**4.3 Further considerations**

We emphasize that the results reported here were generated with a subset of the potential input conditions including constant input parameter values designed to simulate population development in the only known restoration population of chestnuts, the West Salem stand (Rogstad & Pelikan, 2011). However, conditions at other restoration sites will surely differ (e.g., density of competitors and rates-distances of establishment, age-specific offspring and pollen production, age-specific mortality rates, gene dispersal distances, etc.). Further, other species will often have drastically different conditions from those modeled here (e.g., short lived perennials or annuals, different densities, different gene dispersal patterns). Finally, the ecological niche will vary across species in ways that might affect geometric patterning (e.g., the section of a forest the species naturally inhabits: one species that would typically be found living on the outer regions of a forest would have different life history characteristics than a species that would inhabit the center part of that forest). NEWGARDEN can be used to explore such intra- and interspecific differences in the conditions of population establishment and development.

Previous studies (Rogstad & Pelikan, 2011) have indicated that differences in the geometric placement of founders (e.g., spacing between individuals; arranged in lines versus squares; founder subdivision into a series of smaller squares) can affect rates of population growth and genetic diversity maintenance. When planting a founding population, the simplest pattern is to plant trees in straight lines to make rectangular or square founder areas. In our experiments, the founders were established in a 13 x 13 square of individuals to be easily manipulated for each trial of varying inset distances. This square shape only allowed for one offspring to establish within the founding square between founding parents, which may not allow for higher rates of population growth in the first few years of reproduction if the offspring have limited dispersal. One question not addressed in our trials was whether or not varying geometry of founder establishment patterns (e.g., completely random founder locations, X-shaped lines, various straight lines, circles, or hollow squares) would affect

sacrifice of maximizing population growth, or planting further into a preserve at greater expense. The results here stress the need for accurate knowledge of realized gene dispersal attributes (and of other life history attributes) in any modeling-derived restoration management planning. Lacking such information, restoration managers should preferably take the most conservative approach to restoration using as accurate estimations of life history characteristics as possible, in this case, planting the founders at least 1500 m from a

Natural populations establish with varying numbers of founders (often low numbers), degrees of isolation, and geometry of founding. Interpopulation and interspecific life history variation compound the complexity of establishment events as indicated in trials here. The results above suggest that these factors can interact differentially among newly founded populations, and that even seemingly slight differences in initial conditions (e.g., just 500 m difference in founder placement) may have significant effects on the future trajectories of population growth and genetic diversity measures. NEWGARDEN can be used to explore

We emphasize that the results reported here were generated with a subset of the potential input conditions including constant input parameter values designed to simulate population development in the only known restoration population of chestnuts, the West Salem stand (Rogstad & Pelikan, 2011). However, conditions at other restoration sites will surely differ (e.g., density of competitors and rates-distances of establishment, age-specific offspring and pollen production, age-specific mortality rates, gene dispersal distances, etc.). Further, other species will often have drastically different conditions from those modeled here (e.g., short lived perennials or annuals, different densities, different gene dispersal patterns). Finally, the ecological niche will vary across species in ways that might affect geometric patterning (e.g., the section of a forest the species naturally inhabits: one species that would typically be found living on the outer regions of a forest would have different life history characteristics than a species that would inhabit the center part of that forest). NEWGARDEN can be used to explore such intra- and interspecific differences in the conditions of population

Previous studies (Rogstad & Pelikan, 2011) have indicated that differences in the geometric placement of founders (e.g., spacing between individuals; arranged in lines versus squares; founder subdivision into a series of smaller squares) can affect rates of population growth and genetic diversity maintenance. When planting a founding population, the simplest pattern is to plant trees in straight lines to make rectangular or square founder areas. In our experiments, the founders were established in a 13 x 13 square of individuals to be easily manipulated for each trial of varying inset distances. This square shape only allowed for one offspring to establish within the founding square between founding parents, which may not allow for higher rates of population growth in the first few years of reproduction if the offspring have limited dispersal. One question not addressed in our trials was whether or not varying geometry of founder establishment patterns (e.g., completely random founder locations, X-shaped lines, various straight lines, circles, or hollow squares) would affect

border.

**4.2 Evolutionary implications** 

**4.3 Further considerations** 

establishment and development.

this variation in theoretical and existing situations.

population growth and genetic diversity. Different establishment patterns may allow for a greater number of offspring to land in unoccupied grid points than in the square pattern used in the above trials, and possibly reduce the loss of genetic diversity. It is also possible that the geometric pattern of the founder establishment interacting with the inset distance would affect the overall population growth and maintenance of genetic diversity. Trial comparisons where geometry is varied in combination with distance from edges and dispersal distances are underway.

For the above trials, 169 founders were used based on previous studies (Lawrence *et al*., 1995; Chakraborty, 1993) that suggest a minimum of approximately 172 founders is needed to capture the greatest majority of alleles from the source population while also minimizing reintroduction costs in restoration projects. NEWGARDEN could be used to further investigate what would be the minimal number of founders needed to minimize allele loss over generations under a range of conditions.

Since it is not possible to investigate differences in all input conditions *a priori*, NEWGARDEN modeling can also be used *a posteriori* to generate simulated populations reflecting conditions and population growth outcomes for stands that have already been established. Such simulations can then be used to evaluate the degree to which population growth and genetic diversity preservation could be improved by supplementations or manipulations of actual populations (e.g., planting more individuals, altering gene exchange distances via increased seed distribution, reducing mortality rates at certain life stages, etc.).

If the restoration program includes harvesting offspring to redistribute within the preserve or at new locations, where should the offspring be collected from? Samples could be taken in the immediate area surrounding the entire founding population. However, this might not be optimal due to travel distance into the preserve. It would be better to collect offspring closer to one edge of the preserve, minimizing travel distance. However, perhaps the farther in one direction the offspring are from the founders, the greater the risk of loss of genetic diversity and increased offspring subdivision. One area for further study would be to analyze cohort (not population) growth, heterozygosity and F values, and loss of genetic diversity in subregions that are at varying distances from the founders. This would allow restoration managers to determine how close to an edge they could collect offspring that would still retain the greatest genetic diversity for new plantings. The results of such experiments would also provide information on the erosion of genetic diversity over space and time in entire populations and the degree to which erosion might be localized.
