**2.2 Variable input parameters**

#### **2.2.1 Region and founder placement**

In the first series of comparative trials, the square of 169 founders was placed at increasing diagonal distances from the preserve border beginning with the founders at the lower left corner (trial a). Seed and pollen dispersal distances were held constant at 25% to or from each distance frame (see below) in this initial series. In a subsequent series of trials, the constant-sized founder square was likewise moved diagonally toward the center of the preserve while offspring and pollen dispersal distances differed in various combinations (Table 2).

#### **2.2.2 Offspring dispersal distribution**

Offspring dispersal on the grid system is based on a nested series of limiting frames called "distance frames". When an offspring is dispersed to a particular distance frame based on given probabilities, the lower and upper values of each frame define the limits of dispersal. For a given dispersal event, one point within the selected distance frame is chosen at random. The limits of the four frames used in our trials and their varying respective dispersal probabilities across trials are described in Table 2. In the "Basic Conditions" trials, offspring establishment was evenly divided to the four distance frames with 25% probability of dispersal to each frame. Modifications to the "basic" trial conditions to create alternate comparative trials are detailed in Table 2. We use the summary phrase "Offspring less distant" to indicate restricted offspring dispersal (compared to the "Basic Conditions" trials) within 65 m of the parent (13 grid points), whereas in "Offspring least distant" trials, the majority of offspring dispersal was within 30 m (6 grid points) of the parent plant. The summary phrase "Offspring more distant" is used for the trials in which the greatest percentage of offspring were dispersed between distances 110 m to 1500m (22 to 300 grid points) from the parent plant (Nathan *et al.*, 2008; Jansen *et al.*, 2008).

#### **2.2.3 Pollen transport distances**

The "Basic Conditions" and "Offspring less/least/more distant" trials had equal probability of pollen dispersal from within each of the four distance frames (Table 2). Trial E has 90% of pollen dispersal limited to from within a 30 m frame of the producing individual. Trial F has 90% of pollen dispersed from 110 m to 1500 m (22 to 300 grid points) from the parent plant.

#### **2.3 Output**

Based on population characteristics developing from the initial input specifications, NEWGARDEN provides means for four statistical measures reported here: population size, mean number of founding alleles retained, observed heterozygosity, and Fit (or F value) calculated as:

$$\mathbf{F}\_{\rm it} = \mathbf{1} - \mathbf{H}\_{\rm cb} / \, \mathbf{H}\_{\rm ex} \tag{1}$$

where Hob equals observed heterozygosity (based on actual counts of heterozygous loci across all loci for all the individuals in the population) and Hex equals the Hardy-Weinberg expected heterozygosity based on the allele frequencies across all loci in the entire population. In general, Fit increases as inbreeding and/or subdivision increase in the population and Fit = 0 in the absence of inbreeding. For the first series of trials (Figures 1 through 3) mean output values are reported for the total number of individuals in the population at the end of each age. For the second series of trials (Figures 4 through 6), values are given only for the total population after 100 bouts of mating.

#### **3. Results**

Under the "basic" conditions of offspring and pollen dispersal (25% to or from each frame respectively; see Table 2), mean population size increased with increasing diagonal distance of the standard square of 169 founders from the preserve corner (Figure 1). At age 100, founders situated at the corner (trial a) had the lowest mean population size (2,018 individuals), while the equally highest mean population sizes (approximately 7,000) were attained by populations with founders inset by 300, 400 and 500 grid points from the corner (trials d, e, and f, respectively). Even an inset distance of 100 grid points (ca. 500 m; trial b) increased the mean population size by 148%, compared to founders placed at the corner. The percent gain in population increase per unit inset distance declines as the inset distances increases beyond 100 grid points, only increasing by approximately 21% when inset distances increases from 100 to 200 grid points, and approximately 13% when inset distances increase from 200 to 300 grid points. Beyond 300 grid points the rise in mean population size was not statistically different.

less distant" to indicate restricted offspring dispersal (compared to the "Basic Conditions" trials) within 65 m of the parent (13 grid points), whereas in "Offspring least distant" trials, the majority of offspring dispersal was within 30 m (6 grid points) of the parent plant. The summary phrase "Offspring more distant" is used for the trials in which the greatest percentage of offspring were dispersed between distances 110 m to 1500m (22 to 300 grid

