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The paper presents a simulation and parameter-estimation approach for evaluating stochastic patterns of population growth and spread of an annual forest herb, Melampyrum pratense (Orobanchaceae). The survival of a species during large-scale changes in land use and climate will depend, to a considerable extent, on its dispersal and colonisation abilities. Predictions on species migration need a combination of field studies and modelling efforts. Our study on the ability of M. pratense to disperse into so far unoccupied areas is based on experiments in secondary woodland in NE Germany. Experiments started in 1997 at three sites where the species was not yet present, with 300 seeds sown within 1m2. Population development was then recorded until 2001 by mapping of individuals with a resolution of 5 cm. Additional observations considered density dependence of seed production. We designed a spatially explicit individual-based computer simulation model to explain the spatial patterns of population development and to predict future population spread. Besides primary drop of seeds (barochory) it assumed secondary seed transport by ants (myrmecochory) with an exponentially decreasing dispersal tail. An important feature of population-pattern explanation was the simultaneