Lecture notes for ZOO 4400/5400 Population Ecology

Lecture 28 (8-Apr-13) Notes concerning required reading by Turchin et al. 2000.

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Required reading: Turchin et al. lemmings. (on WyoWeb).

Population regulation and population cycles: Turchin's paper links the highly abstract concepts we have studied with the predator-prey Lotka-Volterra models and the graphical extensions that we examined (density-dependence for prey and then predator, efficient vs. inefficient predator).  It shows how the implications of a model provide predictions that allow us to test between alternative hypotheses.  It also shows that how a population is regulated (from above when it acts as a prey species or from below when it acts as a predator) can be crucial to its population dynamics.

Lemming photo
    A collared lemming.  These arctic rodents can go through spectacular explosions and crashes. 
   Turchin et al. (2000) argue that their dynamics are those of a classic predator in an unstable resource-consumer model.
The paper begins by making the following point:
Sharp vs. dull peaks in abundance are a general feature of many different kinds of consumer-resource models
Fig. 28.1
Fig. 28.1.  Theoretical expectation for predator population dynamics over time (dashed, sharply peaked line)
vs. prey population dynamics over time (solid, dull-peaked line).  Turchin et al. argue that this pattern is a general expectation under consumer-resource models.  Now we'd like to see how it fits empirical data for voles and lemmings (Fig. 28.2).
    Predator-prey models are just one of a class of models that describe the interactions between consumers (e.g., herbivores, carnivores, parasites or parasitoids) and their resources (e.g., plants, animals, and hosts).  Turchin begins by pointing out that despite differences in formulation (graphical, continuous)  all the models have a feature in common -- the consumers show sharp peaks in their fluctuating abundance over time.  The resources, in contrast, show dull (rounded) peaks.

The difference between consumer dynamics and resource dynamics provides an opportunity to assess the trophic interactions of small rodents (voles and lemmings) whose fluctuating abundances have intrigued and puzzled naturalists for centuries.  Do these small rodents function as resources (controlled largely from above by their predators), or do they function as consumers (responding to the resources on which they feed)?

Assessment of empirical patterns of abundance in voles and lemmings

    1) Graphical visualization.  Turchin et a. begin by plotting the theoretical expectation for predator and prey abundances over time (Fig. 28.1; their Fig. 1).  That shows dull peaks for prey and sharp peaks for predators.  They then plot observed abundances for lemming over time (Fig. 28.2, a, b, and c their Fig. 2 a, b, and c) and vole abundance over time (Fig. 25.4 d, e, and f; their Fig. 2 d, e, and f).  Clearly, the lemmings have sharper peaks than do the voles.  The peak abundance for the lemmings is almost always at a single point in time with a value considerably higher than the abundance before or after it (sharp peak).  [Note that the population index is on a log scale].  In contrast, the voles tended to have two or even three approximately equivalent values for peak density (dull peak).

Fig. 27.2data

Fig. 28.2. Population indices (estimates of relative population size) over time for lemmings (top three panels, a, b, and c) and voles (bottom three panels, d, e, and f) as a function of time.  Note that the lemming graphs show sharp peaks with a single peak point.  The voles, in contrast, show dull peaks with two or three time periods with almost equally large peak population points.  The lemming data are what one would expect from theory for a predator (see Fig. 28.1).  The vole data are what one would expect for a prey species (see Fig. 28.1).
{X-axis is time, Y-axis is a population index as a stand-in for N}

    2) Skewness.  How can we assess the shape of the fluctuations in a more rigorously quantitative way?  If a distribution has a very few low values and many higher values, it will have negative skew (a tail stretching far to the left).  If the distribution has more evenly distributed values it will show no skewness.  The vole data showed significantly more negative skew than did the lemming data.  The voles spent most of their time near peak densities but occasionally dipped to very low levels.  The lemmings, on the other hand showed much less skew.

Fig 28.3 leftFig. 28.3 right

Fig. 28.3.  Skewed curves.  The red curve (left panel) is left-skewed, also described as negative skew (tail is drawn out to the left).  The blue curve (right panel) is right-skewed, also described as positive skew (the tail is drawn out to the right).  Turchin et al. found that the distribution of population sizes over time for voles was negatively skewed as expected for a prey species (compare the left curve above with the theoretical expectation depicted for prey in Fig. 28.1). The curve for lemmings was more symmetric, as expected for a predator (see the predator curve in Fig. 28.1).
    3) The population growth rate (r) prior to the peak.  If the population grows slowly to peak density (dull peak of a prey species) the r-values just before the peak should be smaller (closer to zero) than those for a predator species that grows rapidly to a very high peak then crashes abruptly.  Turchin et al. found that the pre-peak r for lemmings (approximately 3.0) was significantly greater than the pre-peak r for the voles (approximately 0.5; see Table 1 in their paper).

The conclusion: LEMMINGS ACT AS PREDATORS , driving their prey (moss) to extremely low densities and then crashing -- just the way a predator would in the crash phase of one of the large-amplitude cycles ("big eggs") of Fig. 23.2 or in the efficient-predator scenario of Fig. 24.2.

In contrast, VOLES ACT AS PREY -- they respond to predation from above with fluctuations characterized by dull peaks and a lack of pronounced crashes.  That is, they follow the longer, slower edges of the egg shape in Fig. 23.2.

Why do lemmings rush to the sea?  One of the neatest things about this paper is that it helps explain something that, at first, seems like an entirely unrelated question.  Why do lemmings occasionally engage in what seems like mass suicide?  And why would it happen with lemmings and not with voles?
When the lemming crash occurs, they are literally starving to death and "home" is completely uninhabitable -- all the mosses that they feed on are gone and the mosses take a long time to regenerate (time-lags contribute to instability!).  Their only hope is to go somewhere else -- if they stay home they will die anyway.
In contrast, the voles have a food source (leaves) that can regenerate more quickly AND moving away from home would simply expose them to more predation -- predation is acting as the regulatory force for them.  They have no incentive to leave the way the lemmings do.

References (part of required reading)

Turchin, P., L. Oksanen, P. Ekerholm, T. Oksanen, and H. Henttonen. 2000. Are lemmings prey or predators?
           Nature 405: 562-565.

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