**
Theoretical Ecology
Lab Tea**

Theoretical Ecology lab teas are informal talks to the lab group(s) of Simon Levin , Steve Pacala , Andy Dobson , and other interested folks around Princeton or visiting. The speakers come from that same set. The talks are limited to 30 minutes including the usual questions and interruptions. Of course, lively discussion often continues beyond 30 minutes -- after the talk is concluded.

Talk schedules and email lists are maintained by

**
Spring 2001**

Tuesday, January 23 | Jerome Chave |

Tuesday, January 30 | Yannis Kevrekidis |

Wednesday, February 7 | Juan Keymer |

Tuesday, February 13 | Jia Li, U Alabama |

Tuesday, February 20 | Masakazu Shimada , University of Tokyo |

Tuesday, February 27 | Josh Plotkin |

Tuesday, March 6 | Helene Muller-Landau |

Tuesday, March 13 | Ricardo Holdo |

March 20 | - springbreak - |

Tuesday, March 27 | Eduardo Zea |

Tuesday, April 3 | Lee Worden |

THURSDAY, April 12 | Jessica Green , Berkeley |

Tuesday, April 17 | Ben Strauss |

Tuesday, April 24 | Kai Chan |

Tuesday, May 1 | Henry Mwambi |

Tuesday, May 8 | Ran Nathan |

Tuesday, May 15 | Alun Lloyd |

Tuesday, May 22 | Jim Regetz |

Tuesday, May 29 | Nandi Leslie |

** Titles and abstracts**
most recent first (posted approximately one week before the talk):

Tuesday, April 24 @ 2 pm

**
Kai Chan**

**
The Trouble with Development is the Trouble with Us**

The "progress paradigm" that fuelled massive
development efforts over the last five decades is faltering badly because
of strong

anti-development sentiments in both developed
and developing nations. So far the detractors have emphasized the numerous
negative social and

environmental consequences accompanying "economic
progress", which has led development apologists to relabel their efforts
as "people-centered"

and "sustainable". On top of these problems
with the achievement of progress, there is the possibility that we have defined
progress wrongly, and are pursuing the wrong goal.

Most workers assume that we progress when
we maximize wealth or experience. I claim that we ought to maximize
*welfare* and question

whether this entails maximizing either wealth
or experience. Several lines of evidence suggest that welfare is compromised
by excess wealth

or experience, and a plausible theory of interests
and welfare predicts this empirical result. Unlike with wealth or experience,
we have no

accepted method for maximizing welfare.
I will present one simple method, and discuss an example and why it may
not be optimal. I will conclude with a second possibility, and a message
of hope.

Tuesday, April 17 @ 2 pm

**
Ben Strauss**

**
Best foraging strategy to optimize growth of a bumble bee colony: maximize
profit rate or efficiency?**

I will present a demographic model of a bumble bee colony for evaluating the colony fitness consequences of a range of worker bee nectar foraging strategies. These vary along a trade-off axis from more efficient strategies (high energy benefit/cost) to more "speedy" ones (high net rate of energy gain). The greater the rate of nectar supply, the more quickly larvae and pupae mature into new workers. However, the harder workers work, the more rapidly they senesce and die. Colony fitness is estimated as the sterile worker bee population size at the end of the colony growth period, when the colony switches to making reproductives. I expect that the tension between raising juvenile development rate and lowering worker mortality, both mediated by foraging strategy, will lead to different favored foraging strategies for growth periods of different lengths.

THURSDAY, April 12 @ 2 pm

**
Jessica Green**

**
Testing for Self-Similarity in a Northern Californian Serpentine Grassland**

In earlier work, we showed that the power-law species-area relationship (SAR) and range-area relationship (RAR) imply self-similarity in the spatial distribution of species at the community and individual species level, respectively. We also showed that predictions for a host of other fundamental ecological characteristics can be derived from the self-similarity property. Derived community-level characteristics include an endemics-area relationship, an abundance distribution and a commonality formula that describes the fraction of species in common to two patches as a function of patch size and inter-patch distance. Derived species-level characteristics include a power-law relationship between the abundance of a species and its geographic range size, an abundance distribution and a relative neighborhood density function that characterizes the spatial aggregation of individuals. To test theory we censused plants on serpentine substrate, recording the total abundance of every plant species within one 64 m2 plot gridded into 256 0.25 m2 squares. There were a total of 24 species and 37,182 individuals. The species-area relationship is well fit by a power-law, indicating self-similarity at community level. The observed individual species abundance distributions and total abundance of each species are consistent with theory, as are the predicted slopes of plots of log(range size) versus log(abundance). On the other hand, the endemics-area relationship, the community-level abundance distribution, and the commonality formula did not agree with the data. Possible causes of these divergences from theory are discussed.

