assuming a mean flight speed for each species.

We then multiplied the time spent carrying out each of these activities by species- and activity-specific energy costs available from the literature ( i.e. cost of flight, foraging, resting at and time at colony; Appendix D). In addition, we incorporated the energy cost of warming food to derive the total DER for each bird (Gremillet et al. 2003). These DER were converted into grams per day assuming a mean energy density of 6.1 kJg ^-1 (Harris et al. 2008).

2.2.4 Behavioural modes for adults and chicks and subsequent decisions

At the end of each time step each adult was assigned to a behavioural mode that determined its behaviour in relation to chick rearing in the following time step. Behavioural modes for adults were determined by a critical mass threshold below which the adult is assumed to defend its own survival above that of its chick. Therefore, when an adult's body mass was greater than 90% of the average initial pre-breeding season mass for the species (based on empirical data; Appendix D) it would not unattend its chick, even if it had not met its DEE. However, if its body mass was between 90% and 80% of the average pre-breeding season mass it would favour itself, and leave its chick unattended in order to achieve its required DEE. Adults with a bodymass of less than 80% of the average pre-breeding season mass switch to nest abandoned mode and give up the breeding attempt. This necessarily means that their partner also gives up the breeding attempt, resulting in chick death. Should an adult's body mass fall below that deemed critical for survival (60% of the average pre-breeding season adult body mass for each species), the adult is assumed to have died and is removed from the simulation. This causes its partner to switch to nest abandoned mode for the remainder of the simulation.

Behavioural modes for the chick are determined by the body mass of the chick at the start of each day. If the chick's body mass falls below a critical threshold ('chick_mort_f', Table 2:4) it is assumed to have died and is removed from the population, causing its parents to switch to 'nest abandonment' behaviour. Because the value of this parameter is not known for most of the species, it was fit within the model such that model output on chick survival rates in relation to observed data for each species (Table 2:4). If the time a chick's parents spent attending the nest fell below a critical threshold the chick was assumed to die through exposure and was removed from the population ('unnattendance_hrs', Table 2:4) - again causing its parents to switch to 'nest abandonment' mode. We also incorporated an increased risk of predation if a chick was left unattended by both parents for an amount of time less than that which would result in its death through exposure. This was modelled as a probability of death that increased linearly with time left unattended, up until the time threshold was reached at which point the chick was assumed to have died from exposure or predation ('unnattendance_hrs', Table 2:4). Again, because there are no data on which to set a value for the length of time a chick is unattended that is likely to result in death we estimated the value of this parameter by matching model output (chick survival) to observed values for each species (Table 2:4).

For burrow-nesting puffins, once the chick reached a certain energy deficit (80% of the body mass of a chick that have been provisioned with all its requirements at every previous time step) it was assumed the chick ventured to the entrance of the burrow and suffered a linearly increasing predation risk with its body mass deficit as a consequence (between 60% and 80%). Above the threshold body mass value of 80% there was no risk to the chick from unattendance by parents. Below the lower threshold of 60% the chick was assumed to have died.

2.2.5 Adult body mass change

All adult birds updated their body mass at the end of each day based on the energy they gained and expended in foraging and other activities

If the adult was able to successfully meet its estimated DER within the constraints of the time period its body mass was assumed to remain constant. However, if the adult was unable to meet its estimated DER within each time period its mass decayed according to the following equation:

Adult mass at time t = adult mass at time t-1 + (adult mass at time t-1 ^ ( adultmass.a* proportion)) - (initial adult mass ^ adultmass.a)

where adult_mass_a (Table 2:4) was a parameter controlling the extent to which the daily energy deficit results in a reduction in adult body mass at the next time step, and 'proportion' was the percent of daily DEE achieved by the bird. This parameter was estimated from empirical data on the decline in body mass of adult birds during the breeding season ( Appendix F, section F1).

2.2.6 Chick growth

Chick growth between days t-1 and t was a function of the mass on the previous day (t _-1) and the food it received on day t. The new mass at the end of each day was assumed to be related to the mass on the previous day using a sigmoidal function, such that chick growth increased with food provided but reached an asymptote at a maximum growth rate per day (whose value was fixed based on observed data; Appendix D). Similarly, chicks lost mass when adults failed to provide enough to satisfy the chick's DEE, but again mass loss was curtailed such that mass loss per day matched observed patterns. The assumed relationship was of the form

Chick mass at time t = chick mass at time t-1 + ( chickmass.a * exp(-exp(( chickmass.mu * exp(1) / chickmass. a) * ( chickmass.lambda - x) + 1)))

Where chickmass.a was the maximum mass gain (g) per day, chickmass.mu was the rate at which growth rate increased with the increase in food provided by the adult, and chickmass.lambda was the mass of food (g) provided by the adult at which chick growth was positive, and ' x' was the amount of food provided by the adult (g). The equation requires an estimate for the chick's assimilation efficiency (a.e, which was assumed to equal that of an adult).

