Life history models

Life history models may be useful for considering age- or stage-specific variability in sensitivity in the extrapolation of response however, it should not be assumed that smaller or younger stages are always the most sensitive. The few studies that have addressed the impact of time of year on responses of aquatic communities to a stressor indicate that, in freshwater communities, threshold concentrations for direct toxic effects vary within a factor of 2 among seasons — well within the normal range of variation observed in laboratory toxicity tests. However, at greater exposures, the intensity and duration of direct and indirect responses may vary considerably between different periods of the year because of the influence of climatic and seasonal factors on recovery. 

Variable sensitivity within Seasonal, life history Model systems 6 Temporal 6.3.2... 

It appears from the above that microcosm and/or mesocosm tests are limited by the constraints of experimentation, in that usually only a limited number of recovery scenarios can be investigated. Consequently, modeling approaches may provide an alternative tool for investigating likely recovery rates under a range of conditions. Generic models, like the logistic growth mode (for example, see Barnthouse 2004) and life history and individual-based (meta)population models, which also may be spatially explicit, provide mathematical frameworks that offer the opportunity to explore the recovery potential of individual populations. For an overview of these life history and individual-based models, see Bartell et al. (2003) and Pastorok et al. (2003). 

Carroll S. 2002a. Population models life history. In Pastorok RA, Bartell SM, Ferson S, Ginzburg LR, editors. Ecological modeling in risk assessment chemical effects on populations, ecosystems, and landscapes. Boca Raton (FL) Lewis Publishers, p 55-64. 

Barnthouse and colleagues (Barnthouse 1993 Bamthouse et al. 1990, 1989) have explored the use of conventional population models to explore the interactions among toxicity, predation, and harvesting pressure for fish populations. These studies are excellent illustrations of the use of population models in the estimation of toxicant impacts. These models employed the use of information concerning the life history and age structure of the organism being modeled. 

Life History diagram for an age-structured population. The numbers of organisms in the population at time t, is dependent on the numbers of the one-year younger-age class of the year before and the survivorship percentage from t0 to tj. The numbers are also dependent upon the number of offspring from the previous year surviving up to age 1. This is a general model for many plant and animal populations. 

Such models describe the life history of animals as propagation through the different size or mass classes and need a sophisticated formulations of predator-prey interaction. There are several approaches to describe life histories of copepods by models (Carlotti et al., 2000). A new theoretical formulation to allow the consistent embedding of dynamical copepod models into three-dimensional circulation models was given in Fennel (2001). Examples of simulations for the Baltic were given in Fennel and Neumann (2003). The basic idea is that both biomass and abundance of different stages or mass classes are used as state variables, while the process control is related to mean average individuals in each mass class, that is the ratio of biomass over abundance. 

As with the trends previously mentioned, proposals have been promulgated for internal and external constraints. At first pass, it is tempting to account for relations between life history variables almost purely on the basis of fundamental allometric constraints. Metabolic rate, lifespan, fecundity, age at maturity, and maternal investment all vary with body mass as power functions. In fact, relations are invariant between some of these variables. For example, lifespan scales with body mass by a 1/4 power, and heart rate (or the rate of ATP synthesis) scales with body mass by a — 1/4 power. The product yields an approximately constant number of metabolic events in mammal species, independent of body mass or lifespan. Age at maturity / lifespan, and annual maternal investment / lifespan (for indeterminate growers), are also invariant ratios (Chamov, 1993 Chamov et al., 2001 Steams, 1992). West and Brown (2004) point out that invariant ratios, and universal quarter-power allometric trends in general, suggest underlying physical first principles. They employ their model to explain these life history relations (Enquist et al., 1999 Niklas and Enquist, 2001 West et al., 2001). 

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