American Journal of Plant Sciences, 2013, 4, 1932-1937
http://dx.doi.org/10.4236/ajps.2013.410238 Published Online October 2013 (http://www.scirp.org/journal/ajps)
Monitoring Endangered Species Populations: Gene
Dispersal Can Have Pronounced Effects on the
Relationship between Census Size and Genetic Diversity
Steven H. Rogstad1*, Stephan Pelikan2
1Department of Biological Sciences, University of Cincinnati, Cincinnati, USA; 2Department of Mathematical Sciences, University
of Cincinnati, Cincinnati, USA.
Email: *steven.rogstad@uc.edu
Received June 21st, 2013; revised July 22nd, 2013; accepted August 15th, 2013
Copyright © 2013 Steven H. Rogstad, Stephan Pelikan. This is an open access article distributed under the Creative Commons At-
tribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is prop-
erly cited.
ABSTRACT
Anthropogenic activities are increasing habitat fragmentation, as well as the number of threatened and endangered spe-
cies. Thus, isolated fragments with natural remnant stands, or in situ or ex situ endangered species rescue populations,
are on the rise. The most common method for assessing the “conservation health” of such populations is to determine or
estimate the census size. However, while it is known that the census size of a population does not always correlate with
its genetic diversity, methods for modeling how different factors can drive variation in the relationship of census size to
genetic diversity in plant populations are needed. Here we use the computer program NEWGARDEN to investigate
how the relationship of stand size versus genetic diversity (measured as both the percent of the founding alleles retained
and FIT) can be extremely variable depending on founder number, founder density, and gene dispersal distances. Popu-
lations of endangered species that appear to have the same conservation health in terms of similar population numbers
may differ greatly in their conservation health as indicated by the genetic diversity they retain. NEWGARDEN can be
used to explore how different founding and intra- or interspecific life history characteristics can affect genetic diversity
relative to census size. If proper historical data exist, NEWGARDEN can also be used to estimate the percent of found-
ing genetic diversity remaining in a given stand.
Keywords: Biodiversity; Fragmented Populations; Plant Population Modeling; Population Genetics; Restoration
Management; Species Conservation
1. Introduction
The protection of endangered plants includes maintaining
viable populations while preserving their genetic diver-
sity. Endangered species commonly exist in small, isolat-
ed, and/or low density populations. In situ and ex situ re-
storation or rescue populations will also often share these
characteristics. Such small populations are especially su-
sceptible to loss of genetic diversity via random genetic
drift and inbreeding. The latter two processes may drive
reduced fitness for individuals and populations due to in-
breeding depression and genostasis (decline of genetic
variability resulting in a loss of potential evolutionary re-
sponses) [1]. Therefore, the monitoring and maintenance
of genetic diversity in populations of endangered species
are highly recommended [2].
One suggested guideline rule for the minimum size of
populations is the so-called “50/500” rule attributed to
Franklin [3] and Soulé [4], according to which a popula-
tion must have an effective size of 50 breeding individu-
als to prevent inbreeding and 500 individuals to prevent
loss of genetic variation via drift. It is well known that
since these numbers refer to ideal effective population
sizes (i.e., Ne), and most populations do not perform as
ideal populations, Nc (the actual census size of a popula-
tion) is usually greater than Ne [2]. Reviewing data from
studies on over 100 animal and plant species, Frankham
[5] estimated that, on average, Nc is approximately ten
times greater than Ne in wild populations. Thus, the Ne
50/500 rule becomes the Nc 500/5000 rule. But other au-
thors have argued that this is both an overestimate [6] or
an underestimate (in some cases by orders of magnitude
[7]) for the size of Nc relative to Ne. For example, it has
*Corresponding author.
Copyright © 2013 SciRes. AJPS
Monitoring Endangered Species Populations: Gene Dispersal Can Have Pronounced Effects
on the Relationship between Census Size and Genetic Diversity
1933
been proposed that the Ne 50/500 numbers are too small,
and that populations with Ne sizes approaching at least
1000 to 5000 are needed in the long term to prevent
“mutational meltdown” stemming from the accumulation
of deleterious mutations in smaller populations (e.g., [8-
10]).