Because life history theory demonstrates that long-lived species such as seabirds will prioritise their own survival over that of their offspring, we created a variable in the model ('adult_priority', Table 2:4) that determined the extent to which an adult bird favoured its own energy intake over that of providing for its chick. The value of this parameter can take on values from zero to one. A value of zero meant the adult favoured the chick above its own survival ( i.e., all food acquired by the adult was supplied to meet the chick's DEE and any remainder was left for the adult); a value of one meant that the adult favoured itself over its chick ( i.e., all food acquired by the adult was used to satisfy the adult's DEE and any remainder went to its chick). The values for this parameter for each species were set such that observed model output (adult mass change, chick mass change and survival) matched observed data ( Appendix F, section F1).

2.2.7 Time steps and number of flights per day

Variable time steps were set for each species based on understanding of the behaviour of each species and the typical observed length of foraging trips ( Appendix D). For Kittiwakes the model time step was 36 hours with 30 time steps (amounting to a 45 day chick-rearing period); for guillemot and razorbills the model time step was 24 hours with 21 time steps (amounting to a 21 day chick-rearing period); for puffins the model time step was 24 hours with 40 time steps (amounting to a 40 day chick-rearing period); and for gannets the model time step was 72 hours with 30 time steps (amounting to a 90 day chick-rearing period).

The number of flights per day was determined by the success of each bird's first simulated flight at the start of each time step. The number of flights for all species varied between one and three, with the exception of puffins where the number of flights varied between one and four per time step (in accordance with observed data; Appendix D). Given the lack of precise mechanistic understanding for the context- and state-dependence of foraging decisions in seabirds, such as the number and length of foraging trips to make per day, we formulated the foraging model such that the behaviour of birds matched empirical data on observed numbers of trips per day and the approximate duration of time spent foraging and time spent in flight. As such, at the start of each time step one foraging trip was simulated for each individual in the population. If an individual was able to meet one third of the combined DEE for itself and its chick in one third of the time step then the individual simply repeated the same foraging trip two more times to create the energy and time budget for that individual for the entire time step (resulting in three foraging trips to the same location per time step; note that no temporal depletion of prey occurred with the model timestep). If an individual could not meet the combined DEE in one third of the time step, we then calculated if it could meet half of its requirements in one half of the time step. If this were the case, that individual repeated the initial foraging trip one more time to create the final time-energy budget for that bird (resulting in two relatively longer foraging trips to the same location in the time step). Similarly, if an individual could not meet its combined DEE in one third or one half of the time step, we determined if it could meet its requirements within the entirety of the time step, and if so then the individual made just one, longer foraging trip to a single loaction per time step.

However, if the individual could not meet its combined DEE using any of the above possibilities, we assumed that bird would attempt to make two foraging trips within the time step, and randomly selected a second simulated foraging trip from another bird that had made two foraging trips. Therefore the bird would make two foraging trips, each to a different location. These birds would not meet their full requirement for the time step.

2.2.8 Sources and values for parameters in the foraging model.

Where available we set values for all parameters in the foraging model from published literature or CEH data from the long-term study on the Isle of May. When values were not available, parameters were fit such that they matched expert opinion and led to model output that matched empirical data on adult body mass change, chick growth and chick survival, foraging time and flight time. All parameters are listed in Table 2:4 below, and sources are given in Appendix D.

Table 2:4 Values for all parameters used in the foraging model runs with 1000 birds. Please note that parameter estimates for gannets are in Table 2:8, since they were not included in exploratory runs. See Appendix D for source references.

