PopEcol Lect 08

Excel spreadsheet for Type I, II, III survivorship curves is in WyoWeb handouts folder.

Demography: what is it?

I will now turn to the compilation and analysis of demographic data -- demography is the analysis of vital rates (population statistics such as birth rates and death rates). The roots of mathematical demography lie in problems related to urban human populations -- insurance, taxation calculations, the study of disease epidemics. One interesting problem here is that processes that occur at the level of the individual (you either live or die, 0 or 1) have emergent properties at the level of populations (the probability of dying, for a five-year-old bull elk, is 0.227 +- 0.83 [meaning that, on average 22.7% of these bulls die, with a standard deviation around that average of plus or minus 8.3%]. I will list several reasons for knowing something about demography, and then turn to analysis of broad patterns of mortality, including the problem of senescence. In this course we will approach demography largely from the angle of matrix projection models. Before introducing matrix models, I will discuss broad patterns of mortality and natality in natural populations.We will look at patterns of mortality and natality, put those together into life tables, and then see how we can use the data in matrix projection models.

Why does demography matter when studying natural populations of animals or plants?

1. Extinction is a demographic process (deaths outweigh births)

2. Allows us to move from simple, disorganized counting to

a) understanding or predicting process and pattern

b) having a firm statistical basis for comparison and decisions [power of the test & accepting null when false: Taylor& Gerrodette, 1993 pointed out that Russ Lande's (1988a) assessment of l = 0.96 for Spotted Owls, Strix occidentalis, had low power and therefore could not be said to differ from 1.0]

3. Some definitions and contrasts

a) projection vs. forecasting. Projection says what would happen if current conditions hold (like the speedometer of car vs. forecasting, which tries to predict what will happen).

b) Ireland vs. Iceland (when not how many). Irish family sizes are more than twice those of Iceland, yet Iceland has a higher growth rate. Why? Because people in Ireland start their families much later. Timing of reproduction as well as quantity makes a huge difference to population dynamics in age-structured populations.

4. Demography vs. genetics (Lande, 1988b) [but see Lynch, 1996 for why quantitative genetics might really matter] :

a) populations collapse first (for demographic reasons) then face inbreeding (genetic) problems.

b) genetic 'treatments' can be applied only to a few showcase, charismatic species.

c) appropriate uses of genetics: not to determine health, but as a tool in surveying diversity, in decision-making about distinctiveness of taxa, and as a way of making demographic inferences.
Is this endangered taxon distinct enough to merit protection (Dusky Seaside Sparrow case)

5. Other approaches to population dynamics (besides the matrix-based projection models that will be our primary emphasis)

a) PVA or population viability analyses (some of which are matrix-based as in Morris and Doak, 2000)
VORTEX/viability/extinction models (Lindenmayer and Lacy, 1995)

b) metapopulation approaches emphasize patchy landscapes and tension between connectedness and isolation (Hanski, 1998, Hastings, 1994; but see Simberloff, 1995)

c) spatially explicit models (Liu et al., 1995; Kareiva and Wennergren, 1995)

d) individual-based models (Judson, 1994)

Any demographic analysis will almost certainly incorporate the two fundamental forces of birth and death. What are the patterns of birth and death in natural populations?

We will start on the topic of survival and mortality by discussing Type I, II and III survivorship curves.

Mortality is rarely random. That is, it almost always has greater impact on certain classes of individuals than others. Examples include high mortality of newborns and elderly compared to prime of life, higher predation on incubating females, higher mortality of displaying male frogs or elk, differential harvest and many other potential factors.

A 1979 epidemic in Florida Scrub-Jays dropped total jays per 40 ha from 13 to 7.5 (a loss of 6.5 jays per 40 ha), but only 2 of the "6.5 lost" were breeders (breeder density went from 8 per 40 ha to 6 per 40 ha). Thus the mortality had relatively less effect on the breeding population than on the "surplus" individuals. This nonrandom mortality will tend to stabilize the population dynamics because the core breeding population varies much less than fringe of older and younger individuals. (Woolfenden and Fitzpatrick, 1984).

Patterns of mortality across different taxa: What types of animals are generally very long-lived for their body size? Birds compared to mammals.

One hypothesis is that longevity is related to metabolic rates. The two graphs given below show why that is unlikely.

Given the comparative metabolic rate data above, what are the observed patterns of longevity? Do they fit the metabolic rate hypothesis?

Nevertheless, everything dies eventually. Why? Two major hypotheses exist to explain the phenomenon of senescence (Williams, 1957):

II. Lack of selection against mutations with late effects. If a mutation arises that has effects late in life selection barely "sees" it, because most of the reproductive span is already over and the fitness cost is low (compared to a mutation with an onset at the peak of the reproductive value curve).

Both of the above hypotheses depend on the decline of reproductive value with age. Why does senescence occur? Thought experiment. Imagine that we have organisms with a potentially infinite life span. In practice, even in the absence of any intrinsic decline in health or vigor with age, accidents and disasters would make the life span finite. As soon as "accidents" happen that change the lifespan from theoretically infinite to actually finite, we will see a reproductive value curve that declines to zero at the end of the life span. As soon as the reproductive value curve declines with age, selection will favor one of the two mechanisms listed above (or both).
[A considerable body of theory applies to this problem of "accidental" death. Much of it was developed for estimating industrial/commercial problems such as the "lifespan" of light bulbs. Much of that theory of breakage and attrition applies to evolutionary demography. The contributions work both ways -- economists and engineers have learned a great deal from evolutionary demographers, and likewise biologists have learned useful mathematical and modeling techniques from economic and industrial models and techniques].

Nevertheless, senescence in birds at least, has been difficult to detect. Why? Senescence and heterogeneity. Let's start with an example of something called Simpson's paradox:

We examine family sizes of French speaking (generally Catholic) Canadians and English-speaking (generally Protestant) Canadians. For Canada as a whole the numbers are:

Now let's break Canada into two compartments -- the two compartments together account for all of Canada. The statistics are: