Bernard Patten | The University of Georgia (original) (raw)

Papers by Bernard Patten

Ecological Modelling, Mar 1, 1993

Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This ... more Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This paper examines the time dependency of energy-matter flux in ecosystems modeled as flow-storage networks. The temporality of passage is governed by storage, which can be viewed as transport delay, a process contributing to the availability of energy to ecosystem compartments over time. Availability is a prior condition for utilization, which nevertheless is measurable from flow considerations alone. Combined flow-storage analyses are required to determine the temporality of substance availability; flow-only analyses are sufficient to specify utilization. The relations between the two are developed. What we term “tempo” involves the transport and delay as standing stocks of variously aged substance over the direct and indirect pathways of ecosystem networks. Our concept of “mode” refers to utilization alone, without regard for timing or the age distribution of flowing substance. Temporal analysis highlights the importance of turnover time, and thus body size and mass of individual organisms, in the dynamics of energy dependencies in ecosystems.

Ecological Modelling, Mar 1, 1993

Abstract The concept of progressive efficiency is generalized from food chains to food networks o... more Abstract The concept of progressive efficiency is generalized from food chains to food networks of arbitrary structure. Two distinct modes and corresponding pathways of contribution to energy-matter utilization are identified and formulated using continuous time models of energy-matter flows in ecosystems. First passage or root utilization involves first time transfer and transformation (of assimilated substance only) along all direct and indirect food paths originating at a defined source compartment and terminating at a defined destination compartment. First passage paths include acyclic paths plus cyclic paths that do not pass through the destination compartments. Recycling or reutilization involves the subsequent retransformation of previously utilized but not dissipated energy-matter by consumers. Recycling pathways start and end at the defined destination compartment. Total or ultimate utilization by destination compartments is the sum of first passage and recycling utilization. Two properties of ecosystems are demonstrated which depart from those of conventional trophic dynamics. Network virtual amplification is the increase of energy-matter ultimately utilized at destination compartments compared to the quantities originally introduced at source compartments. This is due largely to recycling; no energy is created, no thermodynamic law violated. Network homogenization is the tendency in food cycles for introduced energy-matter to become more or less evenly distributed to all compartments. These properties are illustrated with two models of ecosystem energy-matter flows.

Ecological Modelling, Oct 1, 1984

Published measures of cycling in compartmental models are based on throughflow. Throughflow consi... more Published measures of cycling in compartmental models are based on throughflow. Throughflow consists of flow only, not storage. Inclusive throughflow is introduced as a concept that includes both flow and storage. Cycling measures based on this concept are developed. Two Markov chains expressing the probability of transfer of substance from compartment j to i in one unit of transition time are constructed. The first is the conventional, throughflow-based model; second is an extended model based on inclusive throughflow with adjustable time step. This latter model is considered for two cases: storage accounted for and ignored, and is employed to illustrate derived relationships utilizing a small ecosystem energy flow model. Principal conclusions are: (1) cycling measures derived from the conventional throughflow-based model would overestimate cycling as given by the inclusive throughflow model, because they fail to distinguish storage from true cycling; (2) storages exceed cycled flow over low-ordered paths, but (3) decline in importance with increasing path length; (4) path diversity is greater in systems with storage than in corresponding systems without storage; (5) nonstorage path numbers increase combinatorially with path length; (6) cycling tends to become dominant over storage at higher path lengths, and (7) at differing rates for different compartments; (8) true cycling efficiency of each compartment i for the inclusive through flow model is corrected from the conventional model formulation (q;;-1)/q;; to [qii-1/(1-P;;)]/qii (P;, is the probability of substance in i remaining there over a transition time interval; q, is the cumulative substance returned to i over all paths of all lengths in the system); (9) this corrected cycling efficiency of each compartment with respect to inclusive throughflow equals that of the same compartment with respect to only the throughflow component as derived from the conventional model; (10) on the system level, however, the modified cycling index based on inclusive throughflow gives different values for cycling than the published cycling index derived from conventional throughflow; and (11) the modified cycling measures based on the inclusive throughflow model with an adjustable time step are independent of the chosen time step, and thus valid even for the continuous time case which is approached by the employed discrete time model as the time step approaches zero.

