A stochastic population model to evaluate Moapa dace (Moapa coriacea) population growth under alternative management scenarios

Abstract

The primary goal of this research project was to evaluate the response of Moapa dace ( Moapa coriacea ) to the potential effects of changes in the amount of available habitat due to human influences such as ground water pumping, barriers to movement, and extirpation of Moapa dace from the mainstem Muddy River. To understand how these factors affect Moapa dace populations and to provide a tool to guide recovery actions, we developed a stochastic model to simulate Moapa dace population dynamics. Specifically, we developed an individual based model (IBM) to incorporate the critical components that drive Moapa dace population dynamics. Our model is composed of several interlinked submodels that describe changes in Moapa dace habitat as translated into carrying capacity, the influence of carrying capacity on demographic rates of dace, and the consequent effect on equilibrium population sizes. The model is spatially explicit and represents the stream network as eight discrete stream segments. The model operates at a monthly time step to incorporate seasonally varying reproduction. Growth rates of individuals vary among stream segments, with growth rates increasing along a headwater to mainstem gradient. Movement and survival of individuals are driven by density-dependent relationships that are influenced by the carrying capacity of each stream segment. First, we calibrated the model to a historical time series of Moapa dace abundance estimates. The goal of the calibration was to estimate unknown parameters such as larval survival, carrying capacity of the tributary streams harboring the population of Moapa dace upstream of the gabion barrier, and carrying capacity of the mainstem Muddy River and tributaries. Based on historical abundance estimates, we found that the carrying capacity of the mainstem Muddy River was nearly twice the capacity of the tributary streams where Moapa dace have resided for the past 20 years. Given the calibrated model, we then conducted simulations to assess (1) the effect of altering migration barriers that restrict upstream and downstream movement of dace, and (2) the effect of changes in carrying capacity on equilibrium population sizes. We found that barriers to upstream movement led to extinction of subpopulations upstream of the barriers when initial population sizes were small. The probability of one or more subpopulations going extinct over a 50-year time horizon was >0.80 at initial population sizes of 10 non-larval and 70 larval dace, and was >0.40 at initial population sizes of 50 non-larval and 350 larval dace. The probability of a subpopulation going extinct decreased to zero when the initial population size exceeded 100 non-larval dace. Removal of upstream migration barriers eliminated extinctions of subpopulations, even at low initial population sizes. Compensatory mechanisms such as density-dependent survival and movement acted to buffer against local extinctions because stream segments could be quickly repopulated by dispersal when fish could access all stream segments. Providing access to the mainstem Muddy River through removal of a gabion barrier that restricted upstream and downstream movement increased total population size from about 875 to 3,000 individuals. Additionally, because of higher growth rates of individuals in the mainstem Muddy River, the size structure of the population shifted towards larger individuals with higher fecundity, thereby increasing reproductive capacity of the population. Increasing or decreasing the total carrying capacity of all stream segments resulted in changes in equilibrium population size that were directly proportional to the change in capacity. However, changes in carrying capacity to some stream segments but not others could result in disproportionate changes in equilibrium population sizes by altering density-dependent movement and survival in the stream network. These simulations show how our IBM can provide a useful management tool for understanding the effect of restoration actions or reintroductions on carrying capacity, and, in turn, how these changes affect Moapa dace abundance. Such tools are critical for devising management strategies to achieve recovery goals.