Monaco CJ et al. (2014), A Dynamic Energy Budget (DEB) model for the key...

ECB-ART-43592

PLoS One 2014 Aug 27;98:e104658. doi: 10.1371/journal.pone.0104658.

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A Dynamic Energy Budget (DEB) model for the keystone predator Pisaster ochraceus.

Monaco CJ , Wethey DS , Helmuth B .

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We present a Dynamic Energy Budget (DEB) model for the quintessential keystone predator, the rocky-intertidal sea star Pisaster ochraceus. Based on first principles, DEB theory is used to illuminate underlying physiological processes (maintenance, growth, development, and reproduction), thus providing a framework to predict individual-level responses to environmental change. We parameterized the model for P. ochraceus using both data from the literature and experiments conducted specifically for the DEB framework. We devoted special attention to the model''s capacity to (1) describe growth trajectories at different life-stages, including pelagic larval and post-metamorphic phases, (2) simulate shrinkage when prey availability is insufficient to meet maintenance requirements, and (3) deal with the combined effects of changing body temperature and food supply. We further validated the model using an independent growth data set. Using standard statistics to compare model outputs with real data (e.g. Mean Absolute Percent Error, MAPE) we demonstrated that the model is capable of tracking P. ochraceus'' growth in length at different life-stages (larvae: MAPE = 12.27%; post-metamorphic, MAPE = 9.22%), as well as quantifying reproductive output index. However, the model''s skill dropped when trying to predict changes in body mass (MAPE = 24.59%), potentially because of the challenge of precisely anticipating spawning events. Interestingly, the model revealed that P. ochraceus reserves contribute little to total biomass, suggesting that animals draw energy from structure when food is limited. The latter appears to drive indeterminate growth dynamics in P. ochraceus. Individual-based mechanistic models, which can illuminate underlying physiological responses, offer a viable framework for forecasting population dynamics in the keystone predator Pisaster ochraceus. The DEB model herein represents a critical step in that direction, especially in a period of increased anthropogenic pressure on natural systems and an observed recent decline in populations of this keystone species.

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Genes referenced: LOC100887844 LOC100893907 LOC583082 LOC764183

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	Figure 1. Schematic representation of standard Dynamic Energy Budget model.Arrows represent energy fluxes (J d−1) that drive the dynamics of the four state variables, depicted in boxes (Reserve, Structure, Maturation, and Reproductive Buffer). Energy enters the animal as food, and then assimilated at a rate into Reserves. Mobilization rate, , regulates energy fluxes to cover the demands from somatic maintenance, , structural growth, , maturity maintenance, , maturation, (immature individuals), and reproduction, (mature individuals). The parameter kappa () is the proportion of mobilized energy diverted to and , while the rest (1−) is used for and . Formulations explaining these fluxes are given in the Appendix S1. Overheads associated to assimilation, growth and reproduction arise due to thermodynamic inefficiencies when transforming between substrates.
	Figure 2. Scaled feeding rate as a function of prey density.Observed values (circles) and projection (line), based on a type II feeding functional response (Appendix S1, Eq. 1), are shown for mussels with 2-cm shell length. The estimated value for the half-saturation parameter was 13.9±2.3 (Mean±1 SD) mussels m−2.
	Figure 3. Temperature sensitivity.Observed values (circles) represent relative values of oxygen consumption and feeding rate (coldest temperature treatment) determined at a range of water temperatures from 278 to 299 K. The line of best fit was obtained by first estimating Arrhenius temperature, , and then running a grid-search to find the combination of parameter values for (lower limit of tolerance range), (higher limit of tolerance range), (Arrhenius temperature at lower limit), and (Arrhenius temperature at higher limit) that minimized the RMSE between observed and simulated data.
	Figure 4. Body wet weight in () relation to arm length ().Observed values are shown as dots (N = 457 individuals). By fitting the equation , we estimated the post-metamorphic shape coefficient (). The estimate was then optimized through the covariation method (DEBtool), yielding 0.52±0.03 (Mean±1 SD). The trajectory described by this model is shown as a line crossing the cloud of points below their center, thus better representing the contribution of structure to body weight.
	Figure 5. Larval growth from 0 to 27 d after birth.Birth is considered as the day when larvae begin feeding. Laboratory data (from citation [29]) are shown as dots. The line comes from a Dynamic Energy Budget model simulation, assuming ad libitum food and 12°C water temperature. Root Mean Square (RMS) error, Mean Absolute Error (MAE), and Mean Absolute Percent Error (MAPE) are shown.
	Figure 6. Post-metamorphic change in arm length over time at two water temperature treatments.Laboratory data from ad libitum feeding experiment (from citation [12]) are shown as dots. Solid symbols and black line are from 9°C treatment, open symbols and grey line are from 12°C treatment. Dotted lines are DEB predictions, grey levels as above.
	Figure 7. Post-metamorphic change in wet weight over time as a result of complete starvation.Each panel shows data for a different individual. Laboratory observations from long-term starvation trials are shown by dots and solid lines. Triangles and dotted lines are DEB predictions using the value for parameter that minimized the RMSE between observed and predicted data. The mean of the six estimates of , 11.5 J d−1 cm−3, was used in the DEB model.
	Figure 8. Post-metamorphic change in arm length and wet weight over time since larval settlement.Panel A illustrates arm length, and B wet weight. Laboratory observations (from citation [31]) are shown as dots. Food was provided ad libitum, and water temperature kept at 14.5°C, in accordance to the average reported by [31]. Grey lines are results of 1000 Monte Carlo DEB simulations, which simultaneously sampled parameter values from normal distributions with parameter means and standard deviations (Table 1). Black line is DEB simulation using mean values for all parameters (Table 1). Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percent Error (MAPE) are relative to the DEB simulation that used mean parameter values.
	Figure 9. Change in wet weight under abundant food versus starvation.Values are results of DEB simulation using mean parameter values at a temperature of 13°C. Wet weights of gonad (black), reserve (dark grey), and structure (light grey). Panel A is trajectory with food ad libitum, and B is trajectory during complete starvation.

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