Journal of Theoretical Biology, Sep 1, 1989

For food networks of arbitrary structure, we generalize and develop a trophic-path partitioning o... more For food networks of arbitrary structure, we generalize and develop a trophic-path partitioning of standing stocks and flows, where each trophic path represents a particular chain of trophic transfers that an energy portion has experienced in the past. Based on this, we derive a method for "'unfolding" any given food network along the "trophic level axis" by partitioning all network components, standing stocks and flows, according to the past history of energy in the network. We show a balance relation between total inflow and outflow at each trophic-level component of each compartment (trophic species or guild), which is necessary to justify the trophic-level partitioning of throughflows. By collapsing the unfolded network to a macroscopic chain of trophic levels, each composed of portions of different compartments, conventional concepts of trophic level, energy pyramid, and progressive efficiency previously applied Only to food chains, are generalized to structurally complex food transfer networks.

The American Naturalist, Feb 1, 1989

Page 1. Vol. 133, No. 2 The American Naturalist February 1989 DOMINANCE OF INDIRECT CAUSALITY IN ... more Page 1. Vol. 133, No. 2 The American Naturalist February 1989 DOMINANCE OF INDIRECT CAUSALITY IN ECOSYSTEMS Wiegert and Kozlowski (1984; hereafter, W&K) criticized Patten's (1982a) theory of indirect effects, claiming that indirect influences are not quantitatively ...

Ecological Modelling, 1991

The American Naturalist, 1989

Page 1. Vol. 133, No. 2 The American Naturalist February 1989 DOMINANCE OF INDIRECT CAUSALITY IN ... more Page 1. Vol. 133, No. 2 The American Naturalist February 1989 DOMINANCE OF INDIRECT CAUSALITY IN ECOSYSTEMS Wiegert and Kozlowski (1984; hereafter, W&K) criticized Patten's (1982a) theory of indirect effects, claiming that indirect influences are not quantitatively ...

Journal of Theoretical Biology, 1989

For food networks of arbitrary structure, we generalize and develop a trophic-path partitioning o... more For food networks of arbitrary structure, we generalize and develop a trophic-path partitioning of standing stocks and flows, where each trophic path represents a particular chain of trophic transfers that an energy portion has experienced in the past. Based on this, we derive a method for "'unfolding" any given food network along the "trophic level axis" by partitioning all network components, standing stocks and flows, according to the past history of energy in the network. We show a balance relation between total inflow and outflow at each trophic-level component of each compartment (trophic species or guild), which is necessary to justify the trophic-level partitioning of throughflows. By collapsing the unfolded network to a macroscopic chain of trophic levels, each composed of portions of different compartments, conventional concepts of trophic level, energy pyramid, and progressive efficiency previously applied Only to food chains, are generalized to structurally complex food transfer networks.

Ecological Modelling, 1991

Abstract Trophic structure of a continental shelf ecosystem is analyzed using a general method fo... more Abstract Trophic structure of a continental shelf ecosystem is analyzed using a general method for partitioning (unfolding) network models of energy flows and standing stocks, including those with cycles, according to the number of times that energy-matter was transferred in the system. Model criteria that allow a trophic interpretation of unfolding analysis and procedures for modifying existing models to meet these criteria are presented. The analysis quantifies the distribution of trophic levels to compartments and that of compartments to trophic levels, and the energy contents, dissipations, and productivities of trophic levels. Ninety-nine percent of gross primary production dissipated by trophic level V in an ocean food-web model without microbial cycles as opposed to trophic level X in the continental-shelf ecosystem model with cycles. Progressive efficiencies of the first seven of eight trophic levels in the acyclic model varied between 0.01 and 0.52. Progressive efficiencies in the model with cycles converged to above 0.50 after four trophic levels.

Ecological Modelling, 1984

Published measures of cycling in compartmental models are based on throughflow. Throughflow consi... more Published measures of cycling in compartmental models are based on throughflow. Throughflow consists of flow only, not storage. Inclusive throughflow is introduced as a concept that includes both flow and storage. Cycling measures based on this concept are developed. Two Markov chains expressing the probability of transfer of substance from compartment j to i in one unit of transition time are constructed. The first is the conventional, throughflow-based model; second is an extended model based on inclusive throughflow with adjustable time step. This latter model is considered for two cases: storage accounted for and ignored, and is employed to illustrate derived relationships utilizing a small ecosystem energy flow model. Principal conclusions are: (1) cycling measures derived from the conventional throughflow-based model would overestimate cycling as given by the inclusive throughflow model, because they fail to distinguish storage from true cycling; (2) storages exceed cycled flow over low-ordered paths, but (3) decline in importance with increasing path length; (4) path diversity is greater in systems with storage than in corresponding systems without storage; (5) nonstorage path numbers increase combinatorially with path length; (6) cycling tends to become dominant over storage at higher path lengths, and (7) at differing rates for different compartments; (8) true cycling efficiency of each compartment i for the inclusive through flow model is corrected from the conventional model formulation (q;;-1)/q;; to [qii-1/(1-P;;)]/qii (P;, is the probability of substance in i remaining there over a transition time interval; q, is the cumulative substance returned to i over all paths of all lengths in the system); (9) this corrected cycling efficiency of each compartment with respect to inclusive throughflow equals that of the same compartment with respect to only the throughflow component as derived from the conventional model; (10) on the system level, however, the modified cycling index based on inclusive throughflow gives different values for cycling than the published cycling index derived from conventional throughflow; and (11) the modified cycling measures based on the inclusive throughflow model with an adjustable time step are independent of the chosen time step, and thus valid even for the continuous time case which is approached by the employed discrete time model as the time step approaches zero.

