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ENERGY ACQUISITION AND
ALLOCATION IN PLANTS AND
INSECTS: A HYPOTHESIS
FOR THE POSSIBLE ROLE
OF HORMONES IN INSECT
FEEDING PATTERNS
Journal Article
Author(s):
Gutierrez, A.P.; Schulthess, F.; Wilson, L.T.; Villacorta, A.M.; Ellis, C.K.; Baumgaertner, J.U.
Publication date:
1987
Permanent link:
https://doi.org/10.3929/ethz-b-000423056
Rights / license:
In Copyright - Non-Commercial Use Permitted
Originally published in:
The Canadian Entomologist 119(2), https://doi.org/10.4039/Ent119109-2
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ENERGY ACQUISITION AND ALLOCATION IN PLANTS AND INSECTS:
A HYPOTHESIS FOR THE POSSIBLE ROLE OF HORMONES IN INSECT
FEEDING PATTERNS
A.
P.
GUTIERREZ
Division of Biological Control, University of California, Berkeley, California, USA
F.
SCHULTHESS
International Institute of Tropical Agriculture, Ibadan, Nigeria
L.
T.
WILSON
Department of Entomology, University of California, Davis, California, USA
A.M.
VILLACORTA
Fundi~ao Instituto AgronBmico do Parana, Brazil
C.K.
ELLIS
Division of Biological Control, University of California, Berkeley, California, USA
and
J.U.
BAUMGAERTNER
Institut fur Phytomedizin, ETH, Zurich, Switzerland
Abstract
Can.
Ent.
119: 109-129 (1987)
A
distributed delay age structure model is presented for plants and insects that describes
the dynamics of per capita energy
(dry
matter) acquisition and allocation patterns, and
the within-organism subunit (e.g. leaves, fruit, ova) number dynamics that occur during
growth, reproduction, and development. Four species of plants (common bean, cas-
sava, cotton, and tomato) and two species of insects (pea aphid and a ladybird beetle)
are modeled.
A
common acquisition (i.e. functional response) submodel is used to
estimate the daily photosynthetic rates in plants and consumption rates in pea aphid
and the ladybird beetle. The focus of this work is to capture the essence of the common
attributes between trophic levels across this wide range of taxa. The models are com-
pared with field or laboratory data.
A
hypothesis is proposed for the observed patterns
of reproduction in pea aphid and in a ladybird beetle.
RCsume
On a construit un modele dkmographique avec distribution de dklai applicable
?I
des
plantes et des insectes.
Le
modele dkcrit la dynarnique de l'appropriation et de la
rkpartition de I'knergie (matiere seche) per capita, et la dynamique des nombres des
sous-unites inm-organisme (ex. feuilles, fruits, oeufs).
On
a
ainsi
modklist quatre
sortes de plantes {Eve, cassava, coton et tomate) et deux espkes d'insectes (puceron
du pois et coccinelle). On utilise un sous-modcle comrnun d'acquisition (rdsponse fonc-
tionnelle) pour estimer les vitesses journali&res
de
photosynthkse
des
plantes et d'ali-
mentation du puceron et de la coccinelle. Le but de ce travail est
d'extraire
les carac-
tkristiques essentielles communes aux niveaux trophiques occup6s par ces divers taxons.
Les modkles sont compares avec des donnkes de terrain et de laboratoire. On propose
une hypothese pour expliquer les profils obsew6s de reproduction du puceron du pois
et de la coccinelle.
Introduction
The patterns of energy acquisition and assimilation by organisms must be in harmony
with their ecological role in a biological system. To examine this requires the development
of models of multi-trophic level interactions. The development of multi-trophic level
models has been a goal of many population ecologists (May 1982; Gilbert
et
al.
1976; De
Angelis
et
al.
1975; Gutierrez
et
al.
1981; Gutierrez, Baumgaertner
et
al.
1984; Gutierrez,
Pizzarniglio
et
al.
1984).
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THE
CANADIAN
ENTOMOLOGIST
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1987
Until recently, plant and animal demographers have viewed population processes from
quite different perspectives, but this gap has narrowed (Gutierrez and Wang 1976; Wang
et al. 1977; Gutierrez, Baumgaertner et al. 1984; Gutierrez, Pizzamiglio et al. 1984; Law
1983). For example, plant ecologists (Harper and White 1974; Harper 1979) proposed that
populations of plants consisted of individual plants, each of which had populations of plant
subunits with age structure. Animal ecologists (Gutierrez and Wang 1976; Wang et al.
1977; Curry et al. 1978) have used a series of linked von Foerster (1959) models to simulate
the demography of cotton plants (Gossypium hirsutum L.) and plant subunit populations
in the manner proposed by Harper and White. Growth, development, and reproduction in
insects may also be viewed in a similar manner, as female insects have populations of ova
or embryos growing within them that may have age structure. Immature growth and embryo
production in insects (and other animals) are thus analogous to vegetative growth and fruit
production in plants.
