Size spectra
Size-abundance relationships
Body size has long been thought to influence both the distribution and abundance of animal species, but we are only just beginning to discern the overall role that size plays in organising the Earth’s biota. … It hints at there being as yet undiscovered patterns involving size, energy distribution and abundance … Damuth 1991
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Regularities in the patterns of abundance and size have been appreciated for a long time in numerous domains. They are terrestrial, pelagic and benthic systems and across many different spatio-temporal scales. They suggest the presence of some very fundamental and general mechanisms that interact to create these (macroecological) patterns of size and abundance. Unfortunately, as with most other ecological concepts, no consensus is emerging as to how or why these patterns come to be.
[ Aside: I will add them here in due time. See Choi et al 1999 for some more background and one interesting perspective. ]
Examples of size-spectra
One of the earliest references to this pattern was made by Elton (1927). He named this pattern of decreasing numbers of organisms and energy use with increasing trophic level, the “Pyramid of Numbers and Energy”, and attributed it to the sequential loss of energy at each step of consumption along the trophic chain (i.e., metabolic heat and waste). While the explanation is not entirely correct, as it does not account for the recycling of biomass (e.g., cannibalism, decomposition, microbial activity; Patten 1985), the empirical pattern itself remains one of the very few well-established ecological regularities.
Sheldon et al. (1972, 1977) were among the first to systematically quantify this pattern for marine plankton when they noted that the biomass in logarithmically-scaled body size categories from plankton to whales seemed to be a flat function (slope = 0, although a great deal of spatio-temporal variation was also observed). Another representation of this pattern is the “normalised biomass size spectrum” (Platt and Denman 1978), which represents this pattern in terms of numerical abundance (rather than biomass) as a function of the size of the organisms, both on logarithmic scales. This latter, “size-abundance” relationship has been found to have slopes with values near –1. In the intervening years, numerous other systems have been explored and this pattern has been repeatedly confirmed: a log-linear form of the size-abundance relationship with slopes near –1. Finer-scaled patterns exist (e.g., Gasol et al. 1991, Thibeaux and Dickie 1992, Sprules and Goyke 1994), termed “secondary” scalings (Boudreau et al. 1991), but the “primary” scaling of a log-linear form between size and abundance remains consistent (Boudreau and Dickie 1992, Sprules and Goyke 1994). For example, in examining the plankton (10 um to 8 mm length scales) of the North Pacific Central Gyre, Rodriguez and Mullin (1986) described the slope of the size-abundance relationship to range from –1.34 to –1.07. In studies of the Laurentian Great lakes and some smaller inland lakes, Sprules and Munawar (1986) and Sprules and Goyke (1994) found the slopes, for organisms ranging from phytoplankton to fish, to also range between –1.24 to –0.62. In lake Constance, Gaedke (1992) found the slopes to seasonally range from –1.3 to –0.9 for a size range from bacteria to zooplankton; while in an examination of organisms ranging from bacteria to zooplankton (0.2 to 1600 mm length scale) in smaller Québec lakes, Ahrens and Peters (1991a,b) found the slopes to range from –1.01 to –0.75. Garcia et al. (1995) report an average slope of –1.06 for a shallow saline lake for plankton with length scales ranging from 2 to 4000 mm. These results indicate that the size-abundance relationship is a robustly stable state that extends across a huge range in organism sizes in the pelagic environment.
In the terrestrial literature, these patterns have been independently elucidated by the work of Mohr (1940) and Damuth (1981) for mammals, Nee et al. (1991) for birds, and Yoda et al. (1963) for plants. Studies of benthic ecosystems have also found similar allometric patterns (slopes ranging between –0.97 and –0.81; Schwinghamer 1981, Cattaneo 1993), although there is some uncertainty as to whether there are discontinuities in this pattern (see Cattaneo 1993). These patterns also exist at a global scale (Peters 1983), an ecosystem scale (Marquet et al. 1990, Morse et al. 1985) as well at the population/cohort scale (Yoda et al. 1963, Bohlin et al. 1994). The slopes reported vary greatly, generally ranging between –0.62 and –1.3, but its average form is consistently a value near –0.75 to –1. The recurrence of this pattern has sparked a number of debates, such as what is the “correct” value of the exponent, or is the quantity of energy flowing through a species the same for all species (Damuth 1991, Nee et al. 1991); these questions are yet to be resolved.
