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.

8 Common minke whale DEB

8.1 Model parameters

Table 8 shows the parameter values used in most of the minke whale simulations described in this Chapter. Details of how these values were derived are outlined below.

Table 8. Parameter values used in the minke whale DEB model.
Parameter names Code name Value Description Source
Resource density
R Rmean 2.315 Annual mean resource density See text
abeta a_beta 8.08 Shape parameters of beta distribution defining stochasticity in resource density See text
bbeta b_beta 24.25 See text
amplitude 0.5 Parameter defining the amplitude of seasonal variation in resource density See text
offset 105 days Parameter determining when during the year Rmean has its maximum value See text
Timing of life history events
min_age min_age 6 years Minimum age for reproduction Christensen (1981)
mean_birthday mean_birthday 15 November Mean pupping date for NE Atlantic stock Hauksson et al (2011)
TP Tp 330 days Gestation period See text
TL Tl 150 days Age at weaning (duration of lactation) See text
TR Tr 150 days Age at which calf’s resource foraging efficiency is 50% See text
max_age max_age 50 years Maximum age
max_age_calf 345 days Maximum modelled age of calf
ρ rho 0.3 Target body condition for adults See text
θF Theta_F 0.2 Relative cost of maintaining reserves Hin et al. (2019)
Lb 247 cm Length at birth Hauksson et al. (2011)
L0 L0 415 cm Length at weaning Christensen (1981)
L Linf 907 cm Female maximum length
b b - 0.000389 Von Bertalanffy exponent
ω1 omega1 3.62x10-5 (kg/cm Structural mass-length scaling constant Hauksson et al. (2011)
ω2 omega2 2.758 Structural mass-length scaling exponent
Energetic rates
σM Sigma_M 2.5 Field metabolic maintenance scalar
σG Sigma_G 30 MJ/kg Energetic cost per unit structural mass Derived using the approach of Hin et al. (2019)
ε epsi 27.5 MJ/kg Energy density of reserve tissue Reilly et al. (1996)
ε- epsi_minus 24.75 MJ/kg Catabolic efficiency of reserves conversion
ε+ epsi_plus 34.03 MJ/kg Anabolic efficiency of reserve conversion
μs mu_s 0.2 Starvation mortality scalar Hin et al. (2019)
η eta 20 Steepness of assimilation response See text
ϒ upsilon 2.5 Shape parameter for effect of age on resource foraging efficiency See text
K Kappa 0 for calves & juveniles 0.5 for all other age classes Proportion of the daily assimilated energy allocated to growth See text
fert_success fert_success 0.9 Probability that implantation will occur Hauksson et al (2011)
Fneonate F_neonate Reserves required to cover costs of pregnancy and lactation See text
F_neo_multiplier 0.9 Fraction of F_neonate used as actual threshold
φL phi_L 5.4 Lactation scalar See text
σL Sigma_L 0.86 Efficiency of conversion of mother’s reserves to calf tissue Lockyer (1993)
TN Tn 135 days Calf age at which female begins to reduce milk supply See text
ξc xi_c 0.2 Non-linearity in milk assimilation-calf age relation See text
ξM xi_m 6 Non-linearity in female body condition-milk provisioning relation See text
foetal_mortality foetal_mortality 0.0 Background foetal mortality See text
α1 alpha1 0.00045 Coefficients of age-dependant mortality curve Sinclair et al. (2020)
α2 alpha2 0.943 x 10-4
β1 beta1 0.0004
β2 beta2 1.1 x 10-6
ρS rho_s 0.1 Starvation body condition threshold See text
μs mu_s 0.2 Starvation mortality scalar See text
Distdur days.of.disturbance Number of days on which disturbance occurs See text for values
Diststart first_day First day of disturbance period See text for values
Distend Last_day Last day of disturbance period See text for values
Disteffect disturbance.effect 0.25 Reduction in resource density caused by disturbance See text
AgeDist age.affected Age threshold defining which age class of simulated animals is affected by the disturbance See text

8.1.1 Resources

Resource density (Rmean) Northeast Atlantic minke whales are believed to spend the summer on prey-rich feeding areas in northern latitudes and migrate south in winter to areas with much lower prey density. We modelled this variation by allowing resource density to vary seasonally following the sinusoidal curve shown in Figure 35. This predicts maximum resource density will occur around mid-July and that resource density may be effectively zero at some time during the winter.