However, many factors contribute to the realized Ne
values and rates of drift for populations through time, in-
cluding variable mating systems, demographics, and gene
dispersal distances. Thus, estimating the Ne, and more im-
portantly for endangered plant conservation considera-
tions, the rates of loss of genetic diversity in natural po-
pulations, are difficult. Census size may be deceptive as
to the genetic diversity retained by a population, but, short
of extensive genetic surveys, how can a manager model
what has occurred in the population to gain an estimate
of current diversity retained?
Adding to the complexity of these considerations, for
many endangered species, obtaining and successfully es-
tablishing 500 or 5000, or even 50, genetically distinct
viable propagules can be a challenge, and restoration me-
thodologies that preserve genetic diversity in such small
populations are needed. But conducting sufficiently rep-
licated field experiments to determine general guidelines
on how best to manipulate newly founded populations to
secure stand maintenance and genetic variation going
forward is cost-prohibitive and not feasible, especially
given the array of life-history characteristics distributed
across the wide range of endangered plant species.
To statistically explore the above issues, we have pro-
duced the computer program NEWGARDEN [11,12],
which generates virtual plant populations that develop
through generations as conditioned by input parameters
concerning available habitat size and shape, the size and
geometric placement of the founding population, and the
life history characteristics of the study species. Future
generations develop via matings and offspring produc-
tion processes emerging from the initial input parameters.
Throughout a user-specified number of generations (bouts
of mating), the program provides statistically analyzable
output for the total population (including all age classes)
concerning population growth and genetic diversity (see
below). In the comparative trials presented here, we use
NEWGARDEN to explore, for an annual plant (lacking a
seed bank), how varying founder number and density,
combined with varying gene dispersal distances, can af-
fect population growth and genetic diversity of popula-
tions. Our results demonstrate that plant populations ini-
tiated with the same number of founders can attain iden-
tical subsequent population sizes that retain genetic di-
versity to widely varying degrees due to differences in
gene dispersal. Replicated plant preservation projects
may appear to have similar population sizes, but such
stands may have very different levels of genetic varia-
tion.
2. Materials and Methods
All trials were analyzed using NEWGARDEN version
2.2 (4apr2012). One set of user-defined input parameters
is called a “trial”. For each trial, the user specifies the
number of “runs”, that is, replicate re-runs of those par-
ticular trial input conditions. With output statistics being
produced and stored for each individual run, the ultimate
summary output (which is what we report below) is pro-
vided in the form of mean values across runs with stan-
dard deviation for each output value. In all of the trials
analyzed here, such summary output values (see below)
represent the mean of 100 replicate runs.
Except as noted below, the following input parameter
conditions were held constant across all trials (parame-
ters are discussed in order that they appear in input files).
Each individual was analyzed at 20 loci, each locus hav-
ing 100 alleles at equal frequencies in the source popula-
tion (frequency = 0.01). Each individual was cosexual.
The expected offspring production per generation per adult
was 1.017, distributed among eligible individuals accord-
ing to the Poisson distribution. All individuals could pro-
duce pollen. The species is an annual. The isolated pre-
serve is 2001 by 2001 grid points in size (carrying capac-
ity, or K = 44,004,001 grid points). Individuals can exist
only on grid points, which are meant to represent the ave-
rage minimum distance between individuals when the lo-
cal population is at K. If the distance between points here
is 1 m, then the preserve is approximately 2 km on a side.
Populations developed over 34 bouts of mating (genera-
tions) unless noted. The source population from which
alleles were drawn for the founders was at Hardy-Wein-
berg equilibrium.
Other conditions varied among trials. Although foun-
ders were always scattered randomly throughout the pre-
serve, comparative trials were initiated with either 1000
(high density) or 300 (low density) founders. For each
density condition, 14 trials were run which differed either
in the maximum distances from which pollen in a given
mating could arrive, or to which offspring were dispersed.
These differences in gene dispersal will be described
where results of comparative trials are discussed below.
