174
mation about feeding rates, that represent the strength of the
connections (Ulanowicz 2004). ENA (like the DEB model)
assumes conservation of energy and mass (i.e., all nodes
must be at steady-state, with the same amount of energy
exchanged by input and output processes). Therefore, ENA
considers four types of energy flows: imports, exports, respirations (i.e., losses) and inter-compartmental exchanges. The
energy flow can be expressed in the unit kcal and various
mediums (currencies) such as carbon, nitrogen, phosphorus,
and sulfur. The input of energy into the system usually is
related to the gross primary productivity or even detritus
aggregation that enters the system. The loss of energy corresponds to degraded material that might be represented by
dissipation as heat (i.e., respiration), which is different from
the export of usable energy to other systems (e.g., detritus
that is flushed away from an eelgrass meadow). The intercompartments corresponds to quantification of flows by
energy transferred not only by the predator-prey interaction
but also from living to non-living (and vice and versa) compartments (Kay et al. 1989). For example, this kind of analysis is useful for identifying cascade effects on the processes
in an ecosystem. Indeed, ENA is able to connect information
about the elements of the ecosystem to quantify how indirect
effects spread along the system (Ulanowicz 2004). For
example, ENA has been used for investigating changes due
to eutrophication (Christian et al. 2009). One of the consequences detected was that eutrophication decreased the macrophyte biomass, lowering herbivory and causing impacts to
the functioning of the overall system.
ENA is able to shed light on different aspects of ecosystem functioning. The algorithms of ENA provide indices that
show how the systems respond to changes applied to them
(Baird et al. 2004). Some output variables connected to the
functioning of the systems are:
• The efficiency of the ecosystems in using the energy captured by primary producers can shift under different conditions (e.g., salinity gradients). The efficiency determines
whether an ecosystem is more autotrophic or heterotrophic. The ENA provides the Lindeman spine, which is the
representation of the complex network in terms of a linear
food chain based on discrete trophic levels. It depicts the
transfer of energy along compartments in a simplified
way allowing the calculation of trophic efficiency (Baird
and Ulanowicz 1993).
• Energy cycling can be a good indicator of stress
(Ulanowicz 1995). Cycling refers to the recycling of the
medium within the ecosystem, i.e., the ability of the nodes
involved in the energy transfer to reuse the medium. In
order to obtain a complete picture of the consequences of
cycling it is important to analyze the number of cycles,
length of the cycles (quantity of nodes involved) and species involved. The total amount of cycling is represented
by the Finn cycling index (FCI). Mature ecosystems tend
to have more cycles and increase the amount of energy
circulating through them. However, eutrophication that
represents a stress for ecosystems may also contribute to
generate more cycles. The difference between mature and
eutrophic systems is the length of these cycles. For example, mature ecosystems have longer cycles, while eutrophic systems present a high FCI but the cycles are shorter,
so the energy does not reach higher trophic levels in the
food web resulting in loss of functioning (Baird et al.
2004; Christian et al. 2005).
• Average residence time (ART) is related to the time that
the medium is retained in the network. The residence time
is not necessarily related to the aforementioned cycling
since the intensity of the cycles (i.e., energy flowing
within the cycles) can vary (Baird and Ulanowicz 1989).
The ART is calculated by the ratio of the total system biomass and total output (Baird et al. 2004). The less time it
spends in the system, the less efficient the system is in
using energetic resources (Baird et al. 2004).
• Average path length expresses the quantity of compartments that the medium goes through before leaving the
system. Shorter paths may be the response to stressful
conditions in the ecosystem (Baird and Ulanowicz 1993).
• Total system throughput (TST) is related to the whole
activity because it reports the amount of the medium
flowing through the system. It is used to quantify ecosystems growth.
• Ascendency (A) corresponds to the organization (i.e.,
development) of the system considering the total activity
(TST). It has also been suggested the use of “internal
ascendency” (A I ) that considers only internal flows of the
studied system. Ulanowicz (2004) suggests A I for comparing growth and development of different ecosystems.
• Overhead takes into account the four types of flow while
redundancy indicates the quantity of internal flows only.
Both overhead and redundancy have been used to determine the resilience of the system. Increased values mean
more resilient ecosystem according to Ulanowicz (2004).
• Development capacity is the upper limit of development
that can be attained by ascendency. It is calculated as the
sum of ascendency plus the overhead. It indicates the status of a system. Ascendency/development capacity ratios
are good indicators of organization of the system
(Ulanowicz 2004).
