# Offshore renewable developments - developing marine mammal dynamic energy budget models: report

A report detailing the Dynamic Energy Budget (DEB) frameworks and their potential for integration into the iPCoD framework for harbour seal, grey seal, bottlenose dolphin, and minke whale (building on an existing DEB model for harbour porpoise to help improve marine mammal assessments for offshore renewable developments.

## Figures

Figure 1. Flow diagram describing the details of the model. The same set of processes is applied to females and their offspring, but calves/pups are only followed to an age equivalent to the minimum inter-birth interval. Parallelograms indicate model inputs and rectangles indicate calculations or changes of life history stage. Females also change life history stage if their foetus or calf/pup dies but these changes are not illustrated here. A detailed account of all elements of this flow diagram can be found in the submodel descriptions.

Figure 2. Example of changes in resource density over 1 year modelled deterministically (red) and stochastically (black).

Figure 3. The effect of body condition relative to the target level (and the steepness of the assimilation response (η) on energy assimilation as a proportion of its maximum rate. The relationship for η = 15 is shown in solid black. Curves in green are for values of η = 5 and 10; curves in red are for values of η = 20 and 25.

Figure 4. The effect of the shape parameter γ on the relationship between foraging efficiency and age (shown as a multiple of the age at which a calf/pup achieves 50% foraging efficiency). TR is 1 year. The curve for γ = 3 is shown in solid black. Green curves show the relationship for values of γ <3; red curves represent values >3.

Figure 5. The effect of the non-linearity parameter ξc on the proportion of a calf/pup’s milk demand provided by its mother at different stages of lactation. TΝ (the calf/pup age at which the mother begins to reduce the amount of milk she supplies) was set at 60% of the duration of lactation (TL). The solid black line shows the relationship for ξc = 0.9 (the value used by Hin et al. 2019). Green lines show the relationships for smaller values of ξc (0.5 and 0.75). Red lines show the relationship for larger values (0.95 and 0.99).

Figure 6. The effect of body condition relative to the target level (of the female and the non-linearity parameter ξM on the proportion of a calf/pup’s milk demand provided by its mother. The solid black line shows the relationship for ξM = 2 (the value used by Hin et al. 2019). Green lines show the relationships for larger values of ξM (3 and 5). Red lines show the relationship for smaller values (0.5 and 1.0).

Figure 7. The effect of the starvation-induced mortality parameter (mu_s = μs) on the probability that an individual whose body condition has fallen to ρs/2 will survive for 1 week.

Figure 8. Modelled variation in resource density over the course of the year for a female whose mean pupping date is 17 June (indicated by the vertical green line). The vertical blue line indicates the day on which implantation occurs.

Figure 9. Predicted variation in total body weight (top panel) and Condition (bottom panel) of a female (solid black line) and her pup (solid red line) over 1 year. The dip in condition and total body of the female around day 130 indicates the effect of the moult – when females spend more time hauled out - on energy assimilation.

Figure 10. Predicted variation in foraging efficiency with age, showing the reduction in efficiency during the annual moult, which begins in the second year of life.

Figure 11. Predicted effect of total body weight at different times during pregnancy (decision day) on the probability of pupping assuming that weight at weaning of 45 kg results a probability of 0.5 that a pregnancy will occur in the following year.

Figure 12. Cumulative survival curve for female harbour seals used in simulations, with annual survival values estimated by Sinclair et al. (2020), where juvenile survival is estimated to 0.79 and adult to 0.92 (‘stable population’ red line) and 0.86 and 0.96 respectively (‘increasing’ population, grey line).

Figure 13. examples of annual changes total body mass and body condition of female (black lines) and her offspring (red lines). (a) example of female having pups in three consecutive years, her second pup died soon after post-weaning fast, (b) example of female skipping one breeding year, (c) example of female whose third pup died before the end of lactation. her body mass and condition returned to pre-birth values sooner than females who nurse pups till weaning.

Figure 14. Result of 50 simulations of 1000 females each for two Pattern Oriented Modelling (POM) patterns: Fertility (left) and Pup survival (right). Orange lines mark range of observed values for UK harbour seal populations (see Table 18 in Sinclair et al. 2020).