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.
Line graph showing the relationship between resource density and day of the year for Northeast minke whales. As described in the text above.

The duration of this period of zero resource density, and the difference in mean resource density between summer and winter, is determined by the amplitude of the sinusoidal variation, as shown in Figure 36.

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.
Line graph showing the ratio of mean resource density in summer versus mean resource density in winter, and how this is determined by the amplitude of variation. As described in the text above.

Although it is often assumed that baleen whales do little if any feeding during the winter period, this is almost certainly not the case for Northeast Atlantic minke whales. The values for energy expenditure and energy acquisition in Table 1 of Nordøy et al. (1995) indicate that the energetic content of the reserves accumulated over the summer are only sufficient to cover field metabolic costs for 55 days of fasting in the case of adult females (mean length 8 m) and 64 days in the case of growing animals (mean length of 7 m). Therefore, these animals must be feeding for some of the time during the winter. We therefore set the amplitude of variation to a relatively low value (0.5, equivalent to a 2x difference in resource density between summer and winter) in our initial simulations.

In the original Hin et al. (2019) model resource density is assumed to be constant or to vary smoothly over the course of the year. However, in reality, the resource density encountered by an individual is likely to vary from day to day. This stochasticity in resource density can be modelled by multiplying Rmean for each day by a number drawn at random from a beta distribution with mean=1 and a 90% confidence interval of 0.5-1.5. Extreme values for this multiplier could be as low as 0.1 or as high as 2.4.

We assumed that calves encountered the same resource density as their mothers on each day during lactation.

8.1.2 Timing of life history events

Following Christensen (1981) we assumed that females had to be at least 7 m long before they could ovulate. The mean birthday for all calves was set at mid-November, as suggested by Hauksson et al. (2011).

Gestation period (TP) This is 10 months (~300 days) according to Perrin et al. (2018). However, a value of 330 days is more consistent with observed lengths at birth (see below).

Lactation period/age at weaning (TL) This is 5-6 months according to Perrin et al. (2018). However, Nordøy et al. (1995) and Jonsgård (1951) report that minke whales spend 6 months in Northeast Atlantic waters each year and that calves are not normally seen with these animals. Given the reported annual breeding cycle of minke whales, this suggests that lactation must last less than 6 months and we used a value of 150 days.

8.1.3 Reserves and growth

Reserve threshold (ρ) Nordøy et al. (1995) provided detailed information on changes in the mass and energy density of blubber, muscle and intra-abdominal fat for immature and adult Northeast Atlantic minke whales, from the time they arrive on the feeding grounds (around 14 April) until their departure 183 days later. We combined this with our calculations of the structural mass of animals of different lengths from the growth curve described below to estimate changes in body condition over the course of this period. The blubber mass and muscle mass of all individuals increased over the course of the summer, as did the energy density of these tissues (Nordøy et al. 1995). Nordøy et al. (1995) report that an 800 cm long whale increases its energy reserves by 151 MJ/day over the course of the summer, and we calculated that the average energy density of these tissues was 26 MJ/kg. The total energy accumulated in reserve tissue by an 800 cm long animal over the 183-day summer period is therefore equivalent to 1440 kg, resulting in a body condition of 0.28. However, some animals achieved a greater mass gain than this, and we therefore set ρ at 0.3.

Relative cost of maintaining reserves F) We were unable to find any published data that would allow a value specific to minke whales to be calculated for this parameter. We, therefore, suggest using the value of 0.2 assumed by Hin et al. (2019).

Structural length and structural mass (L0, L∞, ω1, ω2) A number of von Bertalanffy growth curves have been published for the Central and Northeast Atlantic minke whale stocks (Christensen 1981, Olsen and Sunde 2002, Hauksson et al. 2011), but the youngest animals in the samples used to fit these curves are usually at least 2 years old. None of the growth curves provide estimates of length at birth that are in the range 240-270 cm reported by Perrin et al. (2018), and only the Christensen (1981) growth curve is consistent with Jonsgård (1951) suggestion that length at weaning is about 450 cm.