The "Basic Conditions" and "Offspring less/least/more distant" trials had equal probability of pollen dispersal from within each of the four distance frames (Table 2). Trial E has 90% of pollen dispersal limited to from within a 30 m frame of the producing individual. Trial F has 90% of pollen dispersed from 110 m to 1500 m (22 to 300 grid

Based on population characteristics developing from the initial input specifications, NEWGARDEN provides means for four statistical measures reported here: population size, mean number of founding alleles retained, observed heterozygosity, and Fit (or F value)

 Fit = 1 – Hob / Hex (1) where Hob equals observed heterozygosity (based on actual counts of heterozygous loci across all loci for all the individuals in the population) and Hex equals the Hardy-Weinberg expected heterozygosity based on the allele frequencies across all loci in the entire population. In general, Fit increases as inbreeding and/or subdivision increase in the population and Fit = 0 in the absence of inbreeding. For the first series of trials (Figures 1 through 3) mean output values are reported for the total number of individuals in the population at the end of each age. For the second series of trials (Figures 4 through 6), values

Under the "basic" conditions of offspring and pollen dispersal (25% to or from each frame respectively; see Table 2), mean population size increased with increasing diagonal distance of the standard square of 169 founders from the preserve corner (Figure 1). At age 100, founders situated at the corner (trial a) had the lowest mean population size (2,018 individuals), while the equally highest mean population sizes (approximately 7,000) were attained by populations with founders inset by 300, 400 and 500 grid points from the corner (trials d, e, and f, respectively). Even an inset distance of 100 grid points (ca. 500 m; trial b) increased the mean population size by 148%, compared to founders placed at the corner. The percent gain in population increase per unit inset distance declines as the inset distances increases beyond 100 grid points, only increasing by approximately 21% when inset distances increases from 100 to 200 grid points, and approximately 13% when inset distances increase from 200 to 300 grid points. Beyond 300 grid points the rise in mean population size

points) from the parent plant (Nathan *et al.*, 2008; Jansen *et al.*, 2008).

are given only for the total population after 100 bouts of mating.

**2.2.3 Pollen transport distances** 

points) from the parent plant.

**2.3 Output** 

calculated as:

**3. Results** 

was not statistically different.


Table 2. Percent offspring and pollen dispersed to or from each distance frame for NEWGARDEN trials described further in the text. Trials were otherwise identical.

Fig. 1. Mean population sizes for each age of American chestnut populations founded at differing diagonal inset distances. These comparative trials span 101 generations at the basic offspring and pollen dispersal conditions (25% to and from each frame respectively). See text for more details.

Figure 2 shows the mean number of founding alleles retained across 101 generations for the trials depicted in Figure 1. In the source population, 3000 alleles each at frequency of 0.01, were available for the founding population. Drawing 169 founders, approximately 2900 alleles were present at founding (97% of the source population alleles; Figure 2). For example, imagine a restoration project where 1,690 trees are planted with 90% attrition prior to reproduction (e.g., Primack & Miao, 1992). On average such a population would have approximately 97% of the alleles in the original source population. NEWGARDEN can be used to estimate founding population sizes needed given the effects of attrition, to provide target numbers of individuals for establishing new populations or supplemention as needed.

For all populations, the number of alleles retained declined through generations, with populations founded at greater inset distances retaining higher numbers of alleles (Figure 2). The 169 founders were all aged 13 at the beginning of the trials, and given the mortality rate of 2% per generation (Table 1), approximately 22 founders should remain in populations after 100 bouts of mating. This suggests that a significant proportion of the total founding alleles remaining in the population at age 100 are carried by the descendents of founders that have died.

After 100 bouts of mating, there was approximately a 6% decline in number of founding alleles retained for populations inset at least 100 grid points or more (trials b, c, d, e and f), compared to the 9.6% decline seen for populations situated at the corner (trial a). At year 100, placing the founders 100 or more grid units inward from the corner produced a 3.8% (at the least; trials b through e) increase in alleles retained compared to placing the founders at the corner (trial a). The differences between various inset distances from 100 to 500 grid points (trials b through f) were not statistically different (although notice the trend). Variations of inset distances under basic dispersal conditions did not have significant or biologically meaningful effects on observed heterozygosity levels (ranging from 0.97 to 0.99) across generations, at basic dispersal conditions (data not shown).

There was little population subdivision and inbreeding observed across generations under basic dispersal conditions as founders were placed at greater inset distances (Figure 3). At year 100, F values increased slightly across generations, with the highest F values (almost 0.02) being reached by founders inset the furthest (by 500 grid points; trial f). F values tended to be lower for decreasing inset distances (e.g., trials a and b) at year 100. Although all trials are increasing in F, only by increasing the number of generations could it be determined the degree to which F values might become important (e.g., approach 0.05) in future generations.