Ecological Modelling, 1986

In perceiving the structural design of ecosystems, direct interactions are so explicit that in co... more In perceiving the structural design of ecosystems, direct interactions are so explicit that in contrast indirect influences propagated over causal networks tend to be neglected or at best underestimated. An approach has been sought for making indirect effects as explicit as, and thus comparable with, direct ones, and evaluating their relative significance, in the compartmental model framework. In the present paper this course is further explored, based on the notion of path-partitioning of the total influence of one compartment on another. All paths from one compartment to another may be classified into paths associated with the direct and indirect effects portions of the total influence. By means of this path classification, explicit expressions for direct and indirect effects in ecosystems are derived. By examining the ratio of direct to indirect effects, it is shown that indirect effects are no less significant than direct ones, at least in the ecosystems examined to date. In fact, indirect effects tend to dominate direct ones with increasing system order, strength of direct interaction, and system connectance.

Ecological Modelling, 1993

Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This ... more Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This paper examines the time dependency of energy-matter flux in ecosystems modeled as flow-storage networks. The temporality of passage is governed by storage, which can be viewed as transport delay, a process contributing to the availability of energy to ecosystem compartments over time. Availability is a prior condition for utilization, which nevertheless is measurable from flow considerations alone. Combined flow-storage analyses are required to determine the temporality of substance availability; flow-only analyses are sufficient to specify utilization. The relations between the two are developed. What we term “tempo” involves the transport and delay as standing stocks of variously aged substance over the direct and indirect pathways of ecosystem networks. Our concept of “mode” refers to utilization alone, without regard for timing or the age distribution of flowing substance. Temporal analysis highlights the importance of turnover time, and thus body size and mass of individual organisms, in the dynamics of energy dependencies in ecosystems.

Ecological Modelling, 1993

Abstract The concept of progressive efficiency is generalized from food chains to food networks o... more Abstract The concept of progressive efficiency is generalized from food chains to food networks of arbitrary structure. Two distinct modes and corresponding pathways of contribution to energy-matter utilization are identified and formulated using continuous time models of energy-matter flows in ecosystems. First passage or root utilization involves first time transfer and transformation (of assimilated substance only) along all direct and indirect food paths originating at a defined source compartment and terminating at a defined destination compartment. First passage paths include acyclic paths plus cyclic paths that do not pass through the destination compartments. Recycling or reutilization involves the subsequent retransformation of previously utilized but not dissipated energy-matter by consumers. Recycling pathways start and end at the defined destination compartment. Total or ultimate utilization by destination compartments is the sum of first passage and recycling utilization. Two properties of ecosystems are demonstrated which depart from those of conventional trophic dynamics. Network virtual amplification is the increase of energy-matter ultimately utilized at destination compartments compared to the quantities originally introduced at source compartments. This is due largely to recycling; no energy is created, no thermodynamic law violated. Network homogenization is the tendency in food cycles for introduced energy-matter to become more or less evenly distributed to all compartments. These properties are illustrated with two models of ecosystem energy-matter flows.

Ecological Modelling, 2009

Ecological network analysis (ENA), predicated on systems theory and Leontiev input-output analysi... more Ecological network analysis (ENA), predicated on systems theory and Leontiev input-output analysis, is a method widely used in ecology to reveal ecosystem properties. An important ecosystem property computed in ENA is throughflows, the amount of matter/energy leaving each compartment of the ecosystem. Throughflows are analyzed via a matrix N representing their relationships to the driving input at the boundary. Network particle tracking (NPT) builds on ENA to offer a Lagrangian particle method that describes the activity of the ecosystem at the microscopic level. This paper introduces a Lagrangian throughflow analysis methodology using NPT and shows that the NPT throughflow matrix, N, agrees with the conventional ENA throughflow matrix, N, for ecosystems at steady-state with donor-controlled flows. The matrix N is computed solely from the pathways (particles' histories) generated by NPT simulations and its average over multiple runs of the algorithm with longer simulation time agrees with the Eulerian N matrix (Law of Large Numbers). While the traditional NEA throughflow analysis is mostly used with steady-state ecosystem models, the Lagrangian throughflow analysis that we propose can be used with non-steady-state models and paves the way for the development of dynamic throughflow analysis.