Hauksson et al. (2011) fitted the following growth curve for minke whale foetuses, based on animals sampled at the Icelandic whaling station:

Mathematical Equation

where t is the Julian days. Figure 2 of Christiansen et al. (2014) shows a similar pattern of foetal growth, probably because it is – at least in part - based on the same sample of animals. Hauksson et al’s (2011) curve predicts a length at birth of 204 cm if foetal growth begins on 1 January and gestation last 300 days, and 247 cm if gestation lasts 330 days. Only the latter value is consistent with the various estimates of length at birth for the Northeast Atlantic minke whale stock documented in Christensen (1981), supporting our assumption that TP = 330 days.

We estimated foetal weight at age using the following formula derived by Hauksson et al. (2011) from the same sample:

Mathematical Equation

We assumed that growth in length was linear from birth to age TL (with a predicted length of 415 cm at this age) and then used Christensen (1981) growth curve

Mathematical Equation

(re-parameterised to match the formulation used by Hin et al. 2019) from this age onwards. Structural mass at age (Sa) was calculated from La using Hauksson et al.’s (2011) formula for foetuses.

Modelling growth (Κ) The model developed by Hin et al. (2019) assumes that growth in length and core mass continues unabated, regardless of energy intake. This is clearly not the case in many marine mammals. We therefore assumed that growth may be reduced if energy intake is less than the combined costs of metabolism, growth and reproductive activities (pregnancy and lactation). We modelled these circumstances using a modification of the kappa rule, which is a fundamental component of classic DEB models (Kooijman 2010). We assumed that an individual will allocate a proportion of the assimilated energy (It) it acquires on a particular day to growth (including growth of the foetus, because this is treated as part of the female’s core mass), up to a maximum of (1-Κ).It. If this amount of energy is less than the energy required for growth, the growth rate of the female and her foetus is reduced accordingly. The balance of the energy intake is allocated to metabolism. If this is insufficient to cover all of the costs of metabolism, reserves must be metabolised. Values of Κ < 0.5 indicate that growth is prioritised over metabolism.

Following Christiansen et al. (2013) we set Κ to zero for immature animals, which are believed to prioritise growth above all else. Conversely, we assumed that nursing calves would prioritise reserves over growth, because adequate reserves are crucial to their survival in the post-weaning period. We experimented with a range of values of K for adult females.

8.1.4 Energetic rates

Field metabolic maintenance scalarM) Blix and Folkow (1995) estimated the average energy expenditure of 6 free-ranging, tagged minke whales to be 80 kJ/kg/day, based on their respiration rate. Folkow et al. (2000) used this value to calculate that a 5,900 kg adult minke whale would expend 472 MJ/day. This is equivalent to using a scalar of 1.7-2.5, depending on what assumptions are made about the values of ρ and ΘF. We used a value of 2.5 in both summer and winter to account for the potential increase in metabolic rate when animals are in warmer waters during the winter, as appears to be the case for baleen whales (Villegas-Amtmann et al. 2017).

Energetic cost per unit structural massG) We calculated growth efficiency using the same approach as Hin et al. (2019), with a mass at birth of 144 kg (based on a length at birth of 247 cm) and an energy density of 3.8 MJ/kg for the tissue of minke whale foetuses estimated by Nordøy et al. (1995). This produced a value of 33 MJ/kg for σG.

Catabolic and anabolic efficiency of reserve conversion (ε-, ε+,) Nordøy et al. (1995) estimated that the energy density of minke whale blubber on arrival at the summer feeding grounds was 27.5 MJ/kg, very similar to the mean energy density of the tissues accumulated over the summer. Allowing for a 90% efficiency of catabolism, we assumed ε- = 24.75 MJ/kg.

In the absence of any direct measurements of ε+ for minke whales, we followed Hin et al. (2019) and used a value for ε+ that was 40% higher than ε- (i.e., 34.65 MJ/kg).

