Tag Archives: community_ecology

Apparent Ecological Interactions—A Comparison Of Alternative Derivations

The previous post presented a case of apparent predator-prey interactions among ciliate species one might have expected to be competitors.  There are many references to apparent interactions or indirect effects in the ecological literature (e.g., Levine 1976; Holt 1977; Lawlor 1979; Vandermeer 1980; Schaffer 1981; Bender et al. 1984).  Once several ways of defining and estimating interactions from data are distinguished (see earlier post), their differences can be laid out.

Apparent Interactions: Definitions and Estimation

Apparent type 1 interactions should generate trajectories for the members of an apparent community that mimic the actual trajectories for those members, i.e., the trajectories generated by the dynamics of the full community.  Variations of this approach depend on whether the interactions:

a. are assumed to govern trajectories near equilibrium—the method used in Taylor (2005, Chapter 1B);

b. are calculated as if the community were near equilibrium, but then extended to apply away from equilibrium by using a GLV (model 1 in previous post);

c.  are derived by fitting observed trajectories directly to the GLV model; or

d.  are derived by fitting observed trajectories directly to some model other than the GLV.

Other methods include a generalization of MacArthur (1972:33ff) and Schaffer’s (1981) Abstracted Growth Equations.  Assuming certain special conditions, this last method can be used to derive equations for the apparent community when we do not have knowledge of the full system.

Bender et al. (1984)’s PULSE and PRESS methods:  If the time scales of the hidden populations and of the modeled populations are similar, the PULSE method yields estimates of the direct interactions between the modeled populations.  These are unable, in general, to mimic the actual trajectories of the modeled populations (see Taylor 2005, Chapter 1B).  If the time scales are disjunct then PULSE estimates of the direct interactions may absorb effects from the hidden variables.  In other words, they will be estimates of apparent interactions and thus potentially take counter-intuitive values.  The PRESS method has some significant limitations.  It cannot be used in most cases where direct self-interactions are zero (especially those of hidden variables), or where the apparent community has only one member.  When the PRESS method can be applied, the estimated interactions are actually estimates of apparent interactions.

Type 2 interactions focus only on the two populations in question and so, in principle, are not affected by the dynamics of hidden variables.  However, if loop analysis (Levins 1975) is used to calculate the values of type 2 interactions from estimates of type 1 interactions, then the full set of direct interactions must be known.  (Loop analysis using apparent type 1 interactions of the form developed in Taylor 2005, Chapter 1B generate qualitatively good estimates of type 2 interactions, but calculation of such apparent interactions requires knowledge of the full set of direct interactions; Taylor 1985, 119-177.)

Adapted from Taylor, P.J. (2005) Unruly Complexity: Ecology, Interpretation, Engagement (U. Chicago Press).


Bender, E. A., T. J. Case and M. E. Gilpin (1984). “Perturbation experiments in community ecology: Theory and practice.” Ecology 65: 1-13.

Holt, R. D. (1977). “Predation, apparent competition, and the structure of prey communities.” Theoretical Population Biology 12: 197-229

Lawlor, L. R. (1979). “Direct and indirect effects of n-species competition.” Oecologia 43: 355-364

Levine, S. H. (1976). “Competitive interactions in ecosystems.” American Naturalist 110: 903-910

Levins, R. (1975). “Evolution in communities near equilibrium,” in M. L. Cody and J. M. Diamond (Eds.), Ecology and Evolution of Communities.  Cambridge, MA: Harvard University Press, 16-50.

MacArthur, R. H. (1972). Geographical Ecology. New York: Harper and Row.

Schaffer, W. M. (1981). “Ecological abstraction: The consequences of reduced dimensionality in ecological models.” Ecological monographs 51: 383-401.

Taylor, P. J. (1985). Construction and turnover of multispecies communities:  A critique of approaches to ecological complexity. Unpublished Ph. D. dissertation.  Cambridge, MA: Harvard University.

Vandermeer, J. H. (1980). “Indirect mutualism: variations on a theme by     Stephen Levine.” American Naturalist 116: 441-448.