Botanical Gazette, 1959

1. The influence of ammonium phosphate buffers on penetration of 2,4-dichlorophenoxyacetic acid (... more 1. The influence of ammonium phosphate buffers on penetration of 2,4-dichlorophenoxyacetic acid (2,4-D), a-naphthaleneacetic acid (NAA), and 3,6-endoxohexahydrophthalic acid (Endothal) into young bean leaf tissue was studied by measuring internode growth following treatment. 2. Uptake of these biologically active acids was found to be completely independent of their state of dissociation. The plant responses appeared to be mediated instead by the buffer anions. 3. H2PO- 4 enhanced uptake, while HPO-- 4 inhibited it. This ion antagonism resulted in growth inhibition which was proportional in magnitude to the concentration differential of the ion present in excess. This relationship produced empirical correlations between percentage internode repression and curves of buffer capacity.

International Journal of Ecodynamics, 2007

Limnology and Oceanography, 1961

A model gcncralizing negentropy flux in plankton communities is presented. The biomass informatio... more A model gcncralizing negentropy flux in plankton communities is presented. The biomass information equivalent 23 (Z) at time t is

Forests, 2015

Alpine, subalpine and boreal tree species, of low genetic diversity and adapted to low optimal te... more Alpine, subalpine and boreal tree species, of low genetic diversity and adapted to low optimal temperatures, are vulnerable to the warming effects of global climate change. The accurate prediction of these species' distributions in response to climate change is critical for effective planning and management. The goal of this research is to predict climate change effects on the distribution of red spruce (Picea rubens Sarg.) in the Great Smoky Mountains National Park (GSMNP), eastern USA. Climate change is, however, conflated with other environmental factors, making its assessment a complex systems problem in which indirect effects are significant in causality. Predictions were made by linking a tree growth simulation model, red spruce growth model (ARIM.SIM), to a GIS spatial model, red spruce habitat model (ARIM.HAB). ARIM.SIM quantifies direct and indirect interactions between red spruce and its growth factors, revealing the latter to be dominant. ARIM.HAB spatially distributes the ARIM.SIM simulations under the assumption that greater growth reflects higher probabilities of presence. ARIM.HAB predicts the future habitat suitability of red spruce based on growth predictions of ARIM.SIM under climate change and three air pollution scenarios: 10% increase, no change and 10% decrease. Results show that suitable

International Journal of Ecodynamics, 2006

Homo sapiens appears to be evolving into a new kind of species not seen before in organic evoluti... more Homo sapiens appears to be evolving into a new kind of species not seen before in organic evolution. This is Homo holisticus, systems man, the first species in the earth's history with a global reach, entailing global selective forces charting its evolutionary change. Living things make models of their reality, converting physical causes to mixed physical-phenomenal ones, a defining characteristic of life. The ontic biosphere accordingly generates a virtual noosphere, the aggregate of implicit biological epistemologies. These operate collectively to shape global change, to which human change is both entrained and contributes. Developing a network perspective on global change, ecology's 'AWFUL theorem', resulting from zero-sum transactions (ontic, conservative, energy-matter exchanges), is reviewed and illustrated by two examples of anthropogenic environmental degradation. Indirect relations (epistemic, nonconservative and informational) develop automatically in transactional networks and introduce nonzero-sumness into the causal stream. This enables systems to move and remain away from thermodynamic equilibrium, in a process of network aggradation wherein internal negentropy generation exceeds boundary entropy dissipation. A third example shows how more mature ecosystems radiate photons at lower temperatures, reflecting increased internal organization-distance from thermodynamic equilibrium. Six network properties contributing to nonzero-sumness are identified, one being system size (number of components). Nonzero-sumness increases utility, expressed as benefit/cost ratios, and network synergism is the universal tendency in transactional networks to produce ratios >1. However, the degree of positiveness diminishes with system size so that network aggradation experiences diminishing returns as size increases. The organization of nature into a graded series of systems (cells, organs, organisms, etc.) based on size reflects this. Although unlimited network aggradation (negentropic growth and development) is possible with increasing interconnection, diminishing utility returns restrict optimal system size to relatively small numbers of interacting components. The global reach of the emerging H. holisticus may thus contraindicate sustainable entrainment of human change to global change by reducing network synergism even as network aggradation marginally rises.