Figure 15. Relationship between body condition of female (black) and her pup (red) and three periods of disturbance: high - from giving birth to implantation; medium – from implantation till decision day whether to continue with pregnancy; and low – from decision day to giving birth.

Figure 16. The effect of various durations of disturbance on four vital rates for a harbour seal population that are not food-limited (top panels) and one that is food-limited (bottom panels) during four different period of disturbance (see figure 15). all values are expressed as proportion change in comparison to no disturbance.

Figure 17. Main effect plots. Parameters in columns and outputs (patterns) in rows. Horizontal lines (without rectangles) in rows visualise mean values. Right rectangle higher than left rectangle indicates a main effect with a positive sign and vice versa. Rectangles on the same output value (y-axis) indicate no main effect.

Figure 18. Interaction effect plots for two patterns: Pup survival (top set of panels) and condition at the end of lactation (Rhoendlact, bottom set of panels). The two-way interaction effect plots indicate interaction effects if the lines for a factor combination are not parallel. The less parallel the lines are, the higher is the expected interaction effect.

Figure 19. Modelled variation in resource density over the course of the year for a female whose mean pupping date (indicated by the vertical green line) is 23 November. The vertical blue line indicates the day on which implantation occurs.

Figure 20. Predicted variation in total body weight of a female grey seal (solid black line) and her pup (solid green line) over 1 year. Cyclical variation in resource density over this period is indicated by the dotted black line (the dip around day 120 indicates the effect of the moult – when females spend more time hauled out - on energy assimilation). The red dotted line indicates the threshold mass below which pups may experience starvation-related mortality.

Figure 21. The effect of the Kappa rule on calf growth in kg/day. The black line shows daily growth as predicted by the underlying growth curve and the green line shows realised growth with Kappa=0.8. The reduced level of growth during the first 160 days of life is a consequence of the relatively low feeding efficiency of young animals who are unable to assimilate enough energy to cover the combined costs of maintenance and growth.

Figure 22. Predicted variation in foraging efficiency with age, showing the reduction in efficiency during the annual moult, which begins in the second year of life.

Figure 23. Predicted variation in birth rate with age at three different resources densities (Rmean = 1.6 in red, Rmean = 1.63 in black, Rmean = 1.7 in green). Each curve is based on simulations for 2000 females.

Figure 24. Cumulative survival curve for female grey seals used in simulations, with annual survival values estimated by Thomas et al. (2019) shown by open circles.

Figure 25. Effect of disturbance between the end of the pupping season and the day of implantation on the survival of pups born to 21 year old females. The black line is the mean, and the blue lines enclose 90% of 10,000 bootstrapped estimates. Left-hand panel: disturbance effect = 0.14; right-hand panel: disturbance effect = 0.25.

Figure 26. Effect of disturbance between the day of implantation and the day on which females decide whether or not they will continue their pregnancy on the survival of pups born to 21 year old females. The black line is the mean, and the blue lines enclose 90% of 10,000 bootstrapped estimates. Left-hand panel: disturbance effect = 0.14; right-hand panel: disturbance effect = 0.25.

Figure 27. Effect of disturbance between the day of implantation and the day on which females decide whether or not they will continue their pregnancy and the birth rate of 10 year old females. The black line is the mean, and the blue lines enclose 90% of 10,000 bootstrapped estimates.

Figure 28. Effect of disturbance between the day on which females decide whether or not they will continue their pregnancy and the mean date on which those pups are born on the survival of pups born to 21 year old females. The black line is the mean, and the blue lines enclose 90% of 10,000 bootstrapped estimates. Left-hand panel: disturbance effect = 0.14; right-hand panel: disturbance effect = 0.25.

Figure 29. Seasonal patterns of variation in resource density that were evaluated. The vertical dotted line indicates the mean birth date for calves in the Moray Firth. Blue = maximum resource density on 14 April, red = maximum resource density on 15 July, green = maximum resource density on 15 October.

Figure 30. The relationship between resource density (Rmean) and lifetime reproductive success for a female that survives to the maximum age of 65 years. The green line shows the relationship for a lactation duration (TL) of 1095, the black line is for TL = 730, and the red line for TL = 550 days.