To explain an example, in one trial, maximum offspring
dispersal distance might be five grid points with a pollen
dispersal maximum of 250 grid points. This means that
in a given randomly selected mating, offspring can be
dispersed to any point that is within five grid points in
the x or y direction (each axis distance randomly selected
separately), and pollen will come from a randomly se-
lected pollen source that is within 250 x and y grid points
of the selected pistillate individual. Again, x and y dis-
Copyright © 2013 SciRes. AJPS
Monitoring Endangered Species Populations: Gene Dispersal Can Have Pronounced Effects
on the Relationship between Census Size and Genetic Diversity
1934
tances are randomly selected from within that range. In
other words, centered on the selected pistillate plant in a
mating, offspring can be randomly dispersed to one of
the nearest 121 grid points, and pollen can come from a
pollen-producing plant within the nearest 251,001 grid
points. Under these conditions, if an offspring is disper-
sed off the preserve, it “dies” (is removed from further
analyses). If it is dispersed to a point to which other off-
spring are also dispersed, one is chosen to establish there
at random, the others dying. If no pollen donor can be
found within the specified distance range for a particular
mating, the mating fails but is counted as one of the mat-
ing events for a generation.
Output includes mean values for total population size,
number of founding alleles remaining, and FIT [13], a
measure of population inbreeding and differentiation as
explained below. Data points discussed as being different
differ significantly in mean value at the p-value 0.05
criterion. More details regarding the NEWGARDEN pro-
gram are provided elsewhere [11,12].
3. Results
In our first example (Figure 1), populations were initiat-
ed with either 1000 founders (letters in upper case) or
300 founders (lower case letters). Since trials were initi-
ated with different numbers of founders, change in po-
pulation size is expressed as the percent of the original
founders remaining through sequential bouts of mating.
Figure 1. Continuing population size as a percent of the ori-
ginal number of founders through generations for NEW-
GARDEN populations initiated with 1000 founders (letters
in upper case) or 300 founders (lower case) scattered at ran-
dom throughout the preserve. In these trials, maximum off-
spring dispersal is always 5 grid points, while maximum
pollen dispersal distances (in grid points) vary as indicated
in the key to the left of the graph. The letters at the upper
right of the graph denote, in descending order, the trials
clustered at generation 34 to the upper right of the graph.
See text for more details.
In this example, trials have identical conditions, includ-
ing a constant maximum offspring dispersal distance of 5
grid units (distributed to a point chosen at random within
the nearest 121 grid units), while trials with the same
number of founders vary only in that the maximum dis-
tance across which pollen is dispersed from a randomly
chosen eligible staminate individual to a given pistillate
off spring-producing plant differs as indicated in the le-
gend to the left of the graph. While the exact same re-
productive value has been input for all of these trials (r =
1.017), and all populations are declining in size, they de-
cline at different rates depending on the maximum dis-
tance from which pollen can arrive in a given mating.
When pollen dispersal is relatively short as in trials a, A,
b, B, and to some degree, c, the populations decline no-
ticeably more rapidly than for the other trials (grouped as
listed in descending order at the upper right of the graph).
In other words, this graph shows that if a fragmented,
isolated population initiated with 1000 or 300 scattered
individuals experiences relatively limited offspring and
pollen dispersal distances, then populations will decline
more rapidly.
Figure 2 shows that these same trial populations are
more variable as to the degree of genetic diversity loss
Figure 2. Percent of the founding alleles remaining relative
to the size of the continuing population as a percentage of
the original number of founders for the same trials for
which population development data are depicted in Figure
1. These NEWGARDEN populations were initiated with
1000 founders (letters in upper case) or 300 founders (lower
case) scattered at random throughout the preserve. In these
trials, maximum offspring dispersal is always 5 grid points,
while maximum pollen dispersal distances (in grid points)
vary as indicated in the key to the left of the graph. When
populations attain 80% of their founding size, the percent
of the founding alleles remaining ranges from approxima-
tely 100% (e.g. trials A, a, b, and B) to approximately 30%
(e.g., trial g). Percent of the founding alleles remaining de-
picted at 80% founding population size, in vertically de-
scending order, are: A,a,b,B,F,G,E,D,C,c,e,f,d,g. Values in-
terpolated when necessar y.
Copyright © 2013 SciRes. AJPS
Monitoring Endangered Species Populations: Gene Dispersal Can Have Pronounced Effects
on the Relationship between Census Size and Genetic Diversity
1935
when populations have lost equal percentages of indi-
viduals compared to the original founders. For example,
consider all of the trial populations when they have de-
clined to 80% of their founding size. Trials A, a, b, and B
still retain approximately 100% of the founding alleles
when their population size is 80% that of the founders.
