Application of a spatial meta-population model with stochastic parameters to the management of the invasive grass Nassella trichotoma in North Canterbury, New Zealand

Optimising the management of invasive plants requires the identification of the population size outcomes for alternative management strategies. Mathematical models can be useful tools for making such management strategy comparisons. In this paper we develop a generic landscape meta-population model and apply it to the weedy grass, Nassella trichotoma, an invasive species occupying approximately 800 land parcels, predominantly pastoral farms, in the Hurunui district, North Canterbury, New Zealand. Empirical evidence reveals that this meta-population is currently stable (at a median density of 6 plants ha⁻¹) under a community strategy requiring manual removal (termed ‘grubbing’) of plants annually from all land parcels. Reduction in population size requires an alternative management strategy. Field data, collected over a 12 year period, were used to provide stochastic parameter values for land parcel size, carrying capacity, rates of local population growth and grubbing.The model reveals that at steady state, the most significant contribution to population growth on a land parcel comes from within the land parcel itself; the expected annual per capita growth on an individual land parcel is 4 orders of magnitude greater than the expected annual contribution from plants arising from other land parcels. This result implies that many of the farms currently supporting N. trichotoma may pose little or no threat to, nor are threatened themselves by, other farms infested by the weed. However, the steady state distribution (of the weed's population density) was sensitive to the spread rate, revealing a need for data on this process. It was also sensitive to how any increase in the grubbing rate is distributed; increasing it via a uniform distribution U(0, 1) where all rates between 0 and 100% year⁻¹ are equally probable did not affect the steady state, whereas increasing the rates via the uniform distribution U(0.25, 0.75) resulted in fewer farms with high population densities. In general the model provides a basis for exploring the effects of a wide range of alternative grubbing strategies on population growth in N. trichotoma.