Tag Archives: apparent_interactions

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.

Theorizing about Ecological Complexity, mid 1980s-2000

Constructionist and landscape views (Taylor 2005, Chapter 1, Part A) reinforce other currents that have undermined the aspirations of earlier decades for identifying general principles about systems and communities (Kingsland 1995, 213-251; Taylor and Haila 2001).  Since the 1980s ecologists in general have become increasingly aware that situations may vary according to historical trajectories that have led to them; that particularities of place and connections among places matter; that time and place is a matter of scales that differ among co-occurring species; that variation among individuals can qualitatively alter the ecological process; that this variation is a result of ongoing differentiation occurring within populations—which are specifically located and inter-connected—and that interactions among the species under study can be artifacts of the indirect effects of other “hidden” species (see Taylor 2005, Chapter1, section B).

In patch dynamic studies, for example, the scale and frequency of disturbances that create open “patches” is now emphasized as much as species interactions in the periods between disturbances (Pickett and White 1985).  Studies of succession and of the immigration and extinction dynamics for habitat patches pay attention to the particulars of species dispersal and the habitat being colonized, and how these determine successful colonization for different species (Gray et al. 1987).  Meta-population theory examines the persistence not of communities but of populations (or phoretic associations of communities on carrier species) in a landscape of patches (Hastings and Harrison 1994).  On a larger scale such a shift in focus is supported by biogeographic comparisons which show that continental floras and faunas are not necessarily in equilibrium with the extant environmental conditions (Haila and Järvinen 1990).  From a different angle, models that distinguish among individual organisms (in their characteristics and spatial location) have been shown to generate certain observed ecological patterns, such as patterns of change in size distribution of individuals in a population over time, where large scale, aggregated models have not (DeAngelis and Gross 1992).  And, the effects mediated through the populations not immediately in focus or unrecognized upset the methodology of observing the direct interactions among populations and confound many principles, such as the competitive exclusion principle, derived on that basis (Taylor 2005,Chapter 1, section B; Wootton 1994).

By and large philosophers of ecology, environmental ethicists, environmentalists, and others who invoke principles of ecology have yet to address the implications for their fields of this picture of ecological complexity (Taylor 1997a; Taylor and Haila 2001).

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


DeAngelis, D. L. and L. J. Gross (Eds.) (1992). Populations and Communities: An Individual-based Perspective. New York: Chapman and Hall.

Gray, A. J., M. J. Crawley and P. J. Edwards (Eds.) (1987). Colonization, Succession and Stability. 26th Symposium of the British Ecological Society. Oxford: Blackwell.

Haila, Y. and O. Järvinen (1990). “Northern conifer forests and their bird species assemblages,” in A. Keast (Ed.), Biogeography and Ecology of Forest Bird Communities.  The Hague: SPB Acad. Publishing, 65-81.

Hastings, A. and Harrison, S.: 1994, ‘Metapopulation dynamics and genetics’,  Annual Review of Ecology and Systematics 25, 167-188.

Kingsland, S. (1995). Modeling Nature:  Episodes in the History of Population Ecology. Chicago: University of Chicago Press. 2nd. ed., 213-251;

Pickett, S. T. A. and P. S. White (Eds.) (1985). The Ecology of Natural Disturbance and Patch Dynamics. Orlando, FL: Academic Press.

Taylor, P. J. and Y. Haila (2001). “Situatedness and Problematic Boundaries: Conceptualizing Life’s Complex Ecological Context.” Biology & Philosophy 16(4): 521-532

Wootton, J. T. (1994). “The nature and consequences of indirect effects in ecological communities.” Annual Review of Ecology and Systematics 25: 443-466.

Troubled by Heterogeneity? Opportunities for Fresh Views on Long-standing and Recent Issues in Biology and Biomedicine

“Troubled by Heterogeneity? Opportunities for Fresh Views on Long-standing and Recent Issues in Biology and Biomedicine,” was a talk I gave on 13 Oct. ’10 (abstract). I sketched a number of cases to get the audience thinking about my underlying contention that research and application of knowledge resulting from research are untroubled by heterogeneity to the extent that populations are well controlled. Such control can only be established and maintained with considerable effort or social infrastructure, which invites attention to possibilities for participation instead of control of human subjects.

The pdf of the slides and the audio recording are downloadable. (By noticing when my voice rises in volume, which is when I approach the laptop, you can guess when I am clicking from one slide to the next.) Some of the sketches of cases have been addressed in previous posts (see links on the abstract). This blog post consists of some afterthoughts, including questions needing more thought, in response to discussion after the talk.

1. What am I saying researchers should do?

The contention underlying the talk (above) is at first descriptive. But it does assume that heterogeneity (of various types) is ubiquitous and is often not paid attention to. The title suggests that researchers could be troubled by heterogeneity. But what should they do? Given that my framework incorporates a social level of explanation, what should they change first—their thinking and methods, or the social situations that enable the knowledge they arrive at to become significant (including, to be implemented in policy and associated practice)? What would be their motivation for changing?—To get a better view of the world (one that applies in a wider range of circumstances)? Or because there is a cost in controlling populations (maintaining infrastructure, etc.)? Or because that control breaks down, especially in crises?

2. Varieties of heterogeneity

My exploration of heterogeneity in biology and biomedicine took off after I saw the overlooked significance of underlying heterogeneity in heritability studies. Most of the cases in the talk, however, revolved around a simpler form of heterogeneity, namely, variation around a mean. Should I—for expository and/or conceptual reasons—focus separately on the different kinds of heterogeneity. I have an evolving taxonomy of heterogeneities, http://sicw.wikispaces.umb.edu/heterogeneities.

3. Personalized medicine

The figure I used to discuss the issue of misclassification lacked a crucial element—a cut off point between OK and not OK medical outcomes.

Genetic condition
Medical treatment A B
1 (not treated because not sick) OK OK
2 treated (with say drug X) OK result Not OK

4. Isn’t simplification of complexity sometimes/often/always necessary for scientific progress? After researchers get a handle on the simplified situation, they add back variables that they had previous controlled.

Sometimes researchers add back variables; sometimes they continue to engineer the world so the control over those variables is maintained. They may come to see the world the same way as they control it and need ways to be reminded early and often of what has been left out. This is especially so regarding ecological complexity, where variables left out have dynamics of their own that interact with the variables in focus. Chapter 1B of my book, Unruly Complexity (U. Chicago Press, 2005), illustrates the problem of “apparent interactions” that arise. Indeed, I have come to see the “simplification is necessary for science” line as a way to define out of science many situations that deserve systematic study. What do philosophers and theoreticians think about getting to know situations that, from the start, are not amenable to control or are not the same thing if they are carved out from the whole?


Fresh perspectives can be brought to modern understandings of heredity and life-course development by examining the relationship between control and variation, particularity, or, more generally, heterogeneity. Broadly speaking, my contention is that research and application of resulting knowledge are untroubled by heterogeneity to the extent that populations are well controlled. Such control can only be established and maintained with considerable effort or social infrastructure, which invites attention to possibilities for participation instead of control of human subjects. Building on several recent publications of mine on heterogeneity and heritability, I explain why underlying heterogeneity warrants the attention of quantitative geneticists and critical commentators on nature-nurture debates (see post). I elaborate on my contention through brief sketches of cases from biomedicine, involving: genetic testing; gene-environment interaction; personalized medicine; IQ scores; racial-group membership; and life events and difficulties research. My goal is to stimulate wider exploration of heterogeneity and control in relation to biological and social theories and practice.