Next, we ran a series of comparative trials varying not only in the inset distance of the square of 169 founders, but also altering the offspring and pollen dispersal conditions relative to the basic conditions (25% to or from each frame respectively) used in the trials just reviewed in Figures 1 through 3. We conducted this next trial series to investigate how differing types of gene dispersal might interact with founder distance from a border to affect population growth and genetic diversity.

Figure 4 shows population growth results (at population age 100 only) from these trials when both inset distances and dispersal conditions were varied. Trends observed here included increasing mean population sizes as inset distances increased from the corner to

Figure 2 shows the mean number of founding alleles retained across 101 generations for the trials depicted in Figure 1. In the source population, 3000 alleles each at frequency of 0.01, were available for the founding population. Drawing 169 founders, approximately 2900 alleles were present at founding (97% of the source population alleles; Figure 2). For example, imagine a restoration project where 1,690 trees are planted with 90% attrition prior to reproduction (e.g., Primack & Miao, 1992). On average such a population would have approximately 97% of the alleles in the original source population. NEWGARDEN can be used to estimate founding population sizes needed given the effects of attrition, to provide target numbers of individuals for establishing new populations or supplemention as

For all populations, the number of alleles retained declined through generations, with populations founded at greater inset distances retaining higher numbers of alleles (Figure 2). The 169 founders were all aged 13 at the beginning of the trials, and given the mortality rate of 2% per generation (Table 1), approximately 22 founders should remain in populations after 100 bouts of mating. This suggests that a significant proportion of the total founding alleles remaining in the population at age 100 are carried by the descendents of

After 100 bouts of mating, there was approximately a 6% decline in number of founding alleles retained for populations inset at least 100 grid points or more (trials b, c, d, e and f), compared to the 9.6% decline seen for populations situated at the corner (trial a). At year 100, placing the founders 100 or more grid units inward from the corner produced a 3.8% (at the least; trials b through e) increase in alleles retained compared to placing the founders at the corner (trial a). The differences between various inset distances from 100 to 500 grid points (trials b through f) were not statistically different (although notice the trend). Variations of inset distances under basic dispersal conditions did not have significant or biologically meaningful effects on observed heterozygosity levels (ranging from 0.97 to 0.99)

There was little population subdivision and inbreeding observed across generations under basic dispersal conditions as founders were placed at greater inset distances (Figure 3). At year 100, F values increased slightly across generations, with the highest F values (almost 0.02) being reached by founders inset the furthest (by 500 grid points; trial f). F values tended to be lower for decreasing inset distances (e.g., trials a and b) at year 100. Although all trials are increasing in F, only by increasing the number of generations could it be determined the degree to which F values might become important (e.g., approach 0.05) in

Next, we ran a series of comparative trials varying not only in the inset distance of the square of 169 founders, but also altering the offspring and pollen dispersal conditions relative to the basic conditions (25% to or from each frame respectively) used in the trials just reviewed in Figures 1 through 3. We conducted this next trial series to investigate how differing types of gene dispersal might interact with founder distance from a border to affect

Figure 4 shows population growth results (at population age 100 only) from these trials when both inset distances and dispersal conditions were varied. Trends observed here included increasing mean population sizes as inset distances increased from the corner to

across generations, at basic dispersal conditions (data not shown).

needed.

founders that have died.

future generations.

population growth and genetic diversity.

Fig. 2. Mean number of founding alleles retained across 101 generations for trial populations differing only in the distance to which founders were inset from a preserve border (population sizes shown in Figure 1). For all of these trials, the "basic" conditions of offspring and pollen dispersal distances were used (25% to or from each frame respectively). See text for more details.

Fig. 3. F values across 101 generations for trials differing only in founder inset distance. These data are from the same trials depicted in Figures 1 and 2. "Basic" offspring and pollen dispersal conditions were used in each trial (25% to or from each frame respectively). See text for more details.

Fig. 4. Mean population size differences for comparative trial populations differing as to both founder inset distances (x-axis) and with greater or lower offspring and/or pollen dispersal distances (indicated by different letters A through F) relative to the "basic" dispersal conditions (see Table 2). Data points depict population size for each trial at age 100 only. In the trial condition summaries to the right of the graph, if a dispersule type (i.e., offspring versus pollen) is not mentioned, that dispersule disperses according to the basic conditions.

