Abstract
Deep-sea benthic systems are notoriously difficult to sample. Even more than for other benthic systems, many flows among biological groups cannot be directly measured, and data sets remain incomplete and uncertain. In such cases, mathematical models are often used to quantify unmeasured biological interactions. Here, we show how to use so-called linear inverse models (LIMs) to reconstruct material and energy flows through food webs in which the number of measurements is a fraction of the total number of flows. These models add mass balance, physiological and behavioral constraints, and diet information to the scarce measurements. We explain how these information sources can be included in LIMs, and how the resulting models can be subsequently solved. This method is demonstrated by two examples-a very simple three-compartment food web model, and a simplified benthic carbon food web for Porcupine Abyssal Plain. We conclude by elaborating on recent developments and prospects.
Highlights
Deep-sea benthic systems are notoriously difficult to sample
We know little about the taxonomy, natural history, and trophic linkages among the organisms that inhabit deep-sea sediments. This limitation makes it difficult to predict the impact of human activities on deep ecosystems, but such predictions are greatly needed because human pressures on this ecosystem are increasing rapidly (Glover and Smith, 2003)
Benthic food web models study the flows of energy or matter between biological functional groups
Summary
This situation would be the case when the measured total input of organic matter is insufficient to meet the minimum respiration requirements (e.g., estimated from physiological considerations) of the benthic community (e.g., Smith et al, 2001) This result (albeit undesirable) is important, as it shows that data that seem plausible when evaluated individually may be inconsistent when viewed in the perspective of the entire food web. When the data in the under-determined model are internally consistent, there exists an infinite number of valid solutions In this case, the linear equations define an “ensemble” of plausible webs—a multidimensional solution space containing food web configurations that do not violate the equations (Figure 4). A simplified benthic carbon food web for this system is presented in Box 3 and Figures 5 and 6
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