Parameter description	Parameter name	Species 1	Species 2	Species 3	Species 4
Short name	SID	Gu	Rz	Kw	Pu
Species name	Name	Guillemot	Razorbill	Kittiwake	Puffin
initial body mass mean, g	BM_adult_mn	920.34	600	361.64	392.8
initial body mass standard deviation, g	BM_adult_sd	57.44	87	36.14	21.95
Critical mass below which adult is dead, proportion of mean mass	BM_adult_mortf	0.6	0.6	0.6	0.6
Critical mass below which adult abandons chick, proportion of mean mass	BM_adult_abdn	0.8	0.8	0.8	0.8
Chick initial body mass mean, g	BM_chick_mn	75.8	64.9	36	42.2
Chick initial body mass standard deviation, g	BM_chick_sd	1	6.3	2.2	3.7
Critical mass below which chick is dead, proportion of initial mass	BM_Chick_mortf	0.725	0.8	0.6	0.6
Critical time threshold for unattendance at nest above which a chick is assumed to die through exposure or predation, hours	Unnattendance_hrs	96	96	18	NA
Mean adult DEE for initial DEE, kJ per day	adult_ DEE_mn	1489.1	1231.89	802	871.5
Standard deviation for initial adult DEE, kJ per day	adult_ DEE_sd	169.9	95.3	196	80
chick energy expenditure, kj per day	chick_ DEE	221.71	195.67	525.71	325
maximum prey intake rate, g min-1	IR_max	23.17	28.47	22.98	19.71
slope of the functional response assuming a Type III response	IR_mu	0.0008	0.001	0.001	0.006
intake rate does not increase significantly until a prey density of IR_lambda individuals per km2 is exceeded	IR_lambda	9000	10000	8000	1500
forage interference coefficient	IR_m	0.15	0.6	0.3	0.6
Average speed in flight, metre per second	flight_msec	19.1	16	13.1	17.6
Number of trips carried out per day (from observed data)	Nforagetrips	2.02	2.35	1.9	3.34
fraction of dives assumed to be pelagic not to sea bed	pelagic	0.5	1	1	1
mean diving depth (set to 0 for non diving species)	forage_depth_mn	11.71	6.5	0	4.15
sd of diving depth (set to 0 for non diving species)	forage_depth_sd	8.07	5.2	0	2.1
assimilation efficiency	assim_eff	0.78	0.79	0.74	0.78
Diving efficiency parameter 1	diving_eff1	0.36	0.12	NA	0.12
Diving efficiency parameter 2	diving_eff2	-0.0021	0.0005	NA	0.0005
kj per gram from prey	energy_prey	6.1	6.1	6.1	6.1
kJ per day cost of nesting at colony	energy_nest	1168.91	932.17	427.75	665.41
kJ per day cost of flight	energy_flight	7361.72	3581.34	1400.74	3113.85
kJ per day cost of resting at sea	energy_searest	810.28	646.15	400.57	461.24
kj per day cost of foraging	energy_forage	1894.9	1421.45	1400.74	974.97
kJ per day cost of warming food	energy_warming	65.07	47.317	34.15	35.83812
observed mean time attending nest	time_nest_mn	11.86	11.73	11.23	NA
observed sd of time attending nest	time_nest_sd	3.48	4.96	3.9305	NA
adult mass gain parameter	adult_mass_a	0.44	0.4	0.4	0.45
chick mass gain parameter	chick_mass_a	20	7.25	12	12
chick mass gain parameter	chick_mass_mu	0.5	0.5	0.5	0.35
chick mass gain parameter	chick_mass_lambda	12	5	60	15
Division of food between parent and chick	Adult_priority	0.575	0.75	0.5	0.75

2.3 Effect of wind farms

2.3.1 Impact scenarios

Two main behavioural responses to wind farms were simulated in the model: displacement and barrier effects.

At the start of each simulation run, individuals were assigned as either birds that would chose to be displaced if their foraging location fell within the wind farm location ('displacement-susceptible birds'), and/or as birds that would choose to fly around the wind farm ('barrier-susceptible birds') if their chosen foraging location lay on the far size of a wind farm. These values were fixed for the lifetime of each bird meaning that no habituation to wind farms occurred. The proportion of birds that were assigned to be displacement-susceptible and barrier-susceptible depended upon the scenario. In the exploratory scenarios, we considered scenarios in which (a) 100% of birds were both displacement-susceptible and barrier-susceptible, (b) 100% of birds were displacement-susceptible but none were barrier-susceptible, (c) 100% of birds were barrier-susceptible but none were displacement-susceptible and (d) 50% of birds were displacement susceptible and 50% of birds were barrier-susceptible.