Tuesday, April 3 @ 2 pm

**
Lee Worden**

**
HIV quasispecies dynamics and treatment**

The distribution of variant strains of HIV
in the body is probably very important to understanding the long-term behavior
of the disease and its response to drugs that target particular strains.
I will describe a model of the virus-immune system interaction that explicitly
describes the distribution of variants (that is, a quasispecies model) and
look at the

effect of model assumptions on the ability
of the disease to evade treatment. In particular, immunologists have
observed that the wild type virus can be significantly depressed by current
treatments, but that an escape can occur in which several mutations accumulate,
each of which is significantly detrimental, but which produce a fit and
drug-resistant strain when combined (that is, the population crosses a
valley several mutations wide in the fitness landscape). I hope to
describe the analogous behavior in the quasispecies model. This work
is done with Alan Perelson and others at Los Alamos lab and the Santa Fe
Institute.

Tuesday, March 27 @ 2 pm

**
Eduardo Zea**

**
A (kind of) mechanistic model of stomatal control**

Semi-empirical models of stomatal conductance (gs) are usually used to relate gs with assimilation rate, vapor pressure deficit, atmospheric CO2 partial pressure, and soil moisture. I propose a model for the response of stomata to these factors that is based on the mechanisms of: (1)diffusion across stomata, (3)photosynthesis, and (3)plant water transport. The advantage of the model over previous ones is that all the parameters have an explicit physical meaning, potentially allowing independent estimation and model validation using gas exchange measurements. The main assumption is that stomatal conductance has two regimes of behavior, depending on the water supply-demand relation. In one regime, supply is abudant and gs is controlled only by photosynthesis. When supply cannot meet demand, stomatal conductance adjusts so that demand is equal to the maximum possible supply given soil moisture. I will descibe the model, show some simulations, and throw out some ideas about plant strategies defined in terms of the model parameters.

Tuesday, March 13 @ 2 pm

**
Ricardo Holdo**

**
Elephants, fire, and woodland structure**

Trees in many Southern African savanna ecosystems endure high levels of disturbance – fire, frost, elephants – and stress e.g., drought. Several attempts have been made to model the dynamics of these savannas under various disturbance regimes, but so far in all of the models I have encountered the response of trees to disturbance depends solely on tree size, and not on any other state variables. I believe (and may be able to show…) that this type of approach may be inadequate to explain the apparent stability of what could be called the coppice phase (made up of stunted shrubs with a rather weird architecture) in these woodland savannas.

I would like to argue that the response (survivorship and subsequent growth) of plants to damage varies with the frequency, extent, and timing (in terms of phenology) of disturbance i.e., the history of disturbance is important. My research proposes to test the hypothesis that the carbon balance of trees needs to be taken into account when assessing the impact of a given disturbance regime. I am in the process of developing a (still crude) mechanistic model of woodland savanna structure as a function of elephant and fire disturbance, and with any luck, will be able to show some preliminary results from this model on Tuesday.

Tuesday, March 6 @ 2 pm

**
Helene Muller-Landau**

**
Theoretical explorations of the effects of localized specialist pests on
plant communities**

At least since Gillett's 1962 paper, many ecologists have recognized the potential for species-specific pests to contribute to the maintenance of species diversity. Numerous empirical studies, especially in tropical forests, have demonstrated that many pests act in a locally density-dependent way. Yet relatively little theoretical work has explored the implications of local density-dependence, leaving many scientists holding incorrect ideas (e.g., the notion that if such effects are operating, recruitment must peak some distance away from adults and adult trees must be regularly spaced) and debating fruitless points (e.g., does the effect work by keeping common species from becoming more common or by keeping rare species from going extinct).

Through simple simulations and analytical work, Fred Adler and I investigate the consequences of localized specialist natural enemies for plant populations and communities. Specifically, we ask how the dispersal distances of seeds and pests affect rates and patterns of increase of new species, adult spatial patterns, and the maintenance of species diversity. I will present our models and preliminary results.

Tuesday, February 27 @ 2 pm

**
Josh Plotkin**

**
The stability of genomes in populations: applications to cancer biology**

I will dare to discuss some unfinished research I've been conducting along with David Krakauer -- and with Jonathan Dushoff's continual support -- into the stability of genomic sequences in a population at mutation-selection equilibrium. In particular, I will mention several biological mechanisms of mutational buffering and mutational sensitivity, and demonstrate that the former is expected in small-populations, and the latter in large populations. Complex multicellular organisms tend to live in relatively small populations, though the cells of which they are comprised experience huge populations sizes. For such organisms, the interplay of mutational sensitivity and buffering operates on two levels of selection: sensitivity at the cellular level promotes stability at the tissue and organism level. I will model this situation -- the stabilizing effect of apoptosis -- in some detail, providing analytic results on the waiting time until tumorgensis, given the apoptotic profile of a cell.

