From: Alan McGowen <alanm@igc.org>
Newsgroups: sci.environment
Date: 12 Apr 92 13:09 PDT
Subject: ECO CENTRAL 10
Nf-ID: #N:cdp:1466601328:000:8537
Nf-From: cdp.UUCP!alanm    Apr 12 13:09:00 1992


ECO CENTRAL 10

                  Extinction and the Four Horsemen

Extinction can be either *deterministic*, when a resource or 
environmental condition essential for life is removed, or 
*stochastic*. Deterministic extinctions are wrought by 
catastrophes large and small: a volcanic eruption, an asteroid 
impact, a clearcut. The occurrence of the catastrophes themselves 
may be stochastic, but the extinctions they produce are 
deterministic. Depriving plants of light for many months will 
kill them, acidifying a lake sufficiently will kill fish, 
depriving a population of monkeys of their forest with a clearcut 
will kill the monkeys. In general, when the environment moves 
outside the range of the tolerances that define a species' niche, 
deterministic extinction occurs. The characteristic time to a 
deterministic extinction by catastrophe is unrelated to 
population size, i.e. a population of size 2N does not  
typically wait far longer than one of size N.

*Stochastic* extinctions, on the other hand, are more probable 
the smaller a population is, and the characteristic time to 
extinction by stochastic processes increases with population 
size. The waiting time for extinction by *demographic 
stochasticity* increases extremely rapidly with N, and only very 
tiny populations are vulnerable to extinction by this means. 
However, tiny populations are quite vulnerable, and the _coupe de 
gras_ of extinction is frequently dealt to a remnant population 
by demographic fluctuations. The time to extinction increases 
more slowly with K for *environmental stochasticity*. Although 
the details are model-dependent, under fairly plausible 
assumptions about the behavior of the environmental fluctuations, 
the time to extinction increases roughly logarithmically with K 
[Leigh]. 

Thus the possibility exists of determining a K for a *Minimum 
Viable Population* (MVP), such that if the population is smaller 
than MVP, extinction is rapid, while if it is greater, the chance 
of extinction is low and the population will be expected to 
persist for a long time. The greater the population is than the 
MVP, the lower the chances of extinction. The problem of 
determining an MVP is called *population vulnerability analysis.*

The Four Horsemen

There are four extinction processes that need to be considered 
when doing a population vulnerability analysis. These "four 
horsemen" are four positive feedback processes that drive 
populations towards extinction. [Gilpin]

The *demographic process* occurs when chance lowerings of N and 
increases in var(r), make the population more vulnerable to 
extinction. It does not matter how the changes in N or var(r) are 
produced, by demographic randomness or environmental fluctuation. 
The point is that when N is decreased and var(r) [or var(K)] 
increased the population is less stable, and more likely to 
experience further fluctuation. The demographic process is 
usually the proximate cause of a stochastic extinction.

The *fragmentation process* operates through the spatial 
distribution of a population. As habitat is fragmented (e.g. by 
many clearcuts, roads, or scattered developments), larger 
populations are carved up into smaller, more isolated ones. The 
smaller populations are at greater risk of extinction by the 
demographic process. As they go extinct, the mean distance 
between the small populations increases, and reestablishment by 
dispersal becomes less likely, i.e. effective fragmentation 
increases, exacerbating the fragmentation process.

The fragmentation process is generally slower than the 
demographic process.

The remaining two "horsemen" operate through genetics.

The *fitness loss process* occurs as a result of *inbreeding 
depression*. In small populations, genetic drift is strong and 
removes population genetic diversity. One result of this is that 
gene loci become *fixed* to single alleles with no other variants 
in the population. Because genetic drift is quite random, the 
fixed loci are as likely to have a deleterious allele as the only 
one remaining as a beneficial one. Also, the entire population is 
now homozygous at the fixed locus, i.e. both copies of the gene 
are the same allele, rather than two different alleles (a 
condition called *heterozygosity*.] Both the fixation of 
deleterious alleles and loss of heterozygosity (which protects 
against the effects of deleterious recessives) take their toll on 
the organism. It becomes less fertile, shorter-lived, less 
resistant to diseases, less good at predation if a predator and 
less good at escaping from predators if a prey. These effects can 
be very large, substantially reducing r, and this reduction of r 
is inbreeding depression. The reduced r leads to a reduced N, 
and a further increase in inbreeding, and further fitness loses.

The fitness loss process is generally slower than the 
fragmentation process. 

The *adaptation loss process* is another result of the loss of 
genetic diversity due to genetic drift in smaller populations. 
The rate of adaptation is proportional to genetic diversity, a 
result known as the fundamental theorem of natural selection, 
first proved by Ronald Fisher. As population genetic diversity 
decreases, so does the ability of the species to track changes in 
the environment (e.g. evolving diseases, climate shifts, changes 
in abundance of different prey species or plants, etc.) This 
leads to a gradual loss of adaptedness to the environment, 
placing the population at a subtle competitive disadvantage, or 
increasing predation pressure on it, and generally reducing its 
absolute fitness (its numbers). This of course leads to still 
stronger genetic drift, more loss of population genetic 
diversity, slower rates of adaptation, and still more loss of 
adaptedness to the environment.

The adaptation loss process is the slowest -- the most insidious 
-- of the four. The only way to protect against adaptation loss 
is for the population to be large enough that loss of alleles to 
genetic drift is balanced by mutation and natural selection. This 
requires a quite healthy population size.

                   *  *  *  *  *  *  *

When there is no extinction crisis in progress, the extinction 
rate is more or less balanced by the speciation rate, or even 
slightly exceeded by the speciation rate, since species diversity 
has increased throughout the Phanerozoic. The conditions for 
speciation to occur are much like those for adaptation to be 
maintained, except more so: i.e. a species which has many locally 
adapted populations and much geographical variation is most 
likely to produce new species. This generally requires an even 
larger total population size than protection against loss of 
adaptation does. 

Of course speciation is also a stochastic process, and there is 
some possibility that a species with small numbers may 
nevertheless speciate: it seems quite clear that new species 
almost always arise from tiny *founder populations*. However, 
most tiny populations succumb to the four horsemen of extinction. 
In order for a few to speciate, many must become extinct. Thus 
the probability of speciation is increased when a species 
constantly produces many such candidate founder populations. This 
is most likely when the species has a very large total K 
throughout a large range, and much local variation of selection 
pressures acting upon it, i.e. a diverse environment throughout a 
large range. 

Thus we can think of a "fifth horseman" operating at an even 
slower rate than the adaptation loss process: a *speciation loss 
process* in which contraction of ranges and reductions of 
environmental diversity lead to decreased opportunities for 
speciation. When the speciation rate is exceeded by the 
extinction rate, as local populations become extinct the 
diversity of local selection pressures decreases and the ranges 
of species shrink, leading to still lower speciation rates. To 
reverse this process would require significant expansions of 
ranges and increases in local environmental diversity (especially 
species diversity) to restore local variation of selection 
pressures. 

Refs 

Gilpin, Michael E and Michael E. Soule, 1986. Minimum viable 
populations: processes of species extinction. In _Conservation 
Biology: The Science of Scarcity and Diversity_, Sinauer, 
Sunderland, Massachusetts. 

Leigh, E.G. 1981. The average lifetime of a population in a 
varying environment. J. Theoretical Biology 90:213-39


-----------
Alan McGowen

Newsgroups: sci.environment