Within the latter scenario (50% displaced / 50% barrier) the decision on allocating birds as barrier-susceptible was independent of the decision to allocate birds as displacement-susceptible - it follows that approximately 25% of individuals were displacement-susceptible but not barrier-susceptible ( i.e., content to travel through a wind farm but not forage within it), approximately 25% of individuals were barrier-susceptible but not displacement (content to forage within the wind farm but would avoid flying through it), approximately 25% of individuals were neither barrier-susceptible nor displacement-susceptible (wind farm has no effect on behaviour), and approximately 25% of individuals would be susceptible to both displacement and barrier effects (not content to forage within or travel through a wind farm).

2.3.2 Spatial model for displacement and barrier effects

Displacement and barrier effects were determined using a set of zones created around the footprint of each wind farm (Figure 2:3).

If displacement-susceptible birds were simulated to choose a foraging location within the footprint of the wind farm, including a 1km exclusion area, as agreed by the steering group (Zone 4, Figure 2:3) then we assumed that they would instead chose a new foraging location within a 5km buffer zone of the wind farm (Zones 3&5, Figure 2:3). Under heterogeneous prey conditions the prey density at the new location may either be higher or lower than the density at the location that the bird had originally intended to visit. Displacement always incurred an additional outward travel cost, to represent the extra flight cost associated with travelling to the new foraging location (calculated as a direct line between the initial and final foraging locations). Displaced birds that selected a new foraging location in Zone 3 (Figure 2:3; the near-side of the wind farm) occurred no additional travel cost on the return journey, simply returning to the colony in a straight line. However, displaced birds that selected a new foraging location in Zone 5 (Figure 2:3; the far-side of the wind farm) incurred a second additional travel cost on the return journey to represent to consequences of having to travel around the wind farm on their return to the colony (sampled from a normal distribution with a mean of 20km and a standard deviation of 5km).

If barrier-susceptible birds were simulated to choose a foraging location in the far zone of the wind farm (Zone 6, Figure 2:3) then these birds continued to forage at the same location but they incurred additional outward and return travel costs (each being sampled from a normal distribution with a mean of 20km and a standard deviation of 5km in initial exploratory runs). More sophisticated estimates of barrier cost were incorporated into the model in later versions and runs (see Section 2.6.2).

Figure 2:3: The zones used to determine the behavioural response of foraging seabirds to wind farms in relation to their colony. Zone 4 represents the wind farm footprint supplied by each developer, with the addition of a 1km exclusion buffer zone. The large black dot represents the colony location. Zones 3 to 6 define the behavioural response of foraging birds, as described in the text ( Section 2.3.2).

2.4 Translating impacts on adult mass into impacts on adult survival

There are three key outputs from each run of the foraging model:

1. the status of each chick (alive / dead) at the end of the breeding season;

2. the status of each adult (alive / dead) at the end of the breeding season;

3. the mass of each living adult (in grams) at the end of the breeding season.

The first two of these quantify the chick and adult survival rates during the breeding season. The final quantity provides an indirect way of quantifying the adult survival rate during the subsequent winter period. We make use of published relationships between adult mass and annual survival rates in order to convert simulated adult mass values into survival rates. We do this in the same way for baseline simulations and for simulations that have been generated in the presence of wind farms, and we are thereby able to assess the impact of the wind farm upon the adult survival rate.

The procedure for converting individual adult mass values into an overall estimate of adult survival for each simulation run is summarised in Figure 2:4. Our approach is essentially based on the assumption that mass and survival are linked through the equation

where m _ij denotes the standardized mass of individual i in run j and p _ij denotes the survival probability of this individual. The value of b quantifies the strength of the relationship between mass and survival, and the value of s ₀ denotes the 'baseline' survival ( i.e. the survival rate that would be associated with a bird of average mass in the absence of a wind farm). The overall survival rate for a simulation run, P _i is simply assumed to be the average (mean) of the survival probabilities for all of the individuals within it, so that

(where n denotes the total number of individuals).

The validity of this approach will depend primarily upon the validity of the values that are selected for b and s ₀. It is worth noting that the approach also makes one substantive assumption - that the relationship between mass and survival is linear, on a logit-transformed scale - but it would be impossible in practice to check the validity of this assumption using currently available information.

The value of the baseline survival, s ₀, is assumed to vary between species and prey scenarios (poor, moderate or good) - the specific values are based upon the results of the population modelling performed by CEH for Marine Scotland (Freeman et al. 2014), and the specific values are given in Table 2:5.