Steepness of assimilation response (η) We were unable to find any data in the literature that could be used to set a feasible range for this parameter. We explored the implications of values between 5 and 25 and found that predicted changes in body weight and reproductive success were relatively insensitive to the value of this parameter. We therefore carried out most simulations with a value of 20.

Effect of age on resource foraging efficiency (Υ, TR): We could find no information that could be used to estimate these parameters in the literature. Initially, we assumed that calves are 50% efficient at foraging when they are weaned.

8.1.5 Pregnancy

Pregnancy threshold (Fneonate): Jonsgård (1951) observed that most adult females on the feeding grounds were pregnant, suggesting that minke whales have a one-year reproductive cycle. Christiansen et al. (2014) observation that female minke whales on the Icelandic feeding grounds that were in poor condition (as measured by their blubber volume) had smaller foetuses suggests that females respond to reduced energy intake in summer by reducing their investment in their offspring rather than by terminating a pregnancy. However, there is a high risk of starvation-related mortality if females attempt to complete lactation when they have insufficient energy reserves. We, therefore, experimented with a range of value for Fneonate on day 300 of pregnancy. This is equivalent to 15 October in the Northeast Atlantic and represents the date at which most females leave the feeding grounds. We calculated the amount of energy a female would require to complete her pregnancy and provide her calf with 100% of its energy requirements during the lactation period. We then examined the consequences of setting a threshold for continuing a pregnancy that was a fraction of this value. Female fitness, measured by lifetime reproductive success at a particular value of Rmean, increased as the magnitude of the threshold was increased from 0.8* Fneonate to 0.9* Fneonate, but there was little increase beyond this value. We, therefore, carried out all subsequent simulations with a threshold of 0.9* Fneonate.

Probability that implantation will occur (fert_success) The probability of successful implantation was set at 0.88 based on the ovulation rate reported by Hauksson et al. (2011).

8.1.6 Lactation

Efficiency of conversion of mother's reserves to calf/pup tissueL): In the absence of any direct measurements of the relevant efficiencies for minke whales, we suggest using the value of 0.86 that was used by Hin et al. (2019).

Effect of calf/pup age on milk assimilation C, TN): It is generally assumed that resource density is low on the breeding grounds and that females will provide almost all of their calves’ energy requirements up to the age at weaning. We therefore set TC = 0.9*TL.

Effect of female body condition on milk provisioning M) Because calves are weaned on the breeding grounds or during migration to the summer feeding grounds, lactating females that are in poor condition at this time will be close to the starvation threshold and may struggle to recover their depleted reserves. We therefore assumed a “conservative” strategy in which females began reducing milk supply relatively rapidly as their condition declined (i.e., a value of ξM ≥ 5, see Figure 6). Values of ξM > 5 resulted in increased levels of adult female mortality, without any obvious improvement in fitness. We therefore carried out all simulations with ξM = 5.

Lactation scalarL) We calculated the total costs of calf growth and calf metabolism during the period when females are assumed to be providing 100% of their calf’s energy needs and assumed that the calf’s body condition was close to ρ throughout this period.

8.1.7 Mortality

Age-dependent mortality rate We followed the approach used by Hin et al. (2019) and estimated changes in the probability of survival with age using the method developed by Barlow & Boveng (1991). The following function describing the variation in daily survival with age:

Mathematical Equation

where a is age in days, was fitted to the annual age-specific minke whale survival rates from Taylor et al. (2007). We used a maximum age of 50 years, based on the fact that the oldest female in a sample of 288 whales examined by Hauksson et al. (2011) was 42 years old and that Taylor et al. (2007) propose a maximum age of 51 years. The resulting fitted values were:

α1 = 0.00045

β1 = 0.0004

α2 = 0.943 x 10-4

β2 = 1.1 x 10-6

Figure 37 shows the fitted curve. Combined with a pregnancy rate of 0.9, these survival rates generate a population growth rate of 1.05. The life expectancy of each simulated female was calculated by choosing a random number between 0 and 1 and determining the age in days at which cumulative survival equalled this value.

Figure 37. Cumulative survival curve for female minke whales used in simulations, with annual survival rates Taylor et al (2007) shown by open circles.
Line graph showing the relationship between cumulative survival and age (years) for female minke whales. As described in the text above.