Canadian Water Resources Journal, 1982

Ecological Modelling, Mar 1, 1993

Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This ... more Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This paper examines the time dependency of energy-matter flux in ecosystems modeled as flow-storage networks. The temporality of passage is governed by storage, which can be viewed as transport delay, a process contributing to the availability of energy to ecosystem compartments over time. Availability is a prior condition for utilization, which nevertheless is measurable from flow considerations alone. Combined flow-storage analyses are required to determine the temporality of substance availability; flow-only analyses are sufficient to specify utilization. The relations between the two are developed. What we term “tempo” involves the transport and delay as standing stocks of variously aged substance over the direct and indirect pathways of ecosystem networks. Our concept of “mode” refers to utilization alone, without regard for timing or the age distribution of flowing substance. Temporal analysis highlights the importance of turnover time, and thus body size and mass of individual organisms, in the dynamics of energy dependencies in ecosystems.

Ecological Modelling, Mar 1, 1993

Abstract The concept of progressive efficiency is generalized from food chains to food networks o... more Abstract The concept of progressive efficiency is generalized from food chains to food networks of arbitrary structure. Two distinct modes and corresponding pathways of contribution to energy-matter utilization are identified and formulated using continuous time models of energy-matter flows in ecosystems. First passage or root utilization involves first time transfer and transformation (of assimilated substance only) along all direct and indirect food paths originating at a defined source compartment and terminating at a defined destination compartment. First passage paths include acyclic paths plus cyclic paths that do not pass through the destination compartments. Recycling or reutilization involves the subsequent retransformation of previously utilized but not dissipated energy-matter by consumers. Recycling pathways start and end at the defined destination compartment. Total or ultimate utilization by destination compartments is the sum of first passage and recycling utilization. Two properties of ecosystems are demonstrated which depart from those of conventional trophic dynamics. Network virtual amplification is the increase of energy-matter ultimately utilized at destination compartments compared to the quantities originally introduced at source compartments. This is due largely to recycling; no energy is created, no thermodynamic law violated. Network homogenization is the tendency in food cycles for introduced energy-matter to become more or less evenly distributed to all compartments. These properties are illustrated with two models of ecosystem energy-matter flows.

Ecological Modelling, Oct 1, 1984

Published measures of cycling in compartmental models are based on throughflow. Throughflow consi... more Published measures of cycling in compartmental models are based on throughflow. Throughflow consists of flow only, not storage. Inclusive throughflow is introduced as a concept that includes both flow and storage. Cycling measures based on this concept are developed. Two Markov chains expressing the probability of transfer of substance from compartment j to i in one unit of transition time are constructed. The first is the conventional, throughflow-based model; second is an extended model based on inclusive throughflow with adjustable time step. This latter model is considered for two cases: storage accounted for and ignored, and is employed to illustrate derived relationships utilizing a small ecosystem energy flow model. Principal conclusions are: (1) cycling measures derived from the conventional throughflow-based model would overestimate cycling as given by the inclusive throughflow model, because they fail to distinguish storage from true cycling; (2) storages exceed cycled flow over low-ordered paths, but (3) decline in importance with increasing path length; (4) path diversity is greater in systems with storage than in corresponding systems without storage; (5) nonstorage path numbers increase combinatorially with path length; (6) cycling tends to become dominant over storage at higher path lengths, and (7) at differing rates for different compartments; (8) true cycling efficiency of each compartment i for the inclusive through flow model is corrected from the conventional model formulation (q;;-1)/q;; to [qii-1/(1-P;;)]/qii (P;, is the probability of substance in i remaining there over a transition time interval; q, is the cumulative substance returned to i over all paths of all lengths in the system); (9) this corrected cycling efficiency of each compartment with respect to inclusive throughflow equals that of the same compartment with respect to only the throughflow component as derived from the conventional model; (10) on the system level, however, the modified cycling index based on inclusive throughflow gives different values for cycling than the published cycling index derived from conventional throughflow; and (11) the modified cycling measures based on the inclusive throughflow model with an adjustable time step are independent of the chosen time step, and thus valid even for the continuous time case which is approached by the employed discrete time model as the time step approaches zero.

Journal of Theoretical Biology, Sep 1, 1989

For food networks of arbitrary structure, we generalize and develop a trophic-path partitioning o... more For food networks of arbitrary structure, we generalize and develop a trophic-path partitioning of standing stocks and flows, where each trophic path represents a particular chain of trophic transfers that an energy portion has experienced in the past. Based on this, we derive a method for "'unfolding" any given food network along the "trophic level axis" by partitioning all network components, standing stocks and flows, according to the past history of energy in the network. We show a balance relation between total inflow and outflow at each trophic-level component of each compartment (trophic species or guild), which is necessary to justify the trophic-level partitioning of throughflows. By collapsing the unfolded network to a macroscopic chain of trophic levels, each composed of portions of different compartments, conventional concepts of trophic level, energy pyramid, and progressive efficiency previously applied Only to food chains, are generalized to structurally complex food transfer networks.