Why were half the interactions in a community of competing protozoans predator-prey relations?–An introduction to apparent interactions

Vandermeer (1969) reported on a quantitative study of a community of four competing ciliate protozoan populations.  The model he fitted to his observations (see previous post) indicated that three of the six pairs of interactions between the competitors were positive-negative (figure 1).  One would expect this of predator-prey relations, not of competitive interactions   Were these interactions actually predator-prey?  Indeed, were those pairs with negative-negative interactions actually competitors?  How can the values Vandermeer derived be understood and related to the actual ecological relationships among the protozoan populations?

Figure 1.  Community interactions reported by Vandermeer (1969).  PA = Paramecium aurelia, PB = Paramecium bursaria, PC = Paramecium caudatum, BL = Blepharisma sp.

An obvious response might be that Vandermeer’s model was inappropriate or inadequate, so let me examine this first.  The inter-population interaction values he derived for his four protozoan species came from fitting the observed population trajectories to a model of the following form:

Model 1: Generalized Lotka-Volterra (GLV)

Per capita rate of change of population X =

Intrinsic growth rate for X +

Self-interaction within the X’s +

Sum of interactions of the other populations on X;

where the first term is a constant, the second is a constant times the size of population X, and the inter-population terms are constants times the sizes of the other populations.

He estimated the intrinsic growth term and self-interaction term from isolated population growth experiments, and his inter-population interaction terms from two-population experiments.  Contrary to the widely held opinion that the GLV is a poor ecological model, the fit for Vandermeer’s four-population microcosms was fairly good and gave qualitatively correct predictions about coexistence of populations (Vandermeer 1981).

Given that Vandermeer’s model fits his observations well, one needs to look further to explain the anomalous (- +) interaction values between the competing protozoans.  First note that Vandermeer’s equations did not specify all the components of the community.  Each day during his experiment he removed a sample from his experimental tubes and added an equal volume of culture medium with bacteria.  The bacterial populations were alive and able to grow until consumed by the protozoa.  They had dynamics of their own not referred to in the equation above.  In fact, it is possible that the protozoan populations were affecting each other only through these shared bacterial prey.  If all the fitted interactions had indicated competition, the unspecified components might not have caused me any concern—the protozoan populations could be described as exploitative competitors.  Yet the interactions were not all competitive.

Notice that the observed behavior of the protozoan sub-community—the full community minus the bacteria—was fitted with a model containing interactions only within the sub-community.  Because there was no direct reference to the relationships with the hidden part of the community, the fitted interaction values had to incorporate these other indirect relationships, if they existed.  Let me call the fitted interactions apparent interactions and use this term whenever ecologists attempt to specify the ecological dynamics of a sub-community without explicit reference to the dynamics of the community from which it has been elevated.  In practice, fitted interaction values might always be apparent interactions, because there will be components the ecologists do not know about or have no data on—for example, larval and adult life stages will be lumped together, or decomposers or other components in the food web will be omitted.

The critical question is whether the distinction between direct and apparent interactions matters.  Do apparent interactions deviate significantly from direct observations of interactions or from ecologists’ intuition about plausible interactions among populations?  Ecologists tends to think that the protozoan populations should be competitors because they share a food resource, but Vandermeer’s study counters that idea.  Can a more general conclusion be derived?  This question is addressed in Taylor (2005, Chapter 1B).  The next post compares different formulations of the idea of apparent interactions.

Adapted from Taylor, P.J. (2005) Unruly Complexity: Ecology, Interpretation, Engagement (U. Chicago Press).


Vandermeer, J. H. (1969). “The competitive structure of communities: An experimental approach with protozoa.” Ecology 50: 362-371.

—— (1981). “A further note on community models.” American Naturalist 117: 379-380.

What is an ecological interaction?

Ecology is the study of complex interactions.  But what, exactly, is an ecological interaction?  This and the following posts will indicate that our intuition can be misleading.  When I see the Great Blue Heron standing still near the edge of the local river suddenly duck its head under the surface and come up with  fish in its beak, I know that, as a three-year old on my knee once said watching a nature show, the fish won’t be going home to mummy tonight.  The fish is prey; the heron is a predator.  The question, however, is what ecological interaction do herons and fish have?

