Download What is hidden behind the concept of ecosystem efficiency in energy

Ecological Modelling 170 (2003) 185–191
What is hidden behind the concept of ecosystem efficiency
in energy transformation?
L. Valandro a,∗ , R. Caimmi b , L. Colombo a
b
a Department of Biology, University of Padova, via Ugo Bassi, 58/b, Padova 35131, Italy
Department of Astronomy, University of Padova, Vicolo Osservatorio, 2, Padova 35122, Italy
Abstract
The number of energy transformation levels in trophic webs is usually below five, but can be extended up to ten when parasites
and hyper-parasites are included. Research on the structure and function of food webs is relevant to the complexity–stability–
productivity debate. The aim of this theoretical analysis is to link energetic and connectional aspects of ecosystems with
information theory. Updating an energetic model reported by Ricklefs [Ecologia, Zanichelli Editore S.p.A., Bologna, Italy,
1993, p. 896], our approach is integrated with a static analysis of food webs. The length of food webs is theoretically associated
with the average ecological efficiency which can be empirically correlated with the effective connectance between species.
Furthermore, the advantage of greater complexity when applied to a signalling network is qualitatively addressed.
The overall efficiency of energy transformation into biomass throughout a trophic web, in an ecosystem with a given number
of species, is the resultant of the various ecological efficiencies, η, at the transitions between the trophic levels. However, we
propose that an increment in effective connectance and interspecies connectivity based on a superimposed signalling web may
increase the η values, despite the fact that signalling per se has an energetic cost. According to this hypothesis, ecosystem stability
would not be necessarily reduced by increasing the number of trophic levels, N, whenever stability in terms of persistence is
improved by a cost-efficient regulatory network.
© 2003 Elsevier B.V. All rights reserved.
Keywords: Food webs; Ecological efficiency; Trophic levels; Connectance; Complexity; Stability; Productivity; Signalling network
1. Introduction
Communities are open, self-organised systems
whose structure and function have been considered
to be too complex to disclose general patterns (Polis
and Strong, 1996), despite the fact that the trophic–
dynamic aspects of ecosystems have been mathematically analysed in great detail (MacArthur, 1955;
Patten, 1959).
∗ Corresponding author. Tel.: +39-0498276187;
fax: +39-0498276199.
E-mail address: [email protected] (L. Valandro).
In dealing with ecological problems, a cybernetic
approach (Gardner and Ashby, 1970) was followed
by May (1973), who formally demonstrated that a
continuous increment in the number of species, n,
of their interaction strength and connectivity eventually destabilises the ecosystem (May, 1973; chapter 3,
p. 65).
Recently, criticism has been raised by Sterner et al.
(1997) against the theoretical assumption that any increment in the number of trophic levels, N, may reduce ecosystem dynamic stability (Pimm and Lawton,
1977). Furthermore, the relationship between N and
both n and their connectivity in an ecosystem is unclear (De Angelis, 1975; Fonseca and John, 1996).
0304-3800/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0304-3800(03)00225-4
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L. Valandro et al. / Ecological Modelling 170 (2003) 185–191
The food chain length is given by N, which is usually small, and can be roughly estimated taking into
account the net primary productivity, NPP, the total
energy fixed at the last trophic level, E(N), and the
geometric mean of the energy conversion efficiencies
between trophic levels, η (Ricklefs, 1993; chapter 11,
p. 197). NPP represents the first biotic level and can
be limited by a number of environmental constraints
(e.g. ecosystem size, space dimensionality, water and
nutrient availability, light, temperature, latitude, etc.)