Tuesday, February 20 @ 2 pm

**
Masakazu Shimada**

**
Individual-based modeling for high prevalence of multiple Wolbachia infections
in the azuki bean beetle**

Wolbachia is an endosymbiont bacteria and
is widely seen in many arthropods. Wolbachia can operate its host's reproduction
(male-killing, feminization, cytoplasmic incompatibility, etc.) and spread
in the host population, so it is called a selfish genetic element.
However, double coinfections with different Wolbachia strains have been
reported only in several nsects, and triple infections are far rarer.
Considering advantages of multiple infections, it is rather paradoxical
why multiple coinfections with Wolbachia are so rare in nature?

To understand factors
involved in maintenance of multiple infections in a host population, experimental
studies using a model organism with multiple Wolbachia infections are necessary.
Our group has recently found nearly perfect infections with Wolbachia in
the azuki been beetle, Callosobruchus chinensis (Kondo et al. 1999), and
it was very high prevalence (>90%) of the triple coinfection (Ori, Con,
and Aus strains). The triple infection in C. chinensis will be an ideal
research subject for this purpose because the insect has been widely used
in population dynamics experiments for a long time.

An individual-based
model was constructed for examining population dynamics of multiple Wolbachia
infections in C. chinensis. An individual C. chinensis female mates
the male, and CI occurred if the female did not have a Wolbachia strain
the male partner had. Parametric values were determined from our
experiment. In a randomly mating population, the triple infection
class can spread in almost all the population if the fitness cost with
infections is lower than a threshold value. However, the triple infection
class can hardly invade into a large, randomly mating population where
the double infection class has already prevailed. As a factor to promote
the invasion of the triple infection class, the second model included a
meta-population structure and extinction-recolonization processes in local
subpopulations, which agree with actual life histories of C. chinensis.
The second model predicted that the local extinction-recolonization processes
could promote prevalence of the triple infection status with a founder
effect.

Tuesday, February 13 @ 2pm

**
Jia Li**

**
Mathematical modeling of multiple viral strains and their mutations**

In this talk, using influenza as a paradigm, we present some basic mathematical models for epidemics where multiple viral strains or their genetic mutations are a big concern. Fundamental questions such as the threshold conditions (reproductive number), boundary equilibria, endemic equilibria, and the stability of these equilibria will be discussed.

Wednesday, February 7 @ 2 pm

**
Juan Keymer & Bernardo R. Broitman (UCSB)**

**
SPACE UTILIZATION STRATEGIES AND PRODUCTIVITY:**

**
REGIONAL PATTERNS OF FUNCTIONAL
ABUNDANCE---**

**
A THEORETICAL SPECULATION**

In Short: I will be trying (if the super smart and intelligent audience let me) to talk about the ideas my friend Bernardo and I came with to try to explain patterns of abundance of sessile creatures along the coast of Chile while meditating in Santa Barbara and Tijuana.

Abstract

By adopting a functional group approach we characterize regional patterns of community structure as the abundance of space occupiers-- macroalgae and bentihc filter-feeders -- in asociation with an index of ecosystem functioning-- fotosintetic pigment concentration i.e. Productivity. Functional identity follows differences in energy acquisition-utilization pathways, which we define as life- history trade-offs in competitive ability (Tilman 1994). Using a smooth (sensu, Adler 2000) competitive hierarchy we link the index of ecosystem performance -, to demographic process---clearence and recruitment---, assuming the existance of whole group-average competitive and dispersal behaviour. Our model is intended to build a mechanistic explanation for patterns of strong biophysical coupling between benthic and pelagic ecosystems. As such, it explicitly forces the dynamics of benthic community structure to the performance of the pelagic community integrated into the index. We studied the regional variation in functional structure of rocky intertidal communities across regional gradients of primary productivity in the coast of central Chile, and compared them to model predicitons of total space occupancy and space partitioning among funtional groups. Our main theoretical result predicts the existance of productivity thresholds at which the long term functional composition of the community will exchange stability among diffent functional structure states. Community structure surveys show the existance of a sharp transition in functional structure coherent with an abrupt change in productivity. Our results provide a mechanistic basis to the strong dependancy with oceanographical regim that has been experimentally identified in temperate rocky shores. In agreement with our results, different functional groups will partition resources according to a generalized set of life-history trade-offs. Patterns of interaction among functional groups will be influenced by ecosystem linkage processess that have yet to be determined for rocky intertidal communities, but have been characterized elsewhere (Polis et al 2000).

Keywords: Productivity, competitive hierarchy, functional groups, space utilization, space occupancy, metapopulations.