Adapting text from Taylor (2005):

Interactions: Definitions and Estimation

Interactions may be directly observed, but these are interactions between individual organisms. Alternatively, interactions between populations may be inferred from data.  This either

  • requires a theory that tightly links a qualitative outcome (e.g., non-coexistence of similar populations) with the interaction (e.g., competition), or
  • requires quantitative data on population sizes.

Such population data may be construed in two ways:

1) as population sizes changing over time under a fixed set of conditions.  The effect of population j on population i is then defined as its contribution to altering the rate of change of i.  There are three major approaches to the estimation of these effects:

a.  Fit the data to a model postulated to govern the interacting populations, that is, estimate the values of the parameters for which the model best fits the data;

b.  Infer interactions from data on experimental perturbations from equilibrium. Bender et al. (1984) propose two procedures, “PULSE” and “PRESS,” for estimating the parameters of a Generalized Lotka-Volterra (GLV) model (model 1 in Taylor 2005, Chapter 1A).  These procedures require that the populations are initially at equilibrium and that a controlled series of perturbations from that equilibrium can be performed.

c. interactions inferred from data on moving equilibria.  To understand this somewhat paradoxical approach requires first the introduction of the second construal of quantitative data on population sizes:

2) moving equilibria of the population sizes under conditions that are changing, perhaps as induced experimentally.

The effect of population j on population i can be defined in terms of the co-variation of their equilibrium values—does one go up when the other goes down or do they go up and down together?  Such interactions are usually limited to competition, mutualism or null interactions.  This concept of interaction is not closely related to either directly observed interactions or those derived from data construed to be population sizes changing over time under a fixed set of conditions (type 1).  If values for type 1 interactions (approaches a or b) are estimated, then type 2 interactions can be calculated by loop analysis (Puccia and Levins 1985).  If values for type 2 interactions are estimated, then the qualitative values of type 1 interactions can sometimes be inferred by inverse loop analysis (Puccia and Levins 1985)—this constitutes approach c above.


Bender, E. A., T. J. Case and M. E. Gilpin (1984). “Perturbation experiments in community ecology: Theory and practice.” Ecology 65: 1-13

Puccia, C. J. and R. Levins (1985). Qualitative Modeling of Complex Systems: An Introduction to Loop Analysis and Time Averaging. Cambridge, MA: Harvard University Press

Taylor, P.J. (2005) Unruly Complexity: Ecology, Interpretation, Engagement (U. Chicago Press)

Theorizing about Ecological Complexity, through the mid 1980s

A broad distinction can be made between community ecology, which emphasizes population sizes and inter-species interactions, and systems ecology, which emphasizes nutrient and energy flows between compartments (Hagen 1989).  Nevertheless, community ecological theory also involves systems in the sense of entities that have clearly defined boundaries, coherent internal dynamics, and simply mediated relations with their external context (Taylor 1992, 2001, 383ff).  (See also the synthesis of the two schools in DeAngelis 1992 and Taylor and Post 1985.)  One needs to go beyond the dichotomy, however, to capture the range of basic impulses in studying ecological complexity evident in United States ecology from the 1950s through the mid-1980s.  These I identify in the table below, with position from left to right used to denote earlier or later emergence:

1. Ecosystems are complex, yet have SYSTEMIC PROPERTIES
——2. Ecosystems are complex systems of COMPARTMENTS & FLOWS of energy & nutrients
————3. Ecological complexity will be built up from BASIC, GENERAL RULES, especially about populations and their interactions
—————————–4. HIERARCHY THEORY—find natural scales of patterns and processes
————5. Important influences will be evident in PATTERNS in ecological complexity, as revealed in diversity measures or other community descriptors, or through multivariate analyses
—————————–6. Rules & generalizations may emerge from attention to actual PROCESSES through experimental manipulations or long term observations
———————————-7. PARTICULARISM—No generalizations from situation to situation
—————————–8. Ecology advances by refutation of TESTABLE HYPOTHESES