(see Briand and Cohen, 1987; Schoener, 1989; Post
et al., 2000). When NPP is limiting, N may be assumed
to be a function of NPP, although proponents of the
dynamic instability hypothesis claim that such a relationship remains undemonstrated (Pimm and Lawton,
1977). On the other hand, the trophic–dynamic analysis of bioproduction and dissipation of energy in
ecosystems often ignores important parameters, such
as nutrient cycling (De Angelis, 1992) and information processing (Odum, 1988; Burns, 1989; Valandro
et al., 2000). Further, novel thermodynamic indices
(e.g. exergy, Bendoricchio and Jørgensen, 1997; Ray
et al., 2001) have been introduced to better understand ecosystem structure, organisation and dynamics, thus making the thermodynamic work by Nicolis
and Prigogine (1989) more contextual to ecological
problems (see also papers on earlier thermodynamic
indices by Lotka, 1922; Odum and Pinkerton, 1955;
Odum, 1969).
Here, we will focus only on some general aspects
of food web theory more directly addressed by network approaches (Patten, 1995; Ulanowicz, 1997b;
Jørgensen, 2001; Fath et al., 2001) and briefly discuss
community complexity in relation to community persistence (see also May’s afterthoughts, 1973).
According to Ricklefs (1993), N is primarily a function of η, while E(N) and NPP play a minor role.
Though Ryther (1969) found an inverse relationship
between η and N in marine ecosystems, it should be
noted that his estimate was essentially referred to fishery production and not to overall biotic production.
Since the average efficiency of the energy transformation into biomass throughout a trophic web,
with a given n, is the resultant of the various
η1 , η2 , . . . , ηN−1 at the transitions between the
trophic levels, we intend to investigate whether an increment in effective connectance, may increase N by
increasing the η values. The effective connectance, m,
Table 1
List of the parameters used in the text (references therein) for
characterising a trophic web
Symbol
Definition
n
N
NPP
E(N)
η
Number of species
Number of trophic levels
Net primary productivity
Total energy fixed at the last trophic level
Geometric mean of the energy conversion
efficiencies between trophic levels
Number of actual trophic links
Number of topological trophic links
Effective connectance (m = /n)
Topological connectance (m∗ = ∗ /n)
Connectivity (C = m/m∗ )
∗
m
m∗
C
is defined as the ratio of the number of actual trophic
links in the web, , to the number of species, n, that
is m = /n. A trophic link is intended as a trophic relationship between two species. In this view, ecosystem stability would not be necessarily depressed by
increasing N, whenever stability is improved by a
cost-efficient regulatory network.
More specifically, our attention will be devoted to
the following points:
(i) The existence of an empirical correlation between
the total number of trophic levels in a food web,
N, and the effective connectance, m, for a sample
of 113 community webs.
(ii) The dependence of the above correlation on the
environment (aquatic or terrestrial).
(iii) The comparison on the cartesian plane between
the empirical dependence of the effective connectance, m, on the topological connectance, m∗ ,
and the theoretical limiting curve, m = f (m∗ ),
calculated by Ulanowicz (1997a) based on a criterion first formulated by May (1973).
The above-mentioned parameters are listed in
Table 1 for sake of completeness.
2. Materials and methods
The values of the number of species, n, and of the
total number of trophic links, , of 113 communities
were selected from Briand and Cohen (1987). Within
this initial set, a further selection was made to separate
L. Valandro et al. / Ecological Modelling 170 (2003) 185–191
terrestrial (references 32, 33, 42, 57–59, 86–89, 91,
96) from aquatic communities (references 20, 24,
26, 30, 37, 41, 43, 46, 50, 52–55, 71, 77, 99–104).
Among the latter, we have excluded freshwater and
restricted or temporary communities as well as communities from extreme environments (e.g. Arctic and
Antarctic seas). Regression analysis techniques were
applied to the selected sets to evidence different trends
for aquatic and terrestrial food webs, plotting the
number of trophic levels, N, versus effective connectance, m.
A formula by Ulanowicz (1997a) was applied to
draw the curve of Fig. 4, where the stability and instability conditions for all the 113 communities were
calculated by plotting m against the topological connectance, m∗ . The m∗ parameter is the ratio between
the maximum allowed number of theoretical trophic
links, ∗ , and the number of species in a web, n, m∗ =
∗ /n.
