This study explores Minimium Dynamic Reserves or the minimum area required to buffer against natural disturbance and maintain ecological processes. This work informs the size criterion of ecological benchmarks.
Pickett and Thompson (1978) defined a minimum dynamic area (MDA) as
"the smallest area with a natural disturbance regime, which maintains internal recolonization sources, and hence minimizes extinction".
While the MDA concept posits general design principles for selfsufficient reserves, no explicit or quantitative criteria on how to construct a MDA have been established, although dynamic simulation models (Peters et al. 1997) and temporal reconstruction of patch mosaics using forest history data (Baker 1989) have been proposed. By relaxing the restrictive conditions of the MDA and making criteria more explicit, it may be possible to identify practical approaches for the design of large reserves to incorporate natural disturbance and maintain ecological processes. We refine the MDA concept in an effort to provide a method to account for system dynamics in reserve design. To avoid confusion with Pickett and Thompson's (1978) original formulation of the MDA, we refer to our refinement as a minimum dynamic reserve (MDR).

A minimum dynamic reserve is the minimum reserve area required to incorporate natural disturbance and maintain ecological processes (Leroux et al. 2007).


How to Identify a Minimum Dynamic Reserve
There are three steps to identifying a MDR:
1) Estimate the minimum size of a MDR based on the estimated maximum disturbance event,
2) Identify the realized size and location of a candidate MDR in light of the composition and configuration of species' communities on a landscape, and
3) Evaluate if a candidate MDR maintains its recolonization sources through time under natural disturbance. CONSERV was designed to accomplish these three steps.
1) Estimating the minimum size of a MDR
We must first estimate the minimum size (M) of a MDR as a starting point for simulation experiments to identify the realized size and location of an MDR. M is given by:
where y_{i} are the relative proportional areas of the n communities defined as:
where x is the estimated maximum extent of the largest disturbance event, a_{i} is the area occupied by the ith community,and a_{max} is the area occupied by the community with the largest total area. When i = 1, M = x, therefore, the minimum size of a MDR will always be greater or equal to the estimated maximum extent of the largest disturbance event.
The critical quantity needed to calculate M is x, which can be estimated using parametric statistical models of the empirical natural disturbance size distribution (e.g., Cumming 2001). The observed values of y_{i} depend on the state of the system at the time of observation. Stateindependent estimates of y_{i} and M can be obtained by Monte Carlo simulations using landscape models to estimate a mean a_{i} and a_{max} through time. M is a critical parameter that must be estimated in order to run CONSERV's MDR builder (Fig 1).

Fig 1.CONSERV’s MDR builder. The user must specify the minimum size of the MDR (M) and the proportional area of each community type to be included in the MDR (y_{i}). 
2) Identifying the realized size and location of a candidate MDR
M is the minimum size of a MDR but it is unlikely that the composition of communities on the landscape is such that a random MDR of size M will satisfy the minimum area requirements for all communities. Consequently, the user must identify the size and location of a realized, or candidate MDR, given the configuration of communities on the landscape. The realized size is the smallest area ≥ M that satisfies the minimum area requirements over time, and depends on the spatial distribution of communities in the region, and transition of these groups over time or after disturbance. The MDR builder algorithm in CONSERV (Fig 1) estimates the realized size and location of a candidate MDR as follows:
i) Partition the region into base units, U_{i}, of size at least M. U_{i }can become larger than M (see Step iii). Overlapping U_{i} may characterize the landscape more completely.
ii) Determine which U_{i} satisfy all the minimum requirements of y_{i}.
iii) If U_{1} does not meet the minimum requirements of y_{i}, iteratively increase the size of U_{i }and calculate the area of each community for each U_{i} with minimum requirements of y_{i}, until a candidate MDR is found.
If a landscape does not have a U_{i} that meets the minimum requirements, it does not have a candidate MDR. If multiple candidate MDRs are found, the candidates can be ranked using additional ecological criteria, such as a diversity index. For a candidate MDR to be successful in maintaining internal recolonization sources, the extent of a_{i} and a_{max} ≥ δ_{i} at all times, where δ_{i} is the minimum area of community i required to maintain internal recolonization sources. Alternative approaches could apply population (Boyce 1992) or community (Ebenman and Jonsson 2005) viability analysis to determine the threshold number of individuals required to maintain longterm persistence.
3) Evaluating if a candidate MDR maintains its recolonization sources through time
To test if a candidate MDR maintains a_{i} and a_{max} ≥ 1 at all times, Monte Carlo CONSERV simulations of the disturbance dynamics can be used to calculate the amount of a_{i} and a_{max} in the candidate MDR through time. If at any point during the simulation a_{i} or a_{max} < 1 in the candidate MDR, the MDR is deemed to be ineffective with respect to maintaining potential recolonization sources. In this case, the process is reiterated with larger U_{i}s until a candidate MDR is found that satisfies a_{i} and a_{max} ≥ 1 at all times, or the maximum size is reached based on the bounds of the study region.
The primary reference for Minimum Dynamic Reserves is:
Leroux, S.J., F.K.A. Schmiegelow, R.B. Lessard, and S.G. Cumming. 2007. Minimum dynamic reserves: A framework for determining reserve size in ecosystems structured by large disturbances. Biological Conservation 138:464473. (email info[at]beaconsproject.ca)for PDF)
For additional details on Minimum Dynamic Reserves see:
Anderson, L.G.G. 2009. Quantitative methods for identifying ecological benchmarks in Canada’s Boreal forest. M.Sc. thesis, University of Alberta, Edmonton, AB. 111pp. (email info[at]beaconsproject.ca for PDF)
Leroux. S. 2006. Incorporating natural disturbance and heritage sites in protected areas design. M.Sc. thesis, University of Alberta, Edmonton, AB. 102pp. (email info[at]beaconsproject.ca for PDF)
References:
Baker, W.L., 1989. Landscape ecology and nature reserve design in the boundary waters canoe area, Minnesota. Ecology 70, 2335.
Boyce, M.S., 1992. Population viability analysis. Annual Review of Ecology and Systematics 23, 481–506.
Cumming, S.G., 2001. A parametric model of the firesize distribution. Canadian Journal of Forest Research 31, 12971303.
Ebenman, B., Jonsson, T., 2005. Using community viability analysis to identify fragile systems and keystone species. Trends in Ecology and Evolution 20, 568575.
Leroux, S.J., F.K.A. Schmiegelow, R.B. Lessard, and S.G. Cumming. 2007. Minimum dynamic reserves: A framework for determining reserve size in ecosystems structured by large disturbances. Biological Conservation 138:464473.
Peters, R.S., Waller, D.M., Noon, B., Pickett, S.T.A., Murphy, D., Cracraft, J., Kiester, R., Kuhlmann,W., Houck, O., Snape III,W.J., 1997. Standard scientific procedures for implementing ecosystem management on public lands. In: Pickett, S.T.A., Ostfeld, R.S., Shachak, M., Likens, G.E. (Eds.), The Ecological Basis of Conservation: Heterogeneity, Ecosystems and Biodiversity. Chapman and Hall, Toronto, pp. 320336.
Pickett, S.T.A., Thompson, J.N., 1978. Patch dynamics and the design of nature reserves. Biological Conservation 13, 2737.