The American Naturalist, Feb 1, 1989

Page 1. Vol. 133, No. 2 The American Naturalist February 1989 DOMINANCE OF INDIRECT CAUSALITY IN ... more Page 1. Vol. 133, No. 2 The American Naturalist February 1989 DOMINANCE OF INDIRECT CAUSALITY IN ECOSYSTEMS Wiegert and Kozlowski (1984; hereafter, W&K) criticized Patten's (1982a) theory of indirect effects, claiming that indirect influences are not quantitatively ...

Ecological Modelling, 1991

The American Naturalist, 1989

Page 1. Vol. 133, No. 2 The American Naturalist February 1989 DOMINANCE OF INDIRECT CAUSALITY IN ... more Page 1. Vol. 133, No. 2 The American Naturalist February 1989 DOMINANCE OF INDIRECT CAUSALITY IN ECOSYSTEMS Wiegert and Kozlowski (1984; hereafter, W&K) criticized Patten's (1982a) theory of indirect effects, claiming that indirect influences are not quantitatively ...

Journal of Theoretical Biology, 1989

For food networks of arbitrary structure, we generalize and develop a trophic-path partitioning o... more For food networks of arbitrary structure, we generalize and develop a trophic-path partitioning of standing stocks and flows, where each trophic path represents a particular chain of trophic transfers that an energy portion has experienced in the past. Based on this, we derive a method for "'unfolding" any given food network along the "trophic level axis" by partitioning all network components, standing stocks and flows, according to the past history of energy in the network. We show a balance relation between total inflow and outflow at each trophic-level component of each compartment (trophic species or guild), which is necessary to justify the trophic-level partitioning of throughflows. By collapsing the unfolded network to a macroscopic chain of trophic levels, each composed of portions of different compartments, conventional concepts of trophic level, energy pyramid, and progressive efficiency previously applied Only to food chains, are generalized to structurally complex food transfer networks.

Ecological Modelling, 1991

Abstract Trophic structure of a continental shelf ecosystem is analyzed using a general method fo... more Abstract Trophic structure of a continental shelf ecosystem is analyzed using a general method for partitioning (unfolding) network models of energy flows and standing stocks, including those with cycles, according to the number of times that energy-matter was transferred in the system. Model criteria that allow a trophic interpretation of unfolding analysis and procedures for modifying existing models to meet these criteria are presented. The analysis quantifies the distribution of trophic levels to compartments and that of compartments to trophic levels, and the energy contents, dissipations, and productivities of trophic levels. Ninety-nine percent of gross primary production dissipated by trophic level V in an ocean food-web model without microbial cycles as opposed to trophic level X in the continental-shelf ecosystem model with cycles. Progressive efficiencies of the first seven of eight trophic levels in the acyclic model varied between 0.01 and 0.52. Progressive efficiencies in the model with cycles converged to above 0.50 after four trophic levels.

Ecological Modelling, 1984

Published measures of cycling in compartmental models are based on throughflow. Throughflow consi... more Published measures of cycling in compartmental models are based on throughflow. Throughflow consists of flow only, not storage. Inclusive throughflow is introduced as a concept that includes both flow and storage. Cycling measures based on this concept are developed. Two Markov chains expressing the probability of transfer of substance from compartment j to i in one unit of transition time are constructed. The first is the conventional, throughflow-based model; second is an extended model based on inclusive throughflow with adjustable time step. This latter model is considered for two cases: storage accounted for and ignored, and is employed to illustrate derived relationships utilizing a small ecosystem energy flow model. Principal conclusions are: (1) cycling measures derived from the conventional throughflow-based model would overestimate cycling as given by the inclusive throughflow model, because they fail to distinguish storage from true cycling; (2) storages exceed cycled flow over low-ordered paths, but (3) decline in importance with increasing path length; (4) path diversity is greater in systems with storage than in corresponding systems without storage; (5) nonstorage path numbers increase combinatorially with path length; (6) cycling tends to become dominant over storage at higher path lengths, and (7) at differing rates for different compartments; (8) true cycling efficiency of each compartment i for the inclusive through flow model is corrected from the conventional model formulation (q;;-1)/q;; to [qii-1/(1-P;;)]/qii (P;, is the probability of substance in i remaining there over a transition time interval; q, is the cumulative substance returned to i over all paths of all lengths in the system); (9) this corrected cycling efficiency of each compartment with respect to inclusive throughflow equals that of the same compartment with respect to only the throughflow component as derived from the conventional model; (10) on the system level, however, the modified cycling index based on inclusive throughflow gives different values for cycling than the published cycling index derived from conventional throughflow; and (11) the modified cycling measures based on the inclusive throughflow model with an adjustable time step are independent of the chosen time step, and thus valid even for the continuous time case which is approached by the employed discrete time model as the time step approaches zero.