The following bounds and inequalities of parameters apply: obviously m∗ ≥ m, connectivity, C (C =
m/m∗ ). Ideally, 0 < C < 1, but empirically Cmin <
C < Cmax in real food webs, where Cmin > 0 and
Cmax < 1 (see Fonseca and John, 1996; Margalef,
1997; Ulanowicz, 1997a).
3. Results
Fig. 1 has been obtained by calculating N as a
function of η at arbitrary, though plausible, values of
the E(N)/NPP ratio at the last trophic level, that is
0.1, 0.01, 0.001. The following equation by Ricklefs
(1993) was used:
N =1+
log[E(N)] − log[NPP]
log(η)
187
Fig. 1. The number of trophic levels, N, of a trophic chain, as a
function of the geometric mean of the energetic transmission yield
between levels, η, for three different choices of the ratio of the
energy fixed at the last trophic level, to net primary productivity,
E(N)/NPP.
R = 0.58, a value about three times greater compared
to other allometries, such as N versus C (R = 0.17)
and N versus m∗ (R = 0.19).
When N was correlated with m separately in all the
21 terrestrial communities and all the 92 aquatic communities investigated, a significant positive correlation
(α 0.01; R = 0.61; slope = 1.27) was found only
in the latter community set (data not shown). When
only 36 aquatic communities were selected according
to the above-mentioned criteria, the positive linear correlation was reinforced (α 0.01; R = 0.77; slope =
2.10) (Fig. 3). Thus, at higher m values, aquatic communities appear to rely on greater N values.
(1)
It can be seen that the values of the E(N)/NPP ratio
are inversely related to N, but that major changes of
this ratio induce only minor variations in the N values which remain low, at least when η < 0.5. The N
values are approximately linearly related to the η values, when η < 0.5, with greater slope values at lower
E(N)/NPP ratios.
In Fig. 2, a significant correlation (α < 0.01) was
found between the empirically determined maximum
number of trophic levels, N, and m in the 113 communities investigated, with a coefficient of correlation of
Fig. 2. The maximum number of trophic levels in a community
web, N, as a function of the effective connectance, m, for a sample
of ntotal = 113 community webs, taken from Briand and Cohen
(1987). The best linear fit is also plotted, together with the equation
of the related straight line (R = 0.58; d.f. = 111; F = 55.05;
α < 0.01).
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L. Valandro et al. / Ecological Modelling 170 (2003) 185–191
Fig. 3. Same as in Fig. 2, but in connection with a subsample of nland = 21 terrestrial community webs (left) and a subsample of
nwater = 36 marine aquatic community webs, taken from the total sample of Fig. 2. The maximum number of trophic levels, N, and the
effective connectance, m, appear to be uncorrelated for terrestrial community webs (R = 0.089; d.f. = 19; F = 0.0003; n.s.), and positively
highly correlated for aquatic community webs (R = 0.77; d.f. = 34; F = 50, 34; α 0.01).
Fig. 4. The effective connectance, m, as a function of the topological connectance, m∗ , in relation to the total sample of Fig. 2. The
inequality m ≤ m∗ must necessarily hold, i.e. no community web is allowed above the straight line, m = m∗ , which is also plotted. The
boundary between instability (above) and stability (below), according to May’s criterion (1973) and analysis by Ulanowicz (1997a), is
represented by filled squares. Individual webs are represented by filled dots.
In Fig. 4, where the effective connectance, m, is
plotted versus the topological connectance, m∗ , three
zones, A–C, were defined by two lines, the first when
m = m∗ , and the second calculated according to
the formula by Ulanowicz (1997a). The plot of m =
f (m∗ ) of the 113 communities investigated shows that
none was located in zone A (forbidden region), six
were positioned in zone B (instability region in terms
of resilience) and the remaining ones in zone C (stability region). An upper limit of m around 3 represents
the borderline between regions B and C. All communities in zone B were characterised by high N values.