In contrast to the extensive empirical work described above, the theoretical understanding of the mechanisms that cause these patterns has progressed little beyond Elton’s simple explanation (1927). The few theoretical models that exist still exclusively adopt Elton’s paradigm and try to explain the empirical patterns through mass transfer and energy loss from small to larger organisms or from lower to higher trophic levels (i.e., predator-prey interactions; Platt and Denman 1978, Borgmann 1987, Thibeaux and Dickie 1992, Sprules and Stockwell 1995). Using such an argument, the scaling exponent in steady state was predicted to be near –1.2 by Platt and Denman (1978). Unfortunately, these models apply only to large heterotrophic consumers (zooplankton and fish), as they do not explain the presence of this pattern amongst autotrophs and heterotrophic bacteria where matter and energy flows are much more complex. Further, these models do not account for the reverse transfers (i.e., feedback cycles) of mass and energy from larger to smaller organisms (e.g., decomposers, parasites or detrital system), which can account for the bulk of the metabolic activity in aquatic systems (> 50%; Winberg 1972, Pomeroy 1974, Williams 1984, Platt et al. 1984, Cole et al. 1988, Strayer 1986, Jahnke and Craven. 1995). The extremely important role of the input of organic carbon (dissolved and particulate) from the littoral zone, the watershed runoff, the resuspension of sedimented organics by abiotic (storms) and biotic (vertically migrating zooplankton and fish) factors, and the internal recycling of carbon in lake ecosystems are also ignored, making this approach a tenuous one at best. Silvert (1982), one of the pioneers of these models, also notes that these simple models are inappropriate as the same size-abundance patterns are also found in more physically structured terrestrial and benthic environments.
At a population level of description, other mechanisms have been proposed to explain this phenomenon. When a cohort is followed through time, a self-thinning of population size occurs, as individuals grow larger. In plant populations, the “self-thinning” rule has been attributed to intra-specific competition for space or resources (light, water, nutrients) and is commonly referred to as the “self-thinning rule” (exponent ?–0.67; Yoda et al. 1963). The same pattern, although considerably more variable, has been demonstrated by Bohlin et al. (1994) for cohorts of Atlantic salmon, brown trout and sea trout in Swedish rivers (slopes ranging from –0.9 to –1). Thus, strong intra-specific competition causing self-thinning of populations over time represents an important mechanism that may potentially generate the patterns of size and abundance that we observe.
A similar competitive mechanism but at an inter-specific level, was suggested by Morse et al. (1985) when examining the abundance of arthropods in vegetation. They attributed the log-linear form of the pattern to the fractal-like nature of habitat space as a limiting resource. Unfortunately, this explanation does not account for the presence of these patterns in physically less structured environments such as, for example, the pelagic system. Nor does it (nor do the other explanations, being based solely upon competitive or predatory relations) account for other important interactions such as parasitism, disease, mutualisms/synergisms and the profoundly complex and intricate nature of spatial, temporal and biological organisation found in real systems.
As mentioned above, there really is no consensus as to how these patterns “emerge”. See Choi et al 1999 for some more background and one meta-perspective. Perhaps it would be sufficient to suggest that every organism is exposed to a great number of mortality causing factors that are often size dependent. The multiplicative effects, due to the stochastic, Markovian nature of such processes in combination with the Law of Large Numbers would suggest an expectation of a lognormal distribution as a function of size.
Now to actually develop such a simulation model would be the next interesting step. One of these days, I get back to this. If you have solved it already, please let me know.
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Damuth, J. 1991. Of size and abundance. Nature 351:268-269.