For the remaining trials at 80% of their initial founding
size, populations initiated with 1000 founders retain from
approximately 73% (trials C, D, and E) to 77% (trials F
and G), and when founded with 300 individuals, allele
retention is approximately 31.3% (trials d and g) to
41.7% (trial c). These trials also differ markedly in F va-
lues (Figure 3). Consider again trial results when popu-
lations have declined to 80% of their founding size. F
values range from 0.07 (interpolated for trial A), sugges-
ting moderate inbreeding and genetic differentiation
within the population, to 0.54 (trial c) indicating that a
very great degree of inbreeding and genetic differentia-
tion have occurred in the population [13]. All of these
trials have limited offspring dispersal distance (5 grid
points). But higher levels of F are achieved when trials
have maximum pollen dispersal distances ranging from
12 grid points (maximum F value for trial A = 0.82) to
500 grid points (trial e). Maximum pollen dispesal distances
to longer distances reduces F values to < 0.14 (moderate
Figure 3. F values relative to the size of the continuing po-
pulation as a percentage of the original number of founders.
These are the same trials for which population developme nt
data are depicted in Figure 1. These NEWGARDEN popu-
lations were initiated with 1000 founders (letters in upper
case) or 300 founders (lower case) scattered at random
throughout the preserve. In these trials, maximum offspring
dispersal is always 5 grid points, while maximum pollen dis-
persal distances (in grid points) vary as indicated in the key
to the left of the graph. When populations attain 80% of
their founding size, F values range from approximately 0.5
(trials c) to approximately 0.07 (trial A). F values depicted
at 80% founding population size, in vertically descending
order, are: c,B,C,d,D,e,E,f,F,G,g, with interpolated values
of 0.095 for a, 0.08 for b, and 0.07 for A.
inbreeding and subdivision).
In another set of trials, the maximum distance from
which pollen could arrive for a particular mating was fix-
ed at 2005 grid points in all trials, with trials varying
only as to the maximum grid point distance that offspring
could be dispersed (Figures 4 and 5). While all of the
trials considered previously were declining through gen-
erations (Figure 1), in this set of trials, some populations
grew while others declined (Figure 4), even though r
was set constant at 1.017 as before. As in the previous
trials, the percentage of founding alleles remaining varies
considerably across trials relative to the percent of the
founding population remaining through generations
(Figure 5). For example, populations that have declined
to 50% of the founding size may have 17% (trial d) to
100% (trials F and G) of the founding alleles remaining.
To examine these data from a different perspective to in-
clude all trials, when the percentage of founding alleles
remaining in all trial populations is 80%, population size
relative to the initial number of founders ranges from ap-
proximately 125% (trial A) to 14% (trial G). In other
words, when populations retain equal amounts of found-
ing alleles, they can vary considerably in their size rela-
tive to the founding population due to differences in off-
spring dispersal. F values for this second set of trials with
varying offspring dispersal ranged from approximately
0.09 (trials F and f) to 0.135 (trials G and g), suggesting
moderate levels of inbreeding and genetic differentiation
were occurring in all of these populations (data not
Figure 4. Continuing population size as a percent of the
original number of founders remaining through generations
for NEWGARDEN populations initiated with 1000 foun-
ders (letters in upper case) or 300 founders (lower case)
scattered at random throughout the preserve. In these trials,
maximum pollen dispersal is always 2005 grid points (grea-
ter than the length of one side of the preserve), while maxi-
mum offspring dispersal distances (in grid points) vary as
indicated in the key to the left of the graft. See text for more
details.
Copyright © 2013 SciRes. AJPS
Monitoring Endangered Species Populations: Gene Dispersal Can Have Pronounced Effects
on the Relationship between Census Size and Genetic Diversity
1936
Figure 5. Percent of the founding alleles remaining relative
to the size of the continuing population as a percentage of
the original number of founders for the same trials for
which population development data are depicted in Figure
4. These NEWGARDEN populations were initiated with
1000 founders (letters in upper case) or 300 founders (lower
case) scattered at random throughout the preserve. In these
trials, maximum pollen dispersal is always 2005 grid points
(greater than the length of one side of the preserve), while
maximum offspring dispersal distances (in grid points) vary
as indicated in the key to the left of the graft. When the
percent of founding alleles remaining has a value of 80%,
the percentage of stand members remaining relative to the
founding population size ranges from approximately 128%
(trial A) to 13% (trial G).
shown). Relatively long distance gene dispersal via pol-
len in all of these trials appears to prevent the higher F
values seen when offspring and pollen dispersal were
more limited (Figure 3).