The strength of the relationship between mass and survival, b, is determined using values given in the published literature. For kittiwakes the value of b is based on the value given in Oro et al. (2002), and for all other species it is based on the value given in Erikstad et al. (2009) - published values do not exist for razorbill, guillemot or gannet, so we assume that they have the same value as that estimated for puffin in the Erikstad et al. (2009) paper. The fitted relationship in Oro et al. 2002 is shown in Figure 2:4. The actual estimated values for b are 1.03 (Erikstad et al., 2009) and 0.037 (Oro et al., 2002), but it is important to note that these values cannot be directly compared because they relate to mass values that are expressed on direct scales: for kittiwakes the mass is standardized solely by deducting the mean mass under the baseline scenario (because the paper by Oro et al. 2002 expresses b in grams), whereas for other species the standardization also involves dividing by the standard deviation under the baseline scenario (because Erikstad et al., 2009, expresses mass as a unit-free quantity).

Table 2:5: Baseline survival probabilities that are used in the conversion between adult mass and overwintering survival (Freeman et al. 2014).

	Poor	Moderate	Good
Kittiwake	0.65	0.80	0.90
Puffin	0.85	0.90	0.95
Guillemot	0.82	0.92	0.94
Razorbill	0.80	0.90	0.95

Figure 2:4: The published significant relationship for kittiwakes relating end of breeding season body mass to subsequent adult survival (Oro et al. 2002).

2.5 Exploratory model runs

This stage of the project involved running the model with 1000 birds for all scenarios.

The foraging model was used to generate five simulations of foraging for four species under each of 66 scenarios - the results that are presented (in Appendix F) are therefore based upon 1320 individual runs of the foraging model. Five simulation runs are used for each scenario in order to provide a quantitative indication of uncertainty - a full description of the way that we accounted for uncertainty in the exploratory runs is described in Appendix E.

The 66 scenarios represent all possible combinations of six scenarios regarding prey quantity and distribution (Table 2:6) and eleven scenarios regarding wind farm effects (Table 2:7).

Table 2:6 Description of prey-related scenarios.

Prey quantity	Prey distribution
Poor	Homogeneous
Poor	Heterogeneous
Moderate	Homogeneous
Moderate	Heterogeneous
Good	Homogeneous
Good	Heterogeneous

The wind-farm related scenarios primarily reflect the decision making process (which wind farms are being proposed: Neart na Gaoithe, Inch Cape, Round 3 Alpha, Round 3 Bravo, or all four combined), but also include scenarios that allow us to assess the impact of uncertainties related to the extent to which displacement and barrier-effects occur, and those related to the buffer distance around the wind farm (Table 2:7).

Table 2:7: Description of wind-farm related scenarios.

Wind farm(s)	% of displacement-susceptible birds	% of barrier-susceptible birds	Buffer around wind farm
None (baseline)	Not relevant	Not relevant	Not relevant
Neart na Gaoithe	100	100	1km
Neart na Gaoithe	100	100	0.5km
Neart na Gaoithe	100	100	0km
Inch Cape	100	100	1km
Round 3 Alpha	100	100	1km
Round 3 Bravo	100	100	1km
All four	100	100	1km
All four	100	0	1km
All four	0	100	1km
All four	50	50	1km

The full results of the exploratory model runs are given in Appendix F, together with the results of the uncertainty analysis.

2.6 Final model runs

2.6.1 Revisions to the full model

One of the key findings of the exploratory analysis was the result that there was a high degree of stochastic variation between different sets of 1000 birds: this suggested that it was possible to reduce uncertainty substantially by re-running the model with larger samples of birds. For computational reasons, however, it would not have been feasible to do this for all scenarios.

A set of ten key scenarios were therefore identified by MSS: these involved running each of the four wind farms, and the cumulative effects, under the two assumptions regarding the spatial distribution of prey (heterogeneous and homogeneous). For all scenarios the prey quantity was assumed to be moderate, the percentage of birds affected by barrier and displacement effects was assumed to be 60% (except for kittiwake, where it was assumed to be 40%; based on advice from JNCC/ SNH), and the buffer around the wind farm was assumed to be 1km (as agreed by the steering group).

For the final simulations the ten short-listed scenarios were each run with 20,000 birds. Increasing the number of simulated birds necessitated changing the value of the foraging interference coefficient ( m) to account for the increased density of birds within each foraging location. The new values for m were determined by matching model output for simulated intake rate with empirical data ( Appendix F, section F1) or using expert opinion, and were as follows: guillemot 0.03; razorbill 0.14, kittiwake 0.08; puffin 0.2725.