500 grid points for population D, up to 400 grid points (E), up to 300 grid points (A), and up to 100 grid points (B, C, and F). For populations B, C and F, increasing founder inset distance to 100 grid points from the corner raised mean population size significantly. However beyond 100 grid points, population sizes remained more or less constant across further increase in inset distances. If actual dispersal patterns match those in trials B, C, or F, a restoration manager will not gain higher rates of population growth by planting founders beyond 100 m into the preserve. Relative to the "basic" dispersal conditions trials just discussed in Figures 1 through 3 (trials marked A in Figure 4), altering offspring and pollen dispersal distances caused various but pronounced differences in rates of population growth. Trial D, with only the offspring dispersing to greater distances, was the only trial that exceeded trial A ("basic" conditions) at founder inset distances greater than 100 grid points. Trial D showed the greatest overall population growth compared to all trials at those inset distances.

For each set of trial conditions (A through F) the greatest allele loss occurred when founders were placed at the preserve corner (Figure 5). More alleles were retained under otherwise

Fig. 4. Mean population size differences for comparative trial populations differing as to both founder inset distances (x-axis) and with greater or lower offspring and/or pollen dispersal distances (indicated by different letters A through F) relative to the "basic" dispersal conditions (see Table 2). Data points depict population size for each trial at age 100 only. In the trial condition summaries to the right of the graph, if a dispersule type (i.e., offspring versus pollen) is not mentioned, that dispersule disperses according to

500 grid points for population D, up to 400 grid points (E), up to 300 grid points (A), and up to 100 grid points (B, C, and F). For populations B, C and F, increasing founder inset distance to 100 grid points from the corner raised mean population size significantly. However beyond 100 grid points, population sizes remained more or less constant across further increase in inset distances. If actual dispersal patterns match those in trials B, C, or F, a restoration manager will not gain higher rates of population growth by planting founders beyond 100 m into the preserve. Relative to the "basic" dispersal conditions trials just discussed in Figures 1 through 3 (trials marked A in Figure 4), altering offspring and pollen dispersal distances caused various but pronounced differences in rates of population growth. Trial D, with only the offspring dispersing to greater distances, was the only trial that exceeded trial A ("basic" conditions) at founder inset distances greater than 100 grid points. Trial D showed the greatest overall population growth compared to all trials at those

For each set of trial conditions (A through F) the greatest allele loss occurred when founders were placed at the preserve corner (Figure 5). More alleles were retained under otherwise

the basic conditions.

inset distances.

constant trial conditions when founders were inset only 100 grid points although even further inset distances caused no further major increases in allele retention for trial conditions A, B, C, and F, while inset distances of 300 grid points were needed to maximize allele retention for trial conditions D and E. Considering all of these trial conditions, the greatest difference in the mean number of founding alleles retained is between trial E at the corner and trial D at 400 grid points (a 10.9% difference).

Fig. 5. Change in mean number of founding alleles retained in NEWGARDEN populations after 100 bouts of mating for trials depicted in Figure 4. Trial conditions differed with regard to both founder inset distance and offspring and pollen dispersal distances as indicated (see summaries for A through F to the right of the graph). Connected data points show alleles retained under one set of trial dispersal conditions when founders were placed at diagonally increasing distances from the preserve corner (x-axis). See text for more details.

Observed heterozygosity values for all trials after 100 mating bouts did not vary by a large amount (ranging from 0.967 to 0.980), showing only a 1.3% difference between the highest and lowest values. At generation 100 there was little population subdivision and inbreeding seen across trials with differing founder inset distances and various dispersal conditions (Figure 6). The highest F values were seen for populations under basic dispersal conditions (trial conditions A), followed by populations with offspring being dispersed less distantly (trial conditions B and C). Populations tended to have slightly greater F values at inset distances beyond 100 grid points, except for trial D, where offspring were more distantly dispersed (80% to the last frame) and trial F, where pollen was more distantly dispersed and offspring least distantly dispersed (80% from the last frame and 90% to the first frame, respectively).

Fig. 6. Changes in F values in populations after 100 bouts of mating (the same populations shown in Figures 4 and 5). Trial conditions differed with regard to both founder inset distance and offspring and pollen dispersal distances as indicated (see summaries for A through F to the right of the graph). Connected data points show F values under one set of trial dispersal conditions when founders were placed at diagonally increasing distances from the preserve corner (x-axis). See text for more details.
