Lecture notes for ZOO 4400/5400 Population Ecology

Lecture 27 (8-Apr-13) Population regulation -- density-dependence vs. density-independence

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We now turn to something that has been an implied theme throughout -- population regulation. We began the course with the exponential model for unchecked growth in the absence of any other forces, but then very quickly added one regulating force -- the density-dependent "crowding effect" of the logistic growth model. Let's develop a list of a number of factors that can help keep populations in check (regulate their numbers) and then adapt the model we used for harvest to look at the interplay between two major kinds of potential regulating factors -- density-dependent factors and density independent factors.

What are some potential regulating mechanisms?

Density-independent factors (possibly more influential in insect dynamics?  Likely to be more important for species that can grow so quickly they do not function very well as self-regulators):
             Weather (storms, cold, drought)
             Density-independent diseases (probability of occurrence does not change with density; human example = cancer)
Density-dependent (possibly more influential in vertebrate dynamics?):
             Space (territories, denning sites, nest cavities)
             Density-dependent epizootics (disease epidemics;
                         transmission/infection likelihood changes with population density -- human example = measles, SARS)
How do we figure out which factor matter? Experiments may be useful. Often factors overlap, so that it is hard to tell whether a factor is really regulatory. Consider the concept of compensatory vs. additive mortality. Applied managers will usually consider hunting harvest to be largely compensatory ("animals would have died anyway"); basic (meaning studying a problem for its own sake, as opposed to applied) biologists will often consider any source of mortality they measure as being additive.

Fig. 27.1

Fig. 27.1. Distinction between additive and compensatory mortality. If a given mortality factor (Factor X, such as harvest, poisoning or predation) causes an immediate reduction in total survival, it is considered an additive mortality factor. A compensatory factor, in contrast, causes no reduction in total survival (until it reaches some threshold value,  C*). Along the horizontal portion of the compensatory mortality line, animals dying from the compensatory factor would have died anyway of some other cause. Consider the implications of compensatory mortality. In a harvest management context, compensatory mortality may be a "good thing" -- we can harvest a reasonable proportion of the population without increasing total mortality (anywhere up to the C* "threshold" point in Fig. 27.1). In a pest management program, however, it will be disheartening if high levels of mortality achieved with great effort and expense are all simply compensatory. The same may be true of some "predator control" programs for species such as coyotes that have fairly high potential reproductive rates. Compensatory mortality can make it difficult to discern the factor that truly regulates a population. A compensatory factor may be sufficient to regulate a population but it may not be necessary (some other factor could, and will, take its place). Look back at notes for Lecture 3, to brush up on necessary vs. sufficient conditions.

Two arguments against density-independence (after A. J. Nicholson. 1933, Australian biologist famous for his work on lab. populations of blowflies):

Analogy to ocean: Nicholson argued that the size of a population is analogous to the depth of ocean. The effects of weather on populations would be analogous to the effects on the surface level of the ocean by wind and tide -- the surface change may be driven by wind or tide, but one would never attribute the cause of total ocean depth variation to wind or tide -- likewise, other factors largely control population size.
Destructive force vs. real control: even if weather has huge effect on population size, it may not be the controlling factor. Imagine a population of insects with a potential l of 100 (100-fold potential increase per season -- or 100 females per mother if we return to the concept of female demographic dominance). Weather destroys 98% of the individuals each season. That still allows the population to double each season -- universe fills up. Now add a predator that responds in a density-dependent manner to remove the "surplus" (1%) from the remainder of the population. That predator (with its density-dependent response) is the controlling factor, even though numerically it destroys only a small fraction of the population.

One of the themes we have dealt with repeatedly recently is the stability of systems. Below, I combine the concepts of
       density-dependence (largely based on biotic interactions with internal feedbacks),
       density-independence (largely due to environmental stochasticity, particularly in weather)
       and the stability or instability of systems.

Fig. 27.2

Fig. 27.2. A diagram to illustrate some potential interactions between density-dependence and density-independence (above or below on the Y-axis) and stability or instability (on the X-axis). The boxes list a few potential mechanisms (the "hows") and kinds of organisms (the "whos") that might fall in each of the category combinations. "Resetting the clock" means that just as a high-l species is about to explode or irrupt, its numbers are set back by some environmental or abiotic factor (such as cold or drought). Many arctic or temperate invertebrate populations may have these sorts of dynamics -- high growth potential that is checked by the end of the growing season.

Of course, many natural populations will occur in intermediate locations in the state space of the graph above, or they will periodically experience effects that differ from the norm (e.g., relatively brief non-equilibrium "crashes" following an unusually severe winter or reaction to the invasion of a new and destabilizing competitor or predator). Further, many natural populations (and the factors that affect them) will be " density vague" meaning that the scatter of points around the relationship between any particular factor and population size will be high enough that it will be difficult to demonstrate unequivocal cause-and-effect relationships. Nevertheless, knowing the range of possible outcomes from the range of simple (at least compared to the complexity of the natural world) models can help us to narrow the choices and think critically about the most likely factors in the wide range of contexts that face any biologist or manager.


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