In addition, we made a correction to the way the model accounted for cumulative effects of wind farms. This was incorrectly calculated in the exploratory model runs and as a result exploratory results were underestimating the cumulative effects of combined wind farms on each species.

The outputs from these simulations are in Section 3. Results are presented for those SPAs that were identified by MSS as being of interest, except those that we found did not interact with birds. Thus, Buchan Ness was excluded, as were the St. Abbs results for guillemot and the St. Abbs and Fowlsheugh results for razorbill - although the models have been run using all SPAs.

2.6.2 Use of a "fast model"

Computational time is a key limitation in using the foraging model that we outlined in Section 2.2. In order to explore wind farm impacts in more detail we developed a "fast" version of the model - the "fast model" runs much more quickly than the full model, but it does so by removing some of the biological realism within the full model.

The fast model is designed to be as identical as possible to the full model, but there are some substantive differences between the two models - some of these differences arise because there were mechanisms that we could not, for computational reasons, include within the fast model, and some arise because we chose to add some desirable features to the fast model that could not readily have been added to the full model. These methodological differences result in differences in the effect sizes recorded in the two models.

The differences between the fast and full models are:

1) the fast model is substantially faster than the full model to run, and can therefore be used to explore new scenarios, or to run sensitivity analyses, much more readily than the full model;

2) the full model allows birds to visit a different location if they will fail to meet their DER by visiting their original location; the fast model does not;

3) the fast model does not estimate cumulative effects;

4) the fast model matches birds between scenarios, so that the assessments of a wind farm quantify the impact of the wind farm on a particular set of birds (rather than comparing a set of birds that have been impacted by the wind farm against a different set of birds that have not).

5) the split in time between time on the nest and time resting at sea is slightly more realistic in the fast model than the full model (with birds favouring spending time at the nest over resting at sea to a greater degree than in previous model versions);

6) the fast model allows for variation in initial mass between adult birds.

7) the fast model has a smaller cell size (0.5x0.5km vs 1.67x1.67km)

8) the fast model includes barrier effects in a more realistic way than the full model

9) the fast model displaces birds into Zones 3 and 5 (the 5km buffer zone around each wind farm) in proportion to the estimated density of birds in those zones. This is in contrast to the full model, which displaces birds randomly into Zones 3 and 5 with no relation to the estimated bird density in those areas;

Points 1, 4, 7 and 8 can be regarded as the key advantages of the fast model, and points 5, 6 and 9 as minor advantages of it, whereas Points 2 and 3 can be regarded as the key advantages of the full model. These differences are explained in more detail in Appendix G.

We used the fast model to estimate the impact of the wind farms on gannets, based on a GIS tracking data set comprising 13 individuals in 2003 ( CEH unpublished data; other GPS data collected at this colony were not available to the project). Earlier models were not run for this species due to time constraints and because this species was of lowest concern. Parameter values for gannets are listed below (Table 2:8). Baseline survival probability used in the conversion between adult mass and overwintering survival was 0.92 under moderate conditions (Wanless et al. 2006; WWT Consulting 2012).

Table 2:8 Parameter values used to simulated foraging gannets in the 'fast model'. See Appendix D for source references.

Type	Units	Parameter	Gannet
Mass	G	BM.adult.mn	2998
Mass	G	BM.adult.sd	234
Mass	G	BM.chick.mn	79.3
Mass	G	BM.chick.sd	11.2
Time	Hours	time.rest.minimum	1
Time	Hours	Unattendance.hrs	96
Speed	m/s	flight.msec	14.9
Depth	m	forage.depth.mn	5.99
Depth	m	forage.depth.sd	5.03
Energy	kJ/day	energy.nest	2512.56
Energy	kJ/day	energy.flight	11316.9
Energy	kJ/day	energy.searest	3227.48
Energy	kJ/day	energy.forage	11316.9
Energy	kJ/day	energy.warming	170.29
Energy	kJ/day	adult. DEE.mn	4865
Energy	kJ/day	adult. DEE.sd	450
Energy	kJ/day	chick. DEE	1593.3
Energy	kJ/gram	energy.prey	6.1
Other	trips/day	Nforagetrips	0.38
Other		BM.adult.mortf	0.6
Other		BM.adult.abdn	0.8
Other		BM.chick.mortf	0.8
Other		adult.priority	0.5
Other		assim.eff	0.75
Other		diving.eff1	1
Other		diving.eff2	0
Other	g/min	IR.max	559.4
Other		IR.mu	0.01
Other	indiv/km2	IR.lambda	25000
Other		m	0.2
Other		adult.mass.a	0.5
Other		chick.mass.a	110
Other		chick.mass.mu	0.35
Other		chick.mass.lambda	10

2.6.3 Adjustment

The full and fast models both had important features that could not be captured within the other model without substantial rewriting of the model code (which was not feasible within the timeframe of the project). We therefore draw inferences about the overall impacts of wind farms by synthesising the results obtained using the two analyses into a single assessment of impact.

