are consistent with the relationship between size and time scale of levels in the hierarchy, as presented by O'Neill et al. (1986).
The energy received by ecosystems as solar radiation comes in small packages (quanta, hv, where h is the Planck constant and v is the frequency), which makes only utilisation on the molecular level possible. The energy can be used on all hierarchical levels by an interactive coupling. The exchange of energy and matter on each level is dependent on openness, measured by the available area for exchange of energy and matter relative to the volume. Openness becomes the measure of the dynamics of the hierarchical level. Openness is inverse to hierarchical space scale.
Exchange of matter and information with the environment of open systems is not absolutely necessary, as energy input (non-isolation) is sufficient (the system is nonisolated) to ensure maintenance far from equilibrium. However, it often gives the ecosystem some additional advantages, for instance by input of chemical compounds needed for certain biological processes or by immigration of species offering new possibilities for a better ordered structure of the system. The importance of the latter consequence of openness is clearly illustrated in the general relationship between number of species, SD, of ecosystems on islands and the area of the islands, A:
where C and z are constants. The perimeter relative to the area of an island determines how "open" the island is to immigration or dissipative emigration from or to other islands or the adjacent continent. The unit (L _1) is the same as the above-used area to volume ratio as a measure of openness.
Another type of allomeric relation at the population level was manifested by Peters (1983). His plot of the abundance of different species of different body mass shows a steep decline in abundance of species of progressively larger size. This dependence is described by the equation
where N (ind/km2) is the population density and W (kg) the mean weight. From this formula, a curious conclusion follows: the mean spatial density of biomass for any animals at the second trophic level is the same: NW = 3 kg/km2 (see also Chapter 12).
Different species have very different types of energy use to maintain their biomass. For example, the blue whale uses most (97%) of the energy available for increasing the biomass for growth and only 3% for reproduction. Whales are what we call K-strategists, defined as species having a stable habitat with a very small ratio between generation time and the length of time the habitat remains favourable. It means that they will evolve toward maintaining their population at its equilibrium level, close to the carrying capacity. K-strategists are in contrast to r-strategists which are strongly influenced by any environmental factor. Due to their high growth rate, they can, however, utilise suddenly emergent favourable conditions and increase the population rapidly. Many fishes, insects, and other invertebrates are r-strategists. The adult female reproduces every season she is alive and the proportion going into reproduction can be over 50%.
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