Thursday, April 10, 2014

Based on the insight from Lev Ginzburg

A simple ratio-dependent explanation of logistic growth...with R of course.

Evolution and ecosystem dynamics: Implementing a simple example from Ellner et al. 2011, Ecology Letters,

An example of measuring the relative importance of evolutionary and ecological dynamics.

Vitousek et al. 1998. Insights from a simple nitrogen budget model

An implementation of a simple nitrogen budget model:

from Vitousek, P. M., Hedin, L. O., Matson, P. A., Fownes, J. H., & Neff, J. (1998). Within-system element cycles, input-output budgets, and nutrient limitation. In M. L. Pace & P. M. Groffman (Eds.), Success, Limitations, And Frontiers Of Ecosystem Science (pp. 432–451). Springer, New York.

Monday, March 25, 2013

The Physiology/Life-history Nexus: life history a la Ricklefs and Wikelski (2002)

Ricklefs and Wikelski (2002) present a conceptual model linking genotypes, phenotypes, performance, and demography to evolutionary responses in the context of the environment.

It is a little mushy because they define life-history in as a set of ... physiological adaptations, and then argue that "physiology mediates the relationship between life-history and the environment" (R&W p. 463).

Demography refers to traits of populations, where the state variable is typically population size, N, and we may characterized rates of change of N due to birth rates, death rates and migration. In contrast, life history refers to traits of individuals, especially individual probabilities of survival and death, lifespan, and the sizes and number of offspring in one bout of reproduction and over an organism's lifetime.

I think they take it for granted that their readers know that life history refers literally to the history of "significant" events in the life of an average individual of a population, focused exclusively on those events, such as clutch size or lifespan, that govern population demographic rates. For instance, different life history stages refer to elements of a life cycle are relatively recognizably distinct, and which might be characterized by different probabilities of death or survival, birth, or different average fecundities. Thus distinct life history stages are characterized by individuals having different properties. The study of life histories includes the study of traits of individuals related directly to survival and reproduction. The traits of interest most commonly include:
  • lifespan and senescence;
  • age at maturity;
  • metamorphosis between stages;
  • age-specific or stage-specific probabilities of survival or death;
  • number of seeds, eggs, or offspring per bout of reproduction (e.g., mast event, clutch, or litter);
  • semelparity vs. iteroparity
  • average size of individual seeds, eggs, or offspring;
  • lifetime reproductive success. 
  • body size.
Life history strategies are set of these traits that seem to us to optimize fitness in a particular context. For instance, r-selection is a life history strategy characterized by early onset of reproduction and large numbers of offspring and which often maximizes fitness in highly unpredictable environments. This strategy can maximize fitness when adult survival (and therefore future reproduction) is unpredictable. At the other end of the r vs. K-selection continuum, K-selected species are characterized by delayed onset of reproduction, and multiple bouts of reproduction (iteroparity). The K-selected strategy tends to maximize fitness in predictable environments. These two life history strategies seem to represent to ends of a continuum in which many of the above life history traits seem to covary.

The study of life histories focuses on the proximate (e.g., phsyiological) and ultimate (evolutionary) causes of variation and covariation in the above traits.

Non-sequitor: Why do we have the impression that aggregate properties (ecosystem variables, diversity, N) exhibit patterns and are suitable objects of study? (I ask this, I think, because of Ricklefs' focus on individuals and species).

The five principles of Ricklefs and Wikelski (2002):
  1. individuals respond to variation in their environments.
  2. responses are constrained by the allocation of limited resources among competing functions, 
  3. individual organisms assume alternative physiological states at different stages in their life cycles because these states are incompatible.
  4. individuals might also assume different states as phenotypic responses to the environment,
  5. the assumption of one or another state can be modulated by demography, especially reproductive value (future reproductive potential).
Specific points
  •  It seems to me that their primary point is that we need to study physiology in order to understand life history.  
  • I could not determine whether they were implying that the environment caused covariation in life history traits, or the covariation was due primarily to physical constraints on different components of organisms' physiologies.
  • Figures I and II in Box 1 seems orthogonal or perpendicular to life history traits. That is, we might imagine that a particular life history strategy such as r-selected traits occupies the phenotype box but different points on the r-K continuum lie perpendicular to the figure, extending out of and into the page.
  • I thought it was odd that they chose to not mention tradeoffs that might arise through "simple" laws of conservation of matter and energy.

Thursday, March 7, 2013

Organisms are built in four dimensions

Here is, I think, one observation, expressed in various and complementary ways:
  • All species exhibit an average relative fitness, w, of approximately $w = 1$.
  • On average, all organisms leave approximately one descendent.
  • Over its lifetime, an organism does the work (joules) required to leave approximately one descendent.
  • Over its lifetime, an organism must do the work required to build another organism of the same size. 
  • A be the total amount of work required to produce a descendent.
  • R be the rate of that work, and
  • T be the time over which the work is done, then
RT = A

My "observation" above implies that A depends strongly on body size: It takes longer to build a large organism.

A 3-D organism has to propagate itself through time, at a velocity sufficient to maintain and replicate itself. The 4-D integral of that mass-time event is directly proportional to the mass of the organism. The rate or velocity measured at any instant in time, $t$, will be a 3-D slice of the 4-D mass-time event. As the event is proportional to the size (mass or volume) of the organism, the 3-D slice will scale to the 3/4 power of the 4-D event or size of the organism.

Sunday, November 11, 2012

Thinking like an ecologist

Here is some advice for budding young ecologists--useful or not useful?

Monday, September 3, 2012

A blueprint for ecology

Scheiner (and Willig's) general theory of ecology
 Scheiner 2012, QRB; Scheiner and Willig 2011 monograph


The spatial and temporal patterns of the distribution and abundance or organisms, including causes and consequences.


  1. Organisms are distributed unevenly in space and time.
  2. Organisms interact with their abiotic and biotic environments.
  3. Variation in the characteristics of organisms results in heterogeneity of ecological patterns and processes.
  4. The distributions of organisms and their interactions depend on contingencies.
  5. Environmental conditions are heterogeneous in space and time.
  6. Resources are finite and heterogeneous in space and time.
  7. Birth rates and death rates are a consequence of interactions with the abiotic and biotic environment.
  8. The ecological properties of species are the result of evolution. 


Stevens' general theory of ecology


Life: its constituent entities, causes, and consequences.


  1. All entities are systems, with some internal complexity.
  2. All entities change.
  3. Some entities may have inputs and outputs.
  4. All rates of change, including inputs and outputs, are influenced directly by physical factors.
  5. Some entities interact.
  6. All observers must choose specific temporal and spatial scales at which to make observations.