2.6.3.1 Individual wind farms

The overall impact of individual wind farms on survival (either adult or chick) was assessed by calculating:

Estimated % change in survival = % change in survival from full model * adjustment factor

where

adjustment factor = % change in survival from fast model run using new barrier effects /

% change in survival from fast model run using old barrier effects

If the full model estimates a reduction of 4%, for example, and the fast model estimates reductions of 2% and 1% (respectively) under the old and new barrier effects, then this formula implies that the adjustment factor is 0.5 and the estimated reduction in survival is 4 * 0.5 = 2%.

It is important to note that the full model was always run using the old barrier effects (sampled from a normal distribution with a mean of 20km and a standard deviation of 5km). This approach assumed that the negative effect of the wind farm on survival would be reduced by moving from the old barrier effect calculations to the new barrier effect calculations, and assumed that the magnitude of this reduction would have been the same in the full model (if we had been able to run it using the new barrier effects). It assumed that the full model gave a more realistic estimate of the impact associated with the old barrier effects than the fast model, so the fast model output was used solely to account for the effect of improving the barrier effect calculations.

The adjustment factor will generally be close to one for scenario-by-wind farm-by- SPA combinations where the wind farm effects tend to be associated primarily with displacement rather than barrier effects, and will be relatively small for combinations that are dominated by barrier effects.

The adjustments may not be stable or robust if we are dealing with wind farm effects that are actually very small, because in these situations the estimated magnitude of wind farm effects (and even the estimated sign of these effects) will be heavily influenced by the effects of stochastic noise. The calculations may also be inappropriate if the models are genuinely behaving in unusual ways ( e.g. if the shift from the old to new barrier effect calculations actually increases the magnitude of the barrier effect). It is therefore desirable to determine which of the adjustment factors have been estimated reliably and which have not. We achieved this by generating an additional 50 stochastic runs from the fast model for each scenario. These additional runs were used to quantify the degree of uncertainty associated with each adjustment factor, and thereby to assess the reliability of the values that were generated within our main simulations. We quantified the reliability of an adjustment factor by calculating:

d = Max(Abs(Main adjustment factor - 25% quantile of adjustment factors from additional runs),

Abs(Main adjustment factor - 75% quantile of adjustment factors from additional runs))

If the value of d is large then the additional simulations suggest that:

a) there is considerable uncertainty regarding the value of this adjustment factor; or

b) the adjustment factor used in the main assessment is well beyond the range of values that other stochastic runs of the model would typically have generated.

In both situations we classified the adjustment factor used in the main assessment as being "unreliable". If the value of d was small then the adjustment factor was classified as "reliable"- in the sense that similar values of the adjustment factor were typically produced through additional stochastic runs from the model. The exact cut-off used in distinguishing between "unreliable" and "reliable" results was subjective, so we classified the results of our assessments into three groups:

1) low reliability ( d greater than 0.2)

2) moderate reliability ( d between 0.1 and 0.2)

3) high reliability ( d below 0.1)

When presenting the results we coloured the adjustment factor values - and corresponding adjusted estimates - as light grey (low reliability), yellow (moderate reliability) or pink (high reliability).

2.6.3.2 Cumulative effects

The fast model cannot be used to generate cumulative effects, so the adjustment factor was, in this case, calculated based on the estimate of the sum of effects of individual wind farms as generated by the unmodified and modified versions of the full model. More specifically, it was equal to

Adjustment factor = SUM(Effect of wind farm i within full model) / SUM(Adjusted effect of wind farm i),

and the estimate is then equal to

Estimated cumulative % change in survival = cumulative % change in survival from full model * Adjustment factor

We only used wind farms with moderate or high reliability in the calculation of cumulative effects (because the adjusted estimates for wind farms whose adjustment factors were classed as having low reliability were not likely to be meaningful), and we therefore did not produce estimates of cumulative effects for scenario-by- SPA combinations for which all wind farm effects were estimated to have low reliability. We also present the results that were obtained solely by using wind farms with high reliability.