4. Discussion
The NEWGARDEN trial examples presented here dem-
onstrate that, all else equal, varying founder number and
initial population density, as well as realized offspring
and pollen dispersal distances, can have pronounced ef-
fects on population size change, retention of alleles, and
degree of inbreeding and subdivision in isolated frag-
ments through generations. In the processes of fragmen-
tation or initiation of endangered species rescue popula-
tions, populations beginning with the same number of
founders can develop along many different population
size change and genetic diversity trajectories, depending
on gene dispersal characteristics. Genetic diversity losses
experienced by an isolated population will set the diver-
sity potential for that population going forward. Popula-
tions differing in gene dispersal characteristics can be re-
duced to the same size but retain differing amounts of the
founding genetic variation such that even if both popula-
tions expand to large equal numbers in the future, they
will likely differ in the amount of genetic variation they
hold. As shown in Figure 3, fragmented populations ini-
tiated with the same number of founders that then decline
to the same size can have large differences in levels of
inbreeding and differentiation due to gene dispersal dif-
ferences, demonstrating the earlier noted principle that
Nc does not equal Ne. Judging the “conservation health”
of a stand is best not estimated based on census number
only.
Increased losses of genetic diversity promote evolu-
tion via drift, reduce the effectiveness of selection and
close potential future avenues of evolution. While in the
examples here we have used loci with alleles at low fre-
quencies, we have found in other NEWGARDEN stu-
dies [11, and in prep.] that increased losses of low fre-
quency alleles translate to greater drift-driven variance in
allele frequencies for more common alleles under the
same trial conditions, with such inflated variance also
promoting the effects of drift over those of selection.
The trial examples presented here are meant to be heu-
ristic, not exhaustive. Our goal is to demonstrate, through
particular examples, that in fragmentation or restoration
situations, especially where founders are limited, it is
crucial to explore how realized gene dispersal distances
can affect future outcomes for the population. The crea-
tion of fragments or rescue populations will often alter
gene dispersal distances from those commonly experi-
enced by a species under consideration in more natural
circumstances. The trials examined here emphasize that
obtaining accurate data on gene dispersal for targeted en-
dangered rescue species can improve modeling to deter-
mine best restoration practices. NEWGARDEN analyses
can be used to examine how varying preserve size or
shape, founder number and genetic diversity, life history
characteristics such as age dependent mortality and re-
production, and gene dispersal distances, can interact to
affect population size and genetic diversity change. As
shown above, previous trends in allele loss for currently
similar size populations are not always obvious. NEW-
GARDEN can thus also be used to attempt to model the
suspected conditions under which a population has de-
veloped to estimate current levels of genetic diversity.
Such analyses might suggest beneficial population mani-
pulations such as supplementing the population with
more individuals, or with individuals from different ge-
netic backgrounds, or altering local densities, promoting
or limiting offspring dispersal, or altering pollen flow
(e.g., hand pollinations or altering local pollination vec-
tor conditions). While we understand that a multitude of
deterministic and stochastic factors beyond those mod-
eled by NEWGARDEN can also impact the development
of populations rendering precisely accurate simulations
more difficult, we hope that NEWGARDEN analyses
can contribute to developing first estimates of best prac-
Copyright © 2013 SciRes. AJPS
Monitoring Endangered Species Populations: Gene Dispersal Can Have Pronounced Effects
on the Relationship between Census Size and Genetic Diversity
Copyright © 2013 SciRes. AJPS
1937
tices in planning endangered species protection and res-
toration projects. The NEWGARDEN program and asso-
ciated materials are available for free at
http://math.uc.edu/~pelikan/NEWGARDEN.
5. Acknowledgements
Both authors contributed equally to this work. We thank
A. Buck, C. Daley, S. Heywood, Y. Kashimshetty, M.
Simkins, and the Department of Mathematical Sciences
and the Department of Biological Sciences at the Univer-
sity of Cincinnati. We thank the Charles Phelps Taft Re-
search Center and the Ohio Plant Biotechnology Consor-
tium for partial funding.
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