Figure 31. Predicted changes in body condition of a female (black line) and her calf (red line) over the course of lactation. A. If the female is 6 years old when the calf is born. B. If the female is 36 years old. The strong cycles in female condition reflect the seasonal variations in resource density.

Figure 32. Cumulative survival curve for female bottlenose dolphins used in simulations, with annual survival rates recommended by Sinclair et al. (2020) for the Moray Firth population shown by open circles.

Figure 33. Predicted variation in the body condition of a female (black line) and her calf (red line) over the course of lactation for a population increasing at 2% per annum. The vertical dotted line represents the mean calving date in the Moray Firth (assumed to be 15 July). The green line represents an index of resource density (Rmean).

Figure 34. Effect of disturbance between 1 May and 31 August on the survival of all calves of mature females that were alive at the start of the disturbance period. The black line is the mean, and the blue lines enclose 90% of 10,000 bootstrapped estimates.

Figure 35. Seasonal pattern of variation in resource density that was used in simulations. The vertical dotted line indicates the mean birth date for calves in the Northeast Atlantic stock, the vertical green line represents the date of arrival on the feeding grounds and the vertical red line the date of departure.

Figure 36. Effect of the amplitude of the variation in resource density on the ratio of mean resource density in summer to mean resource density in winter.

Figure 37. Cumulative survival curve for female minke whales used in simulations, with annual survival rates Taylor et al (2007) shown by open circles.

Figure 38. Figure 1(A) from Nordøy et al. (1995) showing the relationship between blubber mass and body length for females killed early in the whaling season (solid dots) and those killed at the end of the season. The right-hand figure shows the equivalent outputs from the minke whale deb model.

Figure 39. Figure 2 from Christiansen et al. (2013) showing changes in blubber volume over the course of the Icelandic whaling season for pregnant (panel A), mature (panel B) and immature (panel C) minke whales. The right-hand panel shows the equivalent outputs from the deb model.

Figure 40. Effect of disturbance random distributed across the summer period (mid-April to mid-October) on the survival of minke whale calves. The grey lines indicate the 95% credible interval based on 10,000 bootstrap calculations.

Figure 41. Effect of disturbance randomly distributed across the last three months of the summer feeding period (mid-July to mid-October) on the survival of minke whale calves. The grey lines indicate the 95% credible interval based on 10,000 bootstrap calculations.

Figure 42. Changes in maternal (solid) and calf (dashed) body condition for an undisturbed (black) female minke whale, and one subject to 60 days of disturbance at the end of the summer (red) that reduces foraging success by 50%. The vertical green line is the day on which the calf is weaned.

Figure 43. Pairwise plot showing correlation between parameters (grey numbers, only correlation with significance level <0.05 are shown) and their posterior distributions (yellow histograms). See Table 9 for parameter definitions.

Figure 44. Prior (grey) and posterior (orange) distribution of parameters used in step 2 of the ABC. Note that Rmean is a function of Sigma_M and is not, therefore, drawn from a prior distribution but is calculated from the orior value of Sigma_M.

Figure 45. The effect of different number of days of disturbance on calf survival and birth rate for 21year old females (upper two panels) and 10-year-old females (lower two panels). The boxplots represent the spread of results from 100 different parameter settings derived from the ABC analysis. All values are expressed as a proportion of the equivalent value from simulations with no disturbance.

Figure 46. Locations of two disturbances with contrasting potential effect: ‘high’ (red) where observed density of animals is high and ‘low’ (black), where observed density of animals is low. Each location has then 30, 45 and 60 km radius of potential effect of disturbance defined.

Figure 47. Example of a matrix showing number of hours per day each tracked individual spent within one of the defined areas of disturbance. Each column is therefore a day of year (365 columns) and each row is an individual tracked a given year.

Figure 48. Examples from five simulations showing total number of tracked individuals during 5-year simulations, excluding burn-in period. At the beginning of each simulation, 200 individuals are created and tracked but, as some of these individuals die during the burn-in period, smaller number of individuals is tracked at the beginning of actual simulations and even smaller number by the end of these simulations.

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Email: ScotMER@gov.scot

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