Ecological Modelling, 1986

In perceiving the structural design of ecosystems, direct interactions are so explicit that in co... more In perceiving the structural design of ecosystems, direct interactions are so explicit that in contrast indirect influences propagated over causal networks tend to be neglected or at best underestimated. An approach has been sought for making indirect effects as explicit as, and thus comparable with, direct ones, and evaluating their relative significance, in the compartmental model framework. In the present paper this course is further explored, based on the notion of path-partitioning of the total influence of one compartment on another. All paths from one compartment to another may be classified into paths associated with the direct and indirect effects portions of the total influence. By means of this path classification, explicit expressions for direct and indirect effects in ecosystems are derived. By examining the ratio of direct to indirect effects, it is shown that indirect effects are no less significant than direct ones, at least in the ecosystems examined to date. In fact, indirect effects tend to dominate direct ones with increasing system order, strength of direct interaction, and system connectance.

Ecological Modelling, 1993

Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This ... more Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This paper examines the time dependency of energy-matter flux in ecosystems modeled as flow-storage networks. The temporality of passage is governed by storage, which can be viewed as transport delay, a process contributing to the availability of energy to ecosystem compartments over time. Availability is a prior condition for utilization, which nevertheless is measurable from flow considerations alone. Combined flow-storage analyses are required to determine the temporality of substance availability; flow-only analyses are sufficient to specify utilization. The relations between the two are developed. What we term “tempo” involves the transport and delay as standing stocks of variously aged substance over the direct and indirect pathways of ecosystem networks. Our concept of “mode” refers to utilization alone, without regard for timing or the age distribution of flowing substance. Temporal analysis highlights the importance of turnover time, and thus body size and mass of individual organisms, in the dynamics of energy dependencies in ecosystems.

Ecological Modelling, 1993

Abstract The concept of progressive efficiency is generalized from food chains to food networks o... more Abstract The concept of progressive efficiency is generalized from food chains to food networks of arbitrary structure. Two distinct modes and corresponding pathways of contribution to energy-matter utilization are identified and formulated using continuous time models of energy-matter flows in ecosystems. First passage or root utilization involves first time transfer and transformation (of assimilated substance only) along all direct and indirect food paths originating at a defined source compartment and terminating at a defined destination compartment. First passage paths include acyclic paths plus cyclic paths that do not pass through the destination compartments. Recycling or reutilization involves the subsequent retransformation of previously utilized but not dissipated energy-matter by consumers. Recycling pathways start and end at the defined destination compartment. Total or ultimate utilization by destination compartments is the sum of first passage and recycling utilization. Two properties of ecosystems are demonstrated which depart from those of conventional trophic dynamics. Network virtual amplification is the increase of energy-matter ultimately utilized at destination compartments compared to the quantities originally introduced at source compartments. This is due largely to recycling; no energy is created, no thermodynamic law violated. Network homogenization is the tendency in food cycles for introduced energy-matter to become more or less evenly distributed to all compartments. These properties are illustrated with two models of ecosystem energy-matter flows.

Ecological Modelling, 2009

Ecological network analysis (ENA), predicated on systems theory and Leontiev input-output analysi... more Ecological network analysis (ENA), predicated on systems theory and Leontiev input-output analysis, is a method widely used in ecology to reveal ecosystem properties. An important ecosystem property computed in ENA is throughflows, the amount of matter/energy leaving each compartment of the ecosystem. Throughflows are analyzed via a matrix N representing their relationships to the driving input at the boundary. Network particle tracking (NPT) builds on ENA to offer a Lagrangian particle method that describes the activity of the ecosystem at the microscopic level. This paper introduces a Lagrangian throughflow analysis methodology using NPT and shows that the NPT throughflow matrix, N, agrees with the conventional ENA throughflow matrix, N, for ecosystems at steady-state with donor-controlled flows. The matrix N is computed solely from the pathways (particles' histories) generated by NPT simulations and its average over multiple runs of the algorithm with longer simulation time agrees with the Eulerian N matrix (Law of Large Numbers). While the traditional NEA throughflow analysis is mostly used with steady-state ecosystem models, the Lagrangian throughflow analysis that we propose can be used with non-steady-state models and paves the way for the development of dynamic throughflow analysis.

