Typified models

Animal diversity is captured by a family of related DEB models, which are all simple extensions of the most simple one: the standard (std) DEB model. Hundreds of examples of applications can be found in the predict files of the AmP collection. The most used models are presented below.

s-models

s-models assume isomorphy throughout the full life cycle: surface area is proportional to volume to the pwer 2/3.

std

 The standard DEB model follows from the assumptions as listed in Table 2.4 of the DEB book. Within the family of DEB models, it can be seen as a canonical form, which differs from other DEB models by:
  • 1 type of food, 1 type of reserve, 1 type of structure
  • 3 life stages: embryo, juvenile, adult
  • isomorphism for all life stages
  • O2 available without limitation
  • products: faeces and 3 minerals CO2, N waste, H2O
The model equations are summarized in Table 2.5, and in scaled stochastic form in the comments on Section 2.9.

stf

 Like model std but with foetal development (rather than egg development): allocation from mother to embryo, such that development is unlimited.

stx

 Like model stf but with foetal development (rather than egg development) that first starts with a preparation stage and then sparks off at a time that is an extra parameter a baby stage (for mammals) just after birth, ended by weaning, where juvenile switches from feeding on milk to solid food at maturity level EHx. Weaning is between birth and puberty. In its simplest form, it is a two parameter extension of model std at abundant food. Food quality and upregulation can involve more parameters. Milk production is from upregulated feeding/assimilation. The quantification of this process involves further parameters. See Section 7.7 of the DEB book and its comments.

ssj

 Like model std but with a non-feeding stage between events s and j during the juvenile stage that is initiated at a particular maturity level and lasts a particular time. Substantial metabolically controlled shrinking occur during this period, more than can be explained by starvation. It is a two or three parameter extension of model std. This life history is found in Elopiformes, Albuliformes, Notacanthiformes, Anguilliformes, Ophidiiformes and some Echinodermata. The comments on Section 1.1.4 give more background.

sbp

 Like model std but with growth ceasing at puberty, meaning that the kappa-rule is not operational in adults. It has the same parameters as the model std. This life history is found in Calanus, while other copepods accelerate. We obviously need more data and better culturing techniques.

a-models

a-models assume also isomorphy, but during part of the life cycle metabolism accelerates following the rules for V1-morphy. Notice that the parameter values are given before acceleration, because the amount of acceleration depends on food density. Acceleration affects the specific maximum assimilation and the energy conductance, such that reserve density is not affected.

abj

 The DEB model with type M acceleration is like model std, but
  • acceleration between birth and metamorphosis (V1-morph)
  • before and after acceleration: isomorphy.
  • Metamorphosis is before puberty and occurs at maturity EHj, which might or might not correspond with changes in morphology.
This model is a one-parameter extension of model std.

asj

 The DEB model with delayed type M acceleration is like model abj, but start of acceleration is delayed till maturity level EHs before and after acceleration: isomorphy. Metamorphosis is still before puberty. This model is a one-parameter extension of model abj.

abp

 The DEB model with type M acceleration is like model abj, but acceleration between birth and puberty (V1-morph); before acceleration: isomorphy and after acceleration: no growth, so no kappa-rule Metamorphosis can occur before puberty and occurs at maturity EHj, but only affects morphology, not metabolism. This model has the same number of parameters as model std. It appies to copepods, may be also to ostracods, spiders and scorpions.

h-models

h-models are as a-models, but with extra life stages (as found in insects) triggered by the reproduction buffer density

hep

 The DEB model for ephemeropterans, odonata and possibly other insect groups. It characterics are
  • morphological life stages: egg, larva, (sub)imago; functional stages: embryo, juvenile, adult, imago
  • the embryo still behaves like model std
  • acceleration starts at birth and ends at puberty
  • puberty occurs during the larval stage
  • emergence occurs when reproduction buffer density hits a threshold
  • the (sub)imago does not grow or allocate to reproduction. It mobilises reserve to match constant (somatic plus maturity) maintenance

hex

 The DEB model for holometabolic insects. Its characterics are
  • morphological life stages: egg, larva, pupa, imago; functional stages: embryo, adult, pupa, imago
  • the embryo behaves like model std
  • the larval stage accelerates (V1-morph) and behaves as adult, i.e. no maturation, allocation to reproduction
  • pupation occurs when reproduction buffer density hits a threshold
  • pupa behaves like an isomorphic embryo of model std; larval structure rapidly transforms to pupal reserve just after start of pupation
  • the reproduction buffer remains unchanged during the pupal stage
  • emergence of imago occurs if maturity hits a threshold value
  • the imago does not grow or allocate to reproduction. It mobilises reserve to match constant (somatic plus maturity) maintenance

hax

 The DEB model for holometabolic insects with a long larval stage. It is a hybrid between the hep and hax models and its characterics are
  • morphological life stages: egg, larva, pupa, imago; functional stages: embryo, adult, pupa, imago
  • the embryo behaves like model std
  • the larval stage accelerates (V1-morph) till puberty
  • after puerty it no longer accelerate
  • pupation occurs when reproduction buffer density hits a threshold
  • pupa behaves like an isomorphic embryo of model std; larval structure rapidly transforms to pupal reserve just after start of pupation
  • the reproduction buffer remains unchanged during the pupal stage
  • emergence of imago occurs if maturity hits a threshold value
  • the imago does not grow or allocate to reproduction. It mobilises reserve to match constant (somatic plus maturity) maintenance
The model applies to diptera, for instance.

nat

nat model stands for not-a-typified model. It comes with no constrains or checks. It is meant for non-AmP purposes, such as effects of toxicants.

Summary

Model Description
std standard DEB model
stf std with foetal development
stx stf with baby stage until weaning
ssj std with non-feeding stage between s and j
sbp std with growth ceasing at puberty
abj std with acceleration between birth and metamorphosis
asj abj with delayed acceleration starting at s
abp abp with growth ceasing at puberty
hep abj with larval stage after acceleration behaving as an adult
hex hep with accelerating larval stage behaving as an adult and pupal phase
hax hybrid between hep (till pupation) and hex (pupa & imago)
nat not-a-typified model