Model Simulations

If prey PCB concentrations are constant over time, a stable state will finally be reached where PCB, damage, hazard and stress levels are stationary. If density dependence is neglected, also fertilities and survival rates stabilize at constant values and the population grows (or declines) at constant rate. Under these conditions, biomagnification factors and stable population growth rate can be defined. Age-specific biomagnification factors (based on lipid concentrations) were calculated as the ultimate concentration ratios in seals and their prey. The stable population growth rate is calculated as the dominant eigenvalue of the Leslie matrix. For steady-state simulations we tested the effect of different levels of constant sum-PCB lipid concentrations in prey (0–10 mg/kg) and run the TKTD population model for 100 years. Endpoints of interest were simulated temporal changes in mean sum-PCB lipid concentrations and population size for Baltic grey seals.

To describe the impact of parameter uncertainty on model outputs we run a global sensitivity analysis (change one parameter at a time). A sensitivity analysis investigates how uncertainty in input parameters causes uncertainty in population growth and can be used to identify parameters that are critical for population viability (Lacy et al. 2018). Given that Harding et al. (2007) performed a detailed sensitivity analysis of their grey seal Leslie matrix model for Leslie matrix parameters, we did not perform a similar analysis here. Instead, we focus the sensitivity analysis to TK and TD parameters, assuming steady-state conditions. This analysis was performed for three of the TK model parameters: the lactational transfer rate constants kL,i, the placental transfer rate constants kP,i and the removal rate constants kR,i (accounting for the combination of metabolic transformation and fecal egestion). Ratios between lactational transfer rate constants of different age classes were held fixed under perturbations, whereas the placental transfer rate constants were the same for all fertile age classes. The removal rate constant kR,i were dependent on age class through body mass. Sensitivity was also assessed against three TD model parameters across life stages: killing/stress rate constants (σ0, σi, σ~i), recovery rate constants (r0, ri, r~i) and damage threshold levels (dT,0, dT,i, d~T,i). A constant PCB lipid concentration in prey, generating positive stable growth rate over time, was used as input and the toxicokinetic rate constants were varied one at time, whereas other parameters were held constant. Stable population growth rate was plotted as a function of the perturbed relative value of investigated model parameters, defined as the perturbed value (ppert) divided by the value adopted in the model (pmod): prel=ppert/pmod.

Segerstedt (2019) compiled data from previous studies of PCB concentrations in grey seals and their primary prey items (cod, sprat, and herring) from all regions of the Baltic Sea during 1966–2015, converted all concentrations to a lipid weight basis and clustered data into time intervals of 5 years. We linearly interpolated prey PCBs concentrations over each five-year period to obtain yearly PCB concentrations, used as input to the toxicokinetic model (Fig. 4a; SI-Fig. 8). The TKTD population model was used to run simulations for the time period 1966–2015, where data on PCB levels in prey and seals were available. A five-year pre-simulation period (1961–1965) was included to initiate realistic values of PCB and damage levels. Since PCB levels in Baltic fish were low in the early 1960s (Bignert et al. 1998), all PCB, damage, and hazard/stress levels were put to zero at the start of year 1961. Prey concentrations were assumed to increase linearly from zero (at 1961) to the reported levels 1966. The total population size year 1961 has been estimated to 17 639 seals, including males and females (Harding and Härkönen 1999). The initial population size in the simulation (accounting for females exclusively) was put to the half of that amount (8820 seals). Simulation outputs for temporal PCB levels in seals and population size were compared to empirical data.

Time-varying dietary exposure model results for PCB dynamics. a Temporal sample mean sum-PCB lipid concentrations in different prey species from the Baltic Sea during 1966–2015, according to data compiled by Segerstedt (2019). b Mean sum-PCB lipid concentrations in female Baltic grey seals (i = 1–46) between 1966 and 2015. Shown are model predictions and published data (Segerstedt 2019). c Mean sum-PCB lipid concentrations in juvenile Baltic grey seals (i = 1, 2, 3) according to model predictions and published data (Roos et al. 2012). d Mean age-specific sum-PCB lipid concentrations in different cohorts of female Baltic grey seals between 1966 and 2015