2.6.4 Sensitivity analysis

We used the fast model to test the sensitivity of adult and chick survival to the following parameters:

• Unattendance duration at the breakpoint after which chick death is certain to occur (all species except puffins)
• Chick body mass below which chick leaves burrow (puffins only)
• Adult body mass below which adult dies
• Adult body mass below which adult leaves chick unattended
• Chick body mass below which chick dies
• Adult priority of resourcing between self and chick
• Intraspecific competition (m)

The sensitivity analysis involved running the same model but setting the parameter value of interest at, in turn, minimum plausible and maximum plausible values. The outputs from these two models can then be compared to the version using mean values (version 0) to assess the sensitivity of model outputs to variation in the parameter of interest. Minima and maxima were based where possible on empirical data or expert judgement, but in the absence of these the maxima and minima were assumed to be, respectively, 50% high and lower than the parameter values that were used for assessing wind farm impacts. The disadvantage of a fixed percentage change of 50% is that this may bear little relation to the biology: for some parameters a change of 50% may be large, in terms of the underlying biology, and for other parameters it may be small. Thus, the best estimate of the true biological range is more appropriate to use. See Table 2:9 for details.

Table 2:9 Ranges used for each parameter and species in sensitivity analysis.

Parameter		Guillemot	Razorbill	Kittiwake	Puffin	Gannet	Method
1	Unattendance duration at breakpoint (hours)	48-144	48-144	9-27		48-144	Expert judgement
2	Chick body mass below which chick leaves burrow (proportion)				0.7-0.9		Expert judgement
3	Adult body mass below which adult dies (proportion)	0.56-0.64	0.56-0.64	0.56-0.64	0.56-0.64	0.56-0.64	Empirical data
4	Adult body mass below which adult leaves chick unattended (proportion)	0.7-0.9	0.7-0.9	0.7-0.9	0.7-0.9	0.7-0.9	Expert judgement
5	Chick body mass below which chick dies (proportion)	0.5-0.9	0.5-0.9	0.5-0.9	0.5-0.9	0.5-0.9	Expert judgement
6	Adult priority of resourcing between self and chick (unitless)	0.5-0.9	0.5-0.9	0.5-0.9	0.5-0.9	0.5-0.9	Expert judgement
7	Intraspecific competition ( m, unitless)	0.0125-0.0375	0.07-0.21	0.04-0.12	0.13625-0.40875	0.125-0.375	Fixed % change

We assessed the extent to which adult and chick survival were modified by altering the parameter values. Within the outputs the parameter versions were assigned numeric codes, for convenience (Table 2:10). It was ultimately not possible to run versions 5 and 6, because of difficulties in tracking the occurrence of adult mortality during the breeding season within the fast model because of its extreme rarity ( i.e. adults almost never die in the model). These estimates were therefore excluded from our results. Note that Versions 3 and 4 did not result in a change in effect size, so are not presented, and that Version 2 is not presented here because it was considered to provide little additional information in discussion with MSS.

Table 2:10 list of versions in output spreadsheets.

Version no.	Version description
0	Scenario with all values at their mean and barrier effect based on new method [b]
1	Scenario with all values at their mean and barrier effect based on old method (worst case)
2	Scenario with all values at their mean and barrier effect based on new method [a]
3	As Scenario 0 but min values for Unattendance duration at breakpoint (non-puffins) / chick body mass below which chick leaves burrow (puffins)
4	As Scenario 0 but max values for Unattendance duration at breakpoint (non-puffins) / chick body mass below which chick leaves burrow (puffins)
5	As Scenario 0 but min values for Adult body mass below which adult dies
6	As Scenario 0 but max values for Adult body mass below which adult dies
7	As Scenario 0 but min values for Adult body mass below which adult leaves chick unattended
8	As Scenario 0 but max values for Adult body mass below which adult leaves chick unattended
9	As Scenario 0 but min values for Chick body mass below which chick dies
10	As Scenario 0 but max values for Chick body mass below which chick dies
11	As Scenario 0 but min values for Adult priority of resourcing between self and chick
12	As Scenario 0 but max values for Adult priority of resourcing between self and chick
13	As Scenario 0 but min values for Intraspecific competition ( m)
14	As Scenario 0 but max values for Intraspecific competition ( m)