More Detailed Growth Models

Several models have delved more into the details of feeding or bioenergetics to predict growth in fish, and five additional modeling frameworks should be highlighted.

First, a group of researchers at the University of Wisconsin-Madison has produced a software package for modeling the bioenergetics and growth of fish (Fish Bioenergetics, now in its version 3.0). Their basic equation states that an individual's energy budget has to balance:

Consumption = Metabolism + Wastes + Growth

They then identify the following subcategories:

Metabolism = Standard metabolism + Cost of activity + Digestion

Wastes = Egestion + Excretion

Growth = Somatic growth + Gonad production

Each process is thereafter explained in detail and equations are given for size and temperature dependence where necessary. They have also collected necessary parameters for ^30 species of marine and freshwater fishes.

Second, the research groups of Andre deRoos (University of Amsterdam, The Netherlands) and Lennart Persson (Umea University, Sweden) have highlighted the ecological implications of size and growth in theory, modeling, experiments, and field work. Their models are called physiologically structured population models, and are based on a set of differential equations for feeding, including competition, mortality including cannibalism and starvation, and other relevant physiological processes. These models are more technical to implement because they involve frequency and density dependence, but in return, they predict a population's size structure and a rich array of ecological consequences.

Third, Bas Kooijman and colleagues (Vrije Universiteit Amsterdam, The Netherlands) have been developing the theory of dynamic energy budgets (DEB). DEB models are based on the division of an individual's energy into two compartments: structural body mass and reserves. As the individual forages, energy goes to the reserve from where it is distributed to other functions. The energy can be used, following simple mechanistic rules, for somatic maintenance, reproductive maintenance, and reproduction, or it can be used to increase the structural body mass. What makes DEB models dynamic is the fact that the energy allocation rules can change as an individual grows through life, reflecting the different phases of the life cycle. The theory covers all living organisms and provides explanations of how certain physiological traits are scaled with body size.

Fourth, William Neill and his research group at Texas A&M University have developed very detailed simulation software called Ecophys. Fish that predicts the growth of individual fish in a time-varying physical environment. Including factors such as temperature, salinity, oxygenation, and pH, their model quantifies bioenergetics, growth, and stress of individual fish. The model was applied operationally for estimating stocking densities of red drum, and is also in use for monitoring growth and welfare in aquaculture.

Fifth, the traits that govern the division of resources between growth on the one hand and maturation and reproduction on the other can be parametrized using life-history evolution. Several modeling tools are available, such as individual-based genetic-algorithm models or state-dependent optimization models, and they can be

combined with several of the growth models above to find adaptive life-history strategies. This approach has the advantage that it can predict how growth might change when the biotic or abiotic environment changes, for example, due to changes in predation, temperature, harvest, or other aspects of environment. The drawback with evolutionary models is that they often become vulnerable to the underlying assumptions, since they not only predict growth given empirical observations, but should in principle also predict the observed growth given the environmental and ecological forcing on the system.

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