DeAngelis, D. L. (1992). Dynamics of Nutrient Cycling and Food Webs. London: Chapman and Hall.
Hagen, J. B. (1992). The Entangled Bank: The Origins of Ecosystem Ecology. New Brunswick, NJ: Rutgers University Press.
Taylor (1992). “Community,” in E. F. Keller and E. Lloyd (Eds.), Keywords in Evolutionary Biology.  Cambridge, MA: Harvard University Press, 52-60.
—— (2001), “From natural selection to natural construction to disciplining unruly complexity:  The challenge of integrating ecological dynamics into evolutionary theory,” in R. Singh, K. Krimbas, D. Paul and J. Beatty (Eds.), Thinking About Evolution: Historical, Philosophical and Political Perspectives.  Cambridge: Cambridge University Press, 377-393.
—— and W. M. Post (1985). A Description with Some Applications of MSNUCY, A Computer Model Combining Interspecific Interactions with Nutrient Cycling (Environmental Sciences Division Publication 2419). Oak Ridge, TN: Oak Ridge National Laboratory.

Extracted from Taylor, P.J. (2005) Unruly Complexity: Ecology, Interpretation, Engagement (U. Chicago Press).

The challenge of integrating ecological dynamics into evolutionary theory VI: Five approaches

Integrating the structure and dynamics of evolution’s ecological context (see previous posts) remains a neglected project within evolutionary theory.  Nevertheless, the different approaches to theorizing ecological organization can still be read in terms of the ways that evolutionary theory fits into them, whether or not this is made explicit.  Table 1 provides a classification of five basic orientations.

Central to the first three orientations is the notion of system, which I use in the strong sense of an entity that has clearly defined boundaries and has coherent internal dynamics, dynamics that govern the system’s responses to external influences and determine its structure, stability and development over time (Taylor 1992). System in this sense can refer not only to the basic units of systems ecology, but also to the guilds and communities of community ecology.  These three orientations differ according to the relative time scales of ecological and evolutionary processes.  In contrast to viewing ecological organization as system-like, various ecologists have emphasized what I call its “unruly complexity” (Taylor 2005).  That is, organisms and processes transgress the boundaries of any unit of ecological structure, spanning levels and scales; natural categories for and reduction of the complexity are elusive; ecological structures are subject to restructuring; control and generalization are difficult.  The two non-system orientations differ according to whether this unruly complexity can be disciplined theoretically.   Table 1’s distinctions are illustrated in Taylor (2000) through a review of twentieth century theories of ecological organization.

In the next post in the series, I note Darwin’s keen awareness of the structure and dynamics of evolution’s ecological context and mention some research that follows in that tradition.

Table 1. Five orientations to theorizing ecological organization and evolution.

Focus Orientation Time scales
system (or community) system evolves as a Coherent whole Fast return to equilibrium; slow change or evolution of system
individuals in context of system Stable system Fast return to equilibrium

intermediate speed evolution of population of individuals

slow change of system

system transient, yet Regularly reoccurring Fast passing of transient context (e.g.,succession)

intermediate speed evolution of population of individuals

slow change in nature of transient context

ecological organization as not system-like Anti-Theory Relevant processes not separable into “ecological” and “evolutionary” time scales
unruly complexity can be Disciplined

Taylor, P. J. “Community” pp. 52-60 in E.F. Keller & E. Lloyd (eds.) Keywords in Evolutionary Biology, Harvard University Press, 1992
—- “From natural selection to natural construction to disciplining unruly complexity: The challenge of integrating ecology into evolutionary theory,” in R. Singh, K. Krimbas, D. Paul & J. Beatty (eds.), Thinking About Evolution: Historical, Philosophical and Political Perspectives, Cambridge: Cambridge University Press, 377-393, 2000.
—- Unruly Complexity: Ecology, Interpretation, Engagement Chicago: University of Chicago Press, 2005.