Foetal mortality In the absence of any empirical information on foetal mortality, this parameter was assumed to be zero.

Starvation body condition thresholds) We combined information on body composition from Nordøy et al. (1995) with estimates of structural body mass at different lengths from our growth to estimate that the mean body condition of sub-adult and adult animals on arrival at the feeding grounds was 0.12, based on the ratio of blubber mass to total mass. Adult females arriving on the feeding grounds will have just finished lactation and migration from their breeding grounds, so a body condition of 0.12 should represent a typical minimum level in their annual cycle. This suggests that 0.1 is an appropriate value for ρs.

Starvation-induced mortality rate s) No empirical information that could provide a species-specific value of this parameter for minke whales is available. As a starting point for exploratory modelling, we used the value of 0.2 proposed by Hin et al. (2019).

8.2 Model results – pattern-oriented modelling

We used three additional sources of information to investigate the performance of the minke whale DEB model.

Nordøy et al. (1995) documented the relationship between female length and blubber mass in animals killed at the start (average catch date 19 May) and end (average catch date 9 September) of the Norwegian whaling season and found that the slope of the regression relating these two variables was higher in animals taken at the beginning of the whaling season; the DEB model generated similar outputs (Figure 38).

Figure 38. The left panel shows 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 panel figure shows the equivalent outputs from the minke whale deb model.
Referenced line graph showing the relationship between length and blubber mass for females killed in early in whaling season. As described in the text above.

Christiansen et al. (2013) found that the total blubber volume of pregnant and mature female minke whales killed in the Icelandic whale hunt increased over the course of the whaling season, while the blubber volume of immature animals did not (Figure 39). Again, the DEB model predicted very similar changes.

Figure 39. The left panel shows 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 panel shows the equivalent outputs from the deb model.
Six line graphs with three in the left panel showing changes in blubber volume of pregnant and mature female minke whales over the course of whaling season (citied model output). Three right panel show the equivalent outputs from the <abbr title=DEB model. As described in the text above.">

Christiansen et al. (2014) used the same information to show that pregnant females that were in poor body condition (with a lower-than-expected blubber volume at a particular date in the whaling season) had foetuses that were substantially shorter than females that were in average or good condition. We were unable to duplicate this relationship in the DEB model, partly because all simulated females within a particular simulation experienced exactly the same resource density at a particular time of year, and therefore had similar blubber mass. Reducing Rmean to simulate the effects of low resource density for all whales did result in slightly smaller foetuses, but the main effect was to increase starvation-related mortality of females during the lactation period. This suggests that Christiansen et al.’s (2014) observations were the result of short-term variations in energy intake among individuals within a year, a process we were unable to capture in the DEB model.

8.3 Simulating the effect of disturbance

We assumed that common minke whales would only experience disturbance in UK waters during the summer months. Although there is some information on the response of minke whales to military sonars (Kvadsheim et al. 2017, Durbach et al. 2021), there is no equivalent information on the response of minke whales to piling noise. We initially assumed a similar response to that observed in harbour porpoises, with a 25% reduction in foraging efficiency on days when animals were exposed to this kind of noise, but disturbance on this scale had very little effect on vital rates. The following results assume that disturbance results in a 50% reduction in foraging efficiency.

Disturbance had a small effect on calf survival if it was spread randomly across the entire summer (Figure 40), but no effect if it was confined to the first three months of the summer (mid-April to mid-July).

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 indicatethe 95% credible interval based on 10,000 bootstrap calculations.
Line graph showing the relationship between calf survival and number says of disturbance for minke whale calves from mid-April to mid-October. As described in the text above.

However, there was a greater effect on calf survival if disturbance was confined to the period mid-July to mid-October (Figure 41). The effect was greatest on the calves of younger females (<25 years old), whose survival was reduced by 80%.

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.
Line graph showing the relationship between calf survival and number says of disturbance for minke whale calves from mid-July to mid-October. As described in the text above.

Figure 42 shows the changes in maternal and calf condition that cause this additional calf mortality.

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.
Line graph showing the changes in calf body condition with maternal age (in years). As described in the text above.



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