Botanical Gazette, 1959

1. The influence of ammonium phosphate buffers on penetration of 2,4-dichlorophenoxyacetic acid (... more 1. The influence of ammonium phosphate buffers on penetration of 2,4-dichlorophenoxyacetic acid (2,4-D), a-naphthaleneacetic acid (NAA), and 3,6-endoxohexahydrophthalic acid (Endothal) into young bean leaf tissue was studied by measuring internode growth following treatment. 2. Uptake of these biologically active acids was found to be completely independent of their state of dissociation. The plant responses appeared to be mediated instead by the buffer anions. 3. H2PO- 4 enhanced uptake, while HPO-- 4 inhibited it. This ion antagonism resulted in growth inhibition which was proportional in magnitude to the concentration differential of the ion present in excess. This relationship produced empirical correlations between percentage internode repression and curves of buffer capacity.

International Journal of Ecodynamics, 2007

Limnology and Oceanography, 1961

A model gcncralizing negentropy flux in plankton communities is presented. The biomass informatio... more A model gcncralizing negentropy flux in plankton communities is presented. The biomass information equivalent 23 (Z) at time t is

Forests, 2015

Alpine, subalpine and boreal tree species, of low genetic diversity and adapted to low optimal te... more Alpine, subalpine and boreal tree species, of low genetic diversity and adapted to low optimal temperatures, are vulnerable to the warming effects of global climate change. The accurate prediction of these species' distributions in response to climate change is critical for effective planning and management. The goal of this research is to predict climate change effects on the distribution of red spruce (Picea rubens Sarg.) in the Great Smoky Mountains National Park (GSMNP), eastern USA. Climate change is, however, conflated with other environmental factors, making its assessment a complex systems problem in which indirect effects are significant in causality. Predictions were made by linking a tree growth simulation model, red spruce growth model (ARIM.SIM), to a GIS spatial model, red spruce habitat model (ARIM.HAB). ARIM.SIM quantifies direct and indirect interactions between red spruce and its growth factors, revealing the latter to be dominant. ARIM.HAB spatially distributes the ARIM.SIM simulations under the assumption that greater growth reflects higher probabilities of presence. ARIM.HAB predicts the future habitat suitability of red spruce based on growth predictions of ARIM.SIM under climate change and three air pollution scenarios: 10% increase, no change and 10% decrease. Results show that suitable

International Journal of Ecodynamics, 2006

Homo sapiens appears to be evolving into a new kind of species not seen before in organic evoluti... more Homo sapiens appears to be evolving into a new kind of species not seen before in organic evolution. This is Homo holisticus, systems man, the first species in the earth's history with a global reach, entailing global selective forces charting its evolutionary change. Living things make models of their reality, converting physical causes to mixed physical-phenomenal ones, a defining characteristic of life. The ontic biosphere accordingly generates a virtual noosphere, the aggregate of implicit biological epistemologies. These operate collectively to shape global change, to which human change is both entrained and contributes. Developing a network perspective on global change, ecology's 'AWFUL theorem', resulting from zero-sum transactions (ontic, conservative, energy-matter exchanges), is reviewed and illustrated by two examples of anthropogenic environmental degradation. Indirect relations (epistemic, nonconservative and informational) develop automatically in transactional networks and introduce nonzero-sumness into the causal stream. This enables systems to move and remain away from thermodynamic equilibrium, in a process of network aggradation wherein internal negentropy generation exceeds boundary entropy dissipation. A third example shows how more mature ecosystems radiate photons at lower temperatures, reflecting increased internal organization-distance from thermodynamic equilibrium. Six network properties contributing to nonzero-sumness are identified, one being system size (number of components). Nonzero-sumness increases utility, expressed as benefit/cost ratios, and network synergism is the universal tendency in transactional networks to produce ratios >1. However, the degree of positiveness diminishes with system size so that network aggradation experiences diminishing returns as size increases. The organization of nature into a graded series of systems (cells, organs, organisms, etc.) based on size reflects this. Although unlimited network aggradation (negentropic growth and development) is possible with increasing interconnection, diminishing utility returns restrict optimal system size to relatively small numbers of interacting components. The global reach of the emerging H. holisticus may thus contraindicate sustainable entrainment of human change to global change by reducing network synergism even as network aggradation marginally rises.

Canadian Water Resources Journal, 1982