4. Discussion
Empirically based generalisations about real food
webs were reviewed by Pimm (1982) and, currently,
more complete and homogenous databases are being
assembled in order to test these previous assumptions
and to discover new general patterns.
In the present paper, the main conclusions may be
summarised as follows:
(i) An empirical correlation is shown between the
total number of trophic levels in a food web, N,
L. Valandro et al. / Ecological Modelling 170 (2003) 185–191
and the effective connectance, m, with regard to
a sample of 113 community webs reported in
Briand and Cohen (1987).
(ii) The above correlation is strengthened for a
sub-sample of 36 aquatic community webs while,
on the other hand, it is almost vanishing for a
sub-sample of 21 terrestrial community webs.
(iii) The effective connectance versus the topological
connectance for the sample objects shows that six
community webs with a high number of trophic
levels lie within an unstable but feasible region,
according to May’s criterion (1973).
The drawback of our analysis is that this is based on
the references reported in Briand and Cohen (1987)
that are difficult to find in order to check the authors’
subjective views of food web details (i). These community webs are more probably sub-community webs,
constituted by a relatively small number of species,
and our correlation comparing aquatic and terrestrial
communities is, therefore, based on limited samples
(ii). The observation that community webs with a high
number of trophic levels are positioned in the graphical region of instability or metastability is not fully
explained and is worth of further investigation (iii).
The aim of the present study was to apply simple
static analysis of N, η, m, C, and n parameters in food
webs in order to compare the interplay of complexity, inferred from N, m, and n, and stability, inferred
from N, m, and m∗ , between aquatic and terrestrial
trophic communities, where different patterns are expected, given the marked divergence in environmental
constraints (Hairston and Hairston, 1997). Constraints
derived from the dynamical analysis of stability conditions in food webs were also taken into consideration (May, 1973; Pimm and Lawton, 1977; Ulanowicz,
1997a).
The number of trophic levels in community webs
is usually small due to low η1 , η2 , . . . , ηN−1 values,
that express the efficiency of energy conversions between levels. The plot to show the N dependency on η
is obviously tautological if η is the geometric mean of
empirically determined η1 , η2 , . . . , ηN−1 values. Theoretically, however, the plot is informative because it
shows that (1) the E(N)/NPP ratio exerts only a weak
influence on N, (2) the correlation between N and η is
approximately linear only at low η values, and (3) the
choice of the geometric mean tends to confer higher N
189
values to those food webs in which η1 , η2 , . . . , ηN−1
values are more uniform.
According to Ricklefs (1993), η on land is generally lower than η in aquatic ecosystems and, hence,
Nland < Nwater . As a matter of fact, the first energy
flow from primary producers to herbivores is less efficient on land, where most plant biomass is dead
material that does not recycle in the short-medium
term. Furthermore, water availability is often limiting on land and adaptations to temperature variability
and gravity are energetically costly. All these energy
losses reduce η (see also Kozlovsky, 1968; Wiegert
and Owen, 1971; Odum, 1983).
When N was plotted against m, a positive trend by
linear least squares regression was found in aquatic
communities (see Nybakken, 1997), especially if not
belonging to restricted or extreme environments, but
not in terrestrial communities (only a smaller number
of which, however, was considered in this work). Since
m together with n are fundamental determinants of
food web structural complexity, it is suggested that
the increment of complexity, due to more trophic links
in a community of aquatic species, brings about an
improvement of η, which is necessary to allow higher
N values. Interestingly, no significant correlation was
observed between N and n in aquatic communities
(not shown), indicating that the connectance per se
may improve the efficiency of energy transfer between
trophic levels (see Conrad, 1972).
The dependence of N on m, rather than on n, is
likely to have more reversible effects on ecosystem
stability because m is a more flexible parameter than
n, and can be more easily returned to previous values
in order to restore stability. Apart from parasites with
different host species during the larval sequence of
their life cycles, any increment of m should reflect a
more generalistic trophic strategy.
