Physiologically Based Approach

The basic premise of the physiological approach put forth here is that all organisms are consumers and have similar problems of resource acquisition (input) and allocation (output). The conditions that organisms face vary widely, as do the biological adaptations to solve these problems (Gutierrez and Wang, 1977). A model to analyse the effects of climate change on organisms must include the effects on its behaviour and physiology - on its ability to function and compete in the environment. It must include intra-specific competition for resources, prey availability and physiological processes of assimilation of resource to self in a tritrophic setting. Petrusewicz and McFayden (1970) and Batzli (1974) outlined the details of allocation physiology (Fig. 16.4). This well-known physiology is seldom included in population dynamics models, which is unfortunate because it is here that the effects of weather and climate change must enter.

16.4.1 Resource acquisition

Royama (1971, 1992) recognized two kinds of attack or resource acquisition functions: the 'instantaneous' and 'overall' hunting equations. These models are commonly called functional response models (Solomon, 1949; Holling 1966) and the instantaneous form is appropriate for continuous-time differential equation population dynamics models. If the time step of the model is large relative to the life span of the organism, then the integrated form of the instantaneous model or the overall hunting model is more appropriate. The dynamics of such systems should be written as discrete-time difference equations. The consumer may be a parasitoid or a predator, and these important differences must be taken into account in integrating the model. Readers are referred to Royama (1971, 1992) for complete details of this theory and Gutierrez (1996) for some applications.

There are many functional response models, but a variant of Watt's (1959) model is preferable because it incorporates all of the desiderata

Fig. 16.4. The metabolic pool model of a plant and animal (cf. Gutierrez and Wang, 1977).

outlined above. Ivlev (1955) was the first to think about the functional responses from the consumer point of view (Berryman and Gutierrez, 1998), but unfortunately few ecologists followed his lead (e.g. Watt, 1959; Gilbert et al, 1976; Gutierrez and Wang, 1977). Like Ivlev, Watt proposed that a consumer's attack rate depended on how hungry it was, and in addition on competition among consumers. The underlying logic of the models is outlined using the Berryman and Gutierrez notation. If 5h is the food needed to satiate hunger per unit of herbivore mass (H) per dt and f is the amount consumed per unit per dt, then hunger of the consumers is the fraction of its demand not met, i.e. (5h -f)/8h). The relationship of consumption df to the change in resource (dP) must include H as a component of the total demand by all consumers (5hH; see Gutierrez 1996).

The parameter a is the apparency of resource mass P to herbivore mass H. Integrating equation 16.2 gives the variant of Watt's functional response model used for estimating the quantity of resource obtained per unit of consumer as a function of resource and consumer abundance.

Equation 16.2 is an instantaneous hunting equation (see Gutierrez, 1996). In field applications, the amount of nutrients required by a poikilotherm organism per unit mass (5h) depends on temperature. The model saturates asymptotically to 5h as the exponent becomes more negative (Fig. 16.5a). Royama (1971) integrated equation 16.3 to obtain the parasitoid and predator functional response models for use in discrete time dynamics models. The model proposed by de Wit and Goudriaan (1978) for modelling photosynthesis has the same form as equation 16.3, but its analytical origins are quite different.

Food quantity or quality High

Plant

c cn

O EC

E ra

Food quantity or quality High

Plant

Plant

Plant

Temperature

Fig. 16.5. (a) Hypothetical functional responses (consumption) under different levels of resources (solid lines of varying width) as well as the respiration rate (dashed line) both plotted on temperature. (b) Growth rate on temperature as the difference between consumption and respiration at different levels of resources, from (a). (c) Growth rates of the three species at constant resource across temperature.

Temperature

Fig. 16.5. (a) Hypothetical functional responses (consumption) under different levels of resources (solid lines of varying width) as well as the respiration rate (dashed line) both plotted on temperature. (b) Growth rate on temperature as the difference between consumption and respiration at different levels of resources, from (a). (c) Growth rates of the three species at constant resource across temperature.

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