Tuesday, January 30 @ 2 pm

**
Yannis Kevrekidis**

**
Enabling microscopic simulators to perform system-level analysis**

I will discuss a "mathematics-assisted" computational methodology that enhances the scope of existing, state-of-the-art microscopic dynamic simulators, such as Molecular Dynamics, Monte Carlo, or kinetic theory-based methods like Lattice-Boltzmann. Specifically, I will describe a time-stepper-based computational superstructure that can be "wrapped around" existing and future such simulation codes. This methodology will enable advanced, system-level analysis and design methods for complex, nonlinear, distributed processes including materials fabrication, as well as a broad class of transport and chemical reaction phenomena. This framework (for the appropriate type of problem!) exploits the best available dynamic microscopic simulators beyond the direct simulation tasks they currently perform, enabling them to perform system-level stability, operability, bifurcation, parameter sensitivity, design and control tasks. Currently, this type of computation is simply inaccessible to microscopic simulators.

This effort aims at bridging systematically and effectively the enormous gap between the microscopic description of a complex material/transport system and system-level analysis of direct engineering importance. Specifically, this "mathematics-assisted" approach will enable microscopic-level codes to perform system-level tasks directly, without the need to pass through an intermediate or macroscopic-level (conventional) description of the dynamical system through macroscopic (usually partial differential or integro-differential) evolution equations.

This procedure can have general applicability to all systems for which a macroscopic description is conceptually possible but unavailable in closed form; if accurate macroscopic models are available in closed form they should be employed directly. What we propose here is a systematic way to extract from microscopic simulations precisely the computational information one would obtain from macroscopic models, had these models been available in closed form. It is the difficulty in obtaining and closing such models that the proposed approach will circumvent. This will be effected through "technology transfer" from state-of-the-art, time-stepper-based numerical computation of asymptotic dynamics of evolution equations to asymptotic coarse dynamics of microscopic simulators. In a sense, our approach consists of "unavailable model-motivated" processing of microscopic dynamical information.

Tuesday, January 23 @ 2 pm

**
Jerome Chave**

**
The voter model and company**

I won't have time to detail the background on the voter model, so here is a brief update:

The voter model is by far the best-known spatially explicit model. Place one elector per node on a d-dimensional lattice, and assume that, at each time step, this elector takes the opinion of one of his or her neighbors, chosen at random. In its original version, two political opinions were allowed, but the generalization to more opinions is quite straightforward. Notice that this model is different from the "majority vote" model (when the elector polls his or her neighbors, and chooses the most common opinion), and from the well-known "cow skin" model of Henry Horn.

The voter model is so simple because it can be mapped onto a system of coalescing random walks (RW), i.e. RWs that merge upon encounter. Replace the 'political opinions' by 'species' and notice that an individual at site x, at time t, has a unique parent at time t-1, which either was in the immediate neighborhood or at the same position. This ancestor also has a unique parent, and so forth. The path of the ancestors can be seen as a RW, moving backwards in time. Thanks to this duality, probabilists have been able to prove a number of beautiful theorems. A fundamental result, for example, is that one species always take over the system in one and two dimensions (exclusive competition), while a mixture of species coexist in three and more dimensions (Holley and Liggett 1975). It would be tempting to apply this type of model in population genetics and in ecology, and in fact, the stepping stone model of Kimura, as well as Hubbell's neutral model can easily be rephrased in the jargon of the voter model. One only needs to add mutations in the model: a site that has just mutated does not have a 'parent'; a mutation is therefore equivalent to 'killing' a RW of the dual model.

**Summary of
talk**:

1- Voter model without mutation

Recently, we have realized that several two-dimensional
models, which do not possess an obvious dual mapping (and therefore seem
difficult to study analytically) share many common features with the voter
model, for example the number of interfaces decrease as one over the logarithm
of time. Moreover, we have studied a persistence measure that also appears
to be "universal". I will introduce it precisely during the talk. General
conditions for a model to belong to the "voter universality class" will be
stated.

2- Voter model with mutation

In this case there is no coarsening, but a
critical transition is observed, as the mutation rate tends to zero. In other
words, the voter model with no mutation is critical in the sense of phase
transitions. This transition has very simple critical exponents: the correlation
length scales as the mutation rate, raised to the power -1/2. Incidentally,
this contradicts a claim that this transition has non-trivial critical
exponents (de Oliveira, J. Phys. A, 1993).

3- Comparison with other models of diversity

We have compared the voter model to a model
with a competition-mortality tradeoff between the species. I will present
recent simulations of the simplest version of this model (with no space limitation),
which seem to confirm a conjecture by Buttel, Durrett and Levin.

I have also performed preliminary simulations
on a generalization of the voter model where species are labeled from 1
to S, and species i can only interact with species i-1 or i+1 (modulo S-1).
For S=2, this is exactly the voter model. Cox and Griffeath (1989) prove
that a similar one-dimensional model coarsens if S <= 4, and fixates
(as in Horn's cow skin model) if S >4. My runs suggest that in two dimensions,
the model belongs to the voter universality class for S<8, but not for
S>=8.

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