In order to use ENA for evaluating ecological processes
and the impacts of environmental change, we have some recommendations. The first recommendation is to examine food
webs throughout the seasons because the networks depict
static snapshots of energy-matter flows in ecosystems. Traits
of species such as body size, ontogeny and trophic interactions shift along the seasons (Warren 1989). Therefore, the
F. R. Barboza et al.
mation about feeding rates, that represent the strength of the
connections (Ulanowicz 2004). ENA (like the DEB model)
assumes conservation of energy and mass (i.e., all nodes
must be at steady-state, with the same amount of energy
exchanged by input and output processes). Therefore, ENA
considers four types of energy flows: imports, exports, respirations (i.e., losses) and inter-compartmental exchanges. The
energy flow can be expressed in the unit kcal and various
mediums (currencies) such as carbon, nitrogen, phosphorus,
and sulfur. The input of energy into the system usually is
related to the gross primary productivity or even detritus
aggregation that enters the system. The loss of energy corresponds to degraded material that might be represented by
dissipation as heat (i.e., respiration), which is different from
the export of usable energy to other systems (e.g., detritus
that is flushed away from an eelgrass meadow). The intercompartments corresponds to quantification of flows by
energy transferred not only by the predator-prey interaction
but also from living to non-living (and vice and versa) compartments (Kay et al. 1989). For example, this kind of analysis is useful for identifying cascade effects on the processes
in an ecosystem. Indeed, ENA is able to connect information
about the elements of the ecosystem to quantify how indirect
effects spread along the system (Ulanowicz 2004). For
example, ENA has been used for investigating changes due
to eutrophication (Christian et al. 2009). One of the consequences detected was that eutrophication decreased the macrophyte biomass, lowering herbivory and causing impacts to
the functioning of the overall system.
ENA is able to shed light on different aspects of ecosystem functioning. The algorithms of ENA provide indices that
show how the systems respond to changes applied to them
(Baird et al. 2004). Some output variables connected to the
functioning of the systems are:
• The efficiency of the ecosystems in using the energy captured by primary producers can shift under different conditions (e.g., salinity gradients). The efficiency determines
whether an ecosystem is more autotrophic or heterotrophic. The ENA provides the Lindeman spine, which is the
representation of the complex network in terms of a linear
food chain based on discrete trophic levels. It depicts the
transfer of energy along compartments in a simplified
way allowing the calculation of trophic efficiency (Baird
and Ulanowicz 1993).
• Energy cycling can be a good indicator of stress
(Ulanowicz 1995). Cycling refers to the recycling of the
medium within the ecosystem, i.e., the ability of the nodes
involved in the energy transfer to reuse the medium. In
order to obtain a complete picture of the consequences of
cycling it is important to analyze the number of cycles,
length of the cycles (quantity of nodes involved) and species involved. The total amount of cycling is represented
by the Finn cycling index (FCI). Mature ecosystems tend
to have more cycles and increase the amount of energy
circulating through them. However, eutrophication that
represents a stress for ecosystems may also contribute to
generate more cycles. The difference between mature and
eutrophic systems is the length of these cycles. For example, mature ecosystems have longer cycles, while eutrophic systems present a high FCI but the cycles are shorter,
so the energy does not reach higher trophic levels in the
food web resulting in loss of functioning (Baird et al.
2004; Christian et al. 2005).
• Average residence time (ART) is related to the time that
the medium is retained in the network. The residence time
is not necessarily related to the aforementioned cycling
since the intensity of the cycles (i.e., energy flowing
within the cycles) can vary (Baird and Ulanowicz 1989).
The ART is calculated by the ratio of the total system biomass and total output (Baird et al. 2004). The less time it
spends in the system, the less efficient the system is in
using energetic resources (Baird et al. 2004).
• Average path length expresses the quantity of compartments that the medium goes through before leaving the
system. Shorter paths may be the response to stressful
conditions in the ecosystem (Baird and Ulanowicz 1993).
• Total system throughput (TST) is related to the whole
activity because it reports the amount of the medium
flowing through the system. It is used to quantify ecosystems growth.
• Ascendency (A) corresponds to the organization (i.e.,
development) of the system considering the total activity
(TST). It has also been suggested the use of “internal
ascendency” (A I ) that considers only internal flows of the
studied system. Ulanowicz (2004) suggests A I for comparing growth and development of different ecosystems.
• Overhead takes into account the four types of flow while
redundancy indicates the quantity of internal flows only.
Both overhead and redundancy have been used to determine the resilience of the system. Increased values mean
more resilient ecosystem according to Ulanowicz (2004).
• Development capacity is the upper limit of development
that can be attained by ascendency. It is calculated as the
sum of ascendency plus the overhead. It indicates the status of a system. Ascendency/development capacity ratios
are good indicators of organization of the system
(Ulanowicz 2004).
In order to use ENA for evaluating ecological processes
and the impacts of environmental change, we have some recommendations. The first recommendation is to examine food
webs throughout the seasons because the networks depict
static snapshots of energy-matter flows in ecosystems. Traits
of species such as body size, ontogeny and trophic interactions shift along the seasons (Warren 1989). Therefore, the
F. R. Barboza et al.