Mathematical modeling of the white mistletoe (Viscum album l.) Populations for sustainable urban horticulture

The paper deals with the control of the White Mistletoe (Viscum album L.) population growth in urban landscapes in order to enhance sustainable horticulture. Nowadays, the White Mistletoe has been an invasive alien species that poses harmful effects to urban tree stands. At the same time it is a keystone species in urban ecosystems. Hence ecologically sound strategies to curb this species' excessive spread should be undertaken to reduce its damages to urban forestry. The White Mistletoe populations were surveyed in 2006-2010 on the study areas located in the north (147 ha), north-eastern (959 ha), central (736 ha) and south-eastern (158 ha) parts of the city of Kharkiv, Ukraine. Totally ca. 6% of the city area was surveyed with the use of the original technique for mistletoe census and population analysis. To assess the mistletoe abundance on study areas the semi-logarithmic index was developed as follows:”1” is assigned to a discrete group of 1 to 5 individual mistletoe dwarves, “2” corresponds to the number of 6 to 10 dwarves, “3” – to 11-20, “4” – to 21-40, and so on to the maximal observed abundance of more than 500 individual mistletoe dwarves in a single discrete group (abundance index “8”). While analyzing the age structure of local mistletoe populations viewed as discrete groups the specially designed population-demography coefficient K[j-g-s] was applied to reflect the ratio among juvenile, generative and senile shrubs: digits 0, 1, 2, and 3 were combined into single operator to describe the relative share of each age class in the local population. The survey data were used to develop a matrix model of the White Mistletoe population dynamics similar to the M. Williamson's model. The basic assumption was as follows: the population becomes stable, i.e. age class ratio is constant over time, but the population size may change, if the number of individual shrubs of the i-th age makes a geometric progression. The proposed model can be used for both prospective and retrospective analysis of population dynamics. Hence, the modeling approach introduced in the paper implying different scenarios allows developing a tool of prioritization of the White Mistletoe management interventions towards reduction of this species' harm to urban horticulture.