Cannibalism instead short-circuits the trophic level
and the individual ηi→i of this energy exchange
depresses the overall ηj→i value realised by the cannibalistic species with the other prey species, thus
adversely affecting η and N of the food web. Moreover, considering the high number of cannibalistic
species (Polis, 1981), we expect this trophic strategy to influence community structure (Dodds and
Henebry, 1996); on this subject it would be interesting to compare the N values of ecosystems with
and without cannibalistic species, ceteris paribus. We
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L. Valandro et al. / Ecological Modelling 170 (2003) 185–191
suggest that a smaller weight should be attributed to
the cannibalistic link with respect to omnivory.
It is generally assumed that, beyond a critical threshold value, the greater the m value, the less stable becomes the ecosystem (May, 1973). The threshold value
must lie between m = 1−1/n and m = m∗ . In the first
limiting case, the trophic community is rigidly linear
and intuitively highly vulnerable because any temporary rarefaction of a prey species in the chain can provoke the collapse of the upstream sequence of species.
In the other limiting case, the trophic community
is entirely reticular and highly unstable because every species is entangled in a predator–prey relationship with all the other species of the community. This
globalisation effect makes the ecosystem chaotic, with
sudden transitions even between states that are distantly positioned in the abstract space of all possible
conditions. Our plot of m versus m∗ , further supports
the conclusion that no community lies on the straight
line where m = m∗ (Ulanowicz, 1997b; chapter 6,
pp. 113–119).
Actually, community clustering distinctly points to
a threshold value of m near 3. On the other hand, the
fact that six communities are dispersed in the so-called
instability region (Fig. 4) with high m values implies
that some mechanisms must exist to reconcile stability
with a widening of interspecific trophic interactions.
The latter interactions are often difficult to measure
quantitatively (Paine, 1992), but usually they are weak
in complex ecosystems (McCann et al., 1998). An analytical upper limit has been derived from dynamical
stability condition by May (1973).
Chaotic intensification at high m values should certainly occur whenever all trophic links of a species
with the other interacting species are managed randomly in a sort of complete equivalence (all links have
the same probability of energy flux). But this is not the
case in nature, because no trophic web with a given
m value can persist if a regulatory network is not superimposed on it due to the exchange and processing
of active (purposeful) and passive (unintentional) signalling between species. The regulatory network is expected to be more complex than the trophic web due
to a higher m value (regulatory links/n), because not
every interspecific signalling results in a trophic outcome.
The energetic cost of active signalling, whether
intermittent (e.g. rattling sound of a rattlesnake) or
persistent (e.g. aposematic skin colour), is usually
low, whereas signal processing and recognition can
be sometimes more expensive (Colombo, 1996). Yet,
the energetic cost for signal exchange and processing is usually small compared with more demanding
functions, such as locomotion, and may be sustained
whenever the chaotic instability due to higher trophic
m values can be quenched by an increase of regulatory interactions resulting from higher regulatory
m values.
It may be speculated that the complexity of the regulatory network between species is positively related
not only to the trophic m value of the community, but,
more generally, to the overall complexity of its trophic
web given by both trophic m and n. This idea means
that complex regulatory networks are to be expected
in ecosystems in which either trophic m or n, or both,
are high. Also, it would be interesting to compare the
complexity of interspecies regulatory network with respect to the complexity of intraspecific regulatory networks.
Lastly, it may be remarked that the success of humans as a species with a vast array of trophic links
may be conceivably explained by their great capacity
to create and maintain a remarkable radiation of regulatory links (see also Patten, 2001).
Acknowledgements
The research was supported by grant no. 5C 117
from the Ministry of Agriculture and Forestry Policies of Italy, in the purview of the Fifth Triennal Plan
for Fisheries and Aquaculture in Marine and Brackish
Waters.
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