In this paper, a common model is used to simulate the dynamics of growth and devel-
opment of common bean (Phaseolus vulgaris L.), pea aphid (Acyrthosiphonpisum Harris),
cassava (Manihot esculenta Crantz), a ladybird beetle (Hippodamia convergens G.-M.),
cotton, and tomato (Lycopersicon esculentum Mill.). In addition, the same functional
response model from predation theory is used to predict photosynthetic rates in plants and
predation and herbivory rates in insects (Gutierrez et al. 1981). The goal of the work is
to examine the common patterns of energy allocation in widely separated taxonomic groups.
A hypothesis is also proposed for the hormonal control of energy acquisition and allocation
in insects.
Review of Mathematical Models
Population Dynamics.
The von Foerster model used to simulate the dynamics of plant
growth and development may be summarized as follows:
where
N, denotes the mass or number density function of the
j&
plant or animal population
or subunit population (e.g.
j
=
plants, leaves, stem, root, fruit,.
.
.),
and
p,
is the net
birth-death rate of the population at time
"t"
of age "a" measured in temperature-depend-
ent units (e.g. degree days, DD). An analytical solution for [l] given constant age-specific
parameters is possible, and the numerical solution is equivalent to the Leslie (1945) matrix
model (Wang et al. 1977). Sinko and Streifer (1967) provide a very readable summary of
the mathematics of [l] and related deterministic age-structure models. Specific applications
of this model to plant and poikilotherm population dynamics are reviewed by Wang et al.
(1977), Curry et al. (1978), and Gutierrez et al. (1983).
In our model, species parameters vary with age and time and incorporate the detail
of the biology in the term p(.). The parameters that influence p vary over time in response
to changes in density, nutrition, natural enemy activity, physical and many other factors
known to affect real population (Gilbert et al. 1976). Despite the mathematical intracta-
bility of these models, they have proven quite useful in examining many applied (Gutierrez
et al. 1975, 1976; Gutierrez, Leigh et al. 1977; Gutierrez, Butler et al. 1977; Gutierrez,
Baumgaertner et al. 1984; Gutierrez, Pizzamiglio et al. 1984; Wang et al. 1977; Wang
and Gutierrez 1980; Cuff and Hardman 1980) and theoretical problems (Wang and Gutier-
rez 1980; Gutierrez and Regev 1983).
More recently, Gutierrez and Baumgaertner (l984a, 19846) replaced the deterministic
model [I] with a distributed delay model
([2],
cf. Manetsch 1976; Vansickle 1977), and
used it to simulate the stochastic development of cohorts of plants and insects.
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1
19
THE
CANADIAN ENTOMOLOGIST
111
where
x,
and
y,
are the inflow and outflow rates of numbers or mass into the first and last
age groups, respectively, in the
jw
population,
r,,,
is the flow rate into the i
+
lth of
k
age
categories, and
pij(t,.)
equals the net proportion of mortality, birth, immigration, and
emigration in the ith age group at time
t.
In the model, senescence of leaves in plants and
ovaries in insects occurs as transition (ageing) rates through the distributed delay model
[2]. Leaves lose their photosynthetic potential with age and insects lose their reproductive
capacity. In the current application,
N
may be in number, mass, or energy units.
Examples of the application of this model to plant and insect demography and inter-
actions are works by Gutierrez, Baumgaertner
et
al. (1984) and Gutierrez, Pizzamiglio
et
al. (1984). Bellows (1982) applied a distributed delay model which incorporated hazard
rates to examine the dynamics of a laboratory population.
Metabolic Pool Model.
The metabolic pool model for energy acquisition and allocation
links the plant and subunit models (Jones
et
al. 1974; Gutierrez
et
al. 1976). On a per
capita basis, the process of energy acquisition and allocation is modeled as follows (Fig. 1):
where Mi-, is the mass or energy in the i
-
lth trophic level available to the mass in the ith
trophic level to prey upon; dAlda is the per capita assimilation rate in terms of growth
(G),
reproduction
(R),
and/or reserves (0);
7
is temperature;
f(.)
is the predator functional
response model [4]; b is the genetic maximum demand rate (see below);
s
is the predator
search rate;
z(.)
is the monotonically increasing metabolic cost rate as a function of tem-
perature (7); O*
=
(YO is the quantity of reserves used instantaneously to meet respiration
costs; a~[0,1];
p
is the proportion of energy ingested that is egested. Of course, egestion
does not occur in plants in a strict sense, but exudates and other compounds not used for
growth, reproduction, or respiration could be included in
P.
