Patterns in covariation of parameters

Parameter-values are individual-specific, but intra-specific differences between individuals are small relative to inter-specific ones. So it remains meaningfull to talk about species-specific parameters values as means of those of individuals of that species. Once we know the parameters, we can compute many properties (traits), even if these properties have not been measured. DEB theory has implied rules for the covariation of parameters, based on plain physics, but ecological and evolutionary adaptation can modify these rules. Quite a few papers have been written on the various patterns in DEB parameters and derived traits; the Supporting Information for these papers shows how to extract these patterns from the AmP collection, see DEB papers. Clicking on the markers in the resulting plots shows the name of the corresponding species.

Click here for a poster that summerizes the five patterns in parameter values that have been identified so far.
This page shows some examples of relationships between traits.

Left: Log dioxygen consumption as function of log maximum adult body weight at Tref. Dioxygen consumption has a number of adding contributions, such as from digestion, growth and reproduction overheads (or maturation in pre-adults) and maturity and somatic maintenance. DEB theory has no assumptions about respiration and gets it by closing the mass balance for chemical elements (C, H, O and N). In this way it respects the additive nature of contributions to respiration. The reason why respiration of fully grown adults is less than proportional to mass is because reserve density tends to increase with maximum weight (Kooy1986), while reserve does not require maintenance, and because small-bodied species are more frequently in a hurry (Kooy2013). Respiration is roughly proportional to weight3/4, which is known as Kleiber's law.

Right: Log maximum growth as function of log (wet) weight at maximum growth at Tref. Contrary to popular belief, the big dinosaurs did not grow exceptionally fast, given their body mass. Specific growth at maximum growth is proportional to specific somatic maintenance.

Left: Log reserve capacity [Em] as function of log specific assimilation rate {pAm} at Tref. This capacity is the ratio of the surface-area-specific assimilation rate and the energy conductance, i.e. input to and output from reserve, while the latter does not vary that much. Since large-bodied species have a larger capacity, they can starve for a longer period, also because they have a small specific somatic maintenance.

Right: Log volume-specific somatice maintenance [pM] as function of log maximum structural volume Lm3 at Tref. Small-bodied species more frequently compress their life cycle in a short period and synchronize it with a temporary abundance of their resource. They need to combine this with a torpor state in periods when resources are scarce, or else migrate or change diet. Herbivores can only grow fast, for instance, when they manage to squeeze their fast-growth period in that of plants, since only then plants are rich in proteins that herbivores need for growth. The plant growth season might be short in some habitats.

Survivor functions of the log specific somatic maintenance rate [pM] for lophotrochozoans (left) and mammals that feed on various types of food (right), all at Tref. Among the lophotrochozoans, cephalopods and annelids have the highest specific somatic maintenance rates. They are also the only invertebrates with closed capillary networks, allowing changes in cardiac output to be transmitted efficiently to all corners of the body. Among mammals, species feeding on leaves generally have lower specific somatic maintenance than those feeding on seeds or fruits, reflecting the lower seasonality of leaf availability than seed/fruit availability. The vertebrate-eating mammals have the lowest specific somatic maintenance, but they combine this with the highest aerobic scope (VerhKooy2026), so the highest peak metabolic rate. These results support the view that the level of specific somatic maintenance depends on the seasonal dynamics of food (LikaAugu2026).

Connections between inner and outer worlds of individuals

Apart from mass and energy conservation, the inner world of individuals is connected to the outer world via the tetrahedron of life (left). It follows from the allocation scheme of the standard DEB model (right) via the covariation of the supply stress ss and the trophic position of species in the food web (below). "Supply" means: depending on resource availability: the left-over after paying maintenance costs. Extreme starvation affects the allocation scheme.
These plots for fully-grown invertebrates (above) and vertebrates (below) show the minimum scaled fuctional response to reach puberty, fmin (left) and the fraction of assimilation allocated to reproduction, κRA (right), as function of the fraction of mobilised reserve allocated to soma, κ, and the supply stress, ss, i.e. maturity maintenance times the squared somatic one, divided by cubed assimilation. The latter dimensionless quantity can take values between zero (for supply species) and 4/27 (for demand species). The meshes are defined by fmin = ss1/3 κ-2/3 (1 - κ)-1/3 and κRA = 1 - κ - ss/ κ2. All points are on this mesh, but some invertebrates and some ray-finned fish deviate a little due to metabolic acceleration; generally ss remains constant during the life cycle, but decreases during acceleration. No tetrapod accelerates. The values that κ can take depend on the supply stress, as indicated in the plots. The upper boundary is better populated than the lower one. Only for ss=0 can κ span the full range between 0 and 1. Outside this range, puberty cannot be reached, so the life cycle cannot be completed. Notice that ecdysozoa (especially insects) are masters of the supply strategy, and vertebrates (especially birds and mammals) are masters of the demand strategy. The latter two taxa are also endothermic, which further supports their demand position. Many properties of species depend on where they are in the supply-demand spectrum (LikaAugu2014, VerhKooy2026).

The equation for fmin implies that the minimum functional response to reach puberty increases with the supply stress, so with the trophic position. This alines with the finding that the aerobic scope, i.e. the ratio of the peak and the basal metabolic rate, was found to increase with the supply stress (VerhKooy2026); demand species, which have a high supply stress, have an aerobic scope that is 10 times higher than for supply species, a small half-saturation coefficient and a high food searching rate. But if the feeding rate is less than nearly at maximum for demand species, they cannot reproduce, so cannot further increase the pressure on their prey.

The equation for supply stress ss implies that the supply stress needs to be small for the fraction of assimilation to reproduction to be large. Invertebrates and ray-finned fish have a small supply stress, so a low trophic position and are fecund; in constrast cartilaginous fish, amphibians and reptiles have a moderate supply stress and birds and mammals have a high supply stress and are much less fecund.

This structural coupling of traits contributes to regulating energy flow across trophic levels and reduces or avoids over-exploitation of resources in food webs. The implied ecological stability is probably the reason why evolution favoured this particular allocation scheme (Kooy2026a). We found no indication that evolution generally favoured maximazation of reproductive output (KooyLika2014), as is widely assumed in the literature, but never demonstrated.

The survivor functions of the supply stress ss for members for an aquatic (left) and a terrestrial (middle) food chain that typically occupy trophic position 1,2 and 3, and for rodents and carnivorans (Kooy2026); Passeriformes only includes species that feed on invertebrates. Rodents typically have a lower trophic position than carnivorans, and are more fecund, consistent with the equation for the supply stress in the tetrahedron that implies that lower supply stress allows a larger fraction of assimilated energy to reproduction.