Note also that dAlda
=O
is
the metabolic compensation point. The metabolic pool model suggests a priority scheme
for allocation: first to respiration and egestion, then reproduction, and last to growth and
reserves (Gutierrez
et
al. 1975, 1983; Wang
et
al. 1977). The sum of the maximum possible
outflow or assimilation rates to growth, reproduction, and reserves corrected for respiration
and egestion is the maximum genetically controlled demand rate (b), and the inflow from
prey consumption or photosynthesis represents the realized supply rate (M*). In the model,
these maximum demand rates are multiplied by the appropriate level supplyldemand ratio
(e.g. M*lbe[O, 11) to estimate the realized growth rates. This interplay between supply and
demand has been the cornerstone regulating the allocation processes in our models (Gutier-
rez
et
al. 1975; Wang
et
al. 1977; Gutierrez and Baumgaertner 1984a, 1984b). In theory,
the supply (i.e. the functional response, cf. Holling 1966) is always less than the demand
(M*<b), because the search process is imperfect even when conditions are nonlimiting.
Gutierrez and Baumgaertner (1984a) discuss the role of multiple prey in this context.
The Frazer and Gilbert (1976) functional response model [4] was selected to estimate
photosynthesis and prey acquisition rates (M*) in plant and insect models, respectively,
because the demand rate (b) is the major driving variable (Gutierrez and Wang 1976).
where
At
=
ADD.
In the limit, the F-G model approaches
a
Nicholson-Bailey model as
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112.
THE
CANADIAN
ENTOMOLOGIST
February
1987
M,-
,a,
and a linear Lotka-Volterra model as both M, and M,-,a (Gutierrez and Wang
1976). This model more fully characterizes the range of observed predator-prey interac-
tions (Frazer and Gilbert 1976). The model implies that at high resource availability, con-
sumption is saturated; at lower resource levels, availability and not consumption is limiting;
at very low levels, the encounter rate is low but linear, and the rate of change is at its
maximum. Each of these attributes has a direct parallel in photosynthesis. For population
development, true predators seek prey, herbivores seek plants or plant subunits, and plants
seek light energy. Of course all levels may also seek other requisites (e.g. minerals), but
for our purpose here these are assumed to be in adequate supply, unless otherwise indicated
in the results section.
For plants, M,-, is the light incident in their growing space, for the pea aphid M,-,
is the quantity of available plant sap dry matter, and for ladybird beetle it is the quantity
of aphids in their search universe. For consistency of units in the model, the light energy
falling per unit area (cal ~m-~ day-
l)
must be converted to dry matter equivalents (Gutier-
rez and Baumgaertner 1984~). Loomis and Williams (1963) estimated the theoretical max-
imum net photosynthesis per square metre per day at
500
cal ~m-~ day-' as 71 g CH20
m-2 day-
I,
or 129 g gross photosynthesis m-2 day-'. Equation [5] shows the theoretical
energy inputs and the mass components produced during photosynthesis.
Loomis and Williams (1963) suggest that 10.07 Einsteins (E) are required to produce 1
mol of CH,O (30 g). This, as expected, is less than one-sixth the value required to produce
1
mol of glucose (180 g). In practice, a simple conversion constant (3.875) converts cal
~m-~ day-' to g CH,O m-2 day-'.
Prey capture rates (s in [3,4]) increase with predator (herbivore) size, hence
s
per
unit predator mass [6] is characterized as follows:
where
M
is the predator mass and
y
is the prey capture coefficient. Of course prey capture
rates at the individual level are influenced by prey size, but the use of total predator mass
attacking total prey mass simplifies the problem (Gutierrez, Baumgaertner
et
al. 1984).
In this model, small predators would have little impact on populations of large prey (i.e.
small demand rate), but large predators (i.e. large demand rates) could have a large impact
on populations of small prey.
Similarly, light capture rates can be estimated using [6].
Leaf
area is usually a linear
function of leaf mass, and the proportion of light incident in the growing space of the plant
that is intercepted by leaves increases with increasing leaf area (usually expressed as the
leaf area index (LAI)). This relationship was described by M. Monsi and T. Saeki in 1953
([7], Evans 1975), and it has the same form as [6] above.
-y'LAI
s
=
1.-e
E[O,~]. [71
The light extinction coefficient (y') is readily estimated in the field using light meter
readings at different levels of the canopy. Hence s in [7] estimates the proportion of the
potentially available light energy that falls on leaf surface, and is equivalent to Nicholson-
Bailey search parameter (i.e. y) in [6]. The use of this functional response model for
photosynthesis was first proposed by Gutierrez
et
al. (1981), but Mack
et
al. (1981) inde-
pendently pointed out the same shape properties of predation and photosynthesis models.
Rectangular hyperbolic functions describing photosynthetic rates are common in plant
physiology (e.g. Noggle and Fritz 1976). In this paper, linked models [2,4] are used to
estimate photosynthesis and food acquisition rates for modeling per capita plant and insect
growth and development. The extension of this model to plant and animal populations is
given in Gutierrez and Baumgaertner (1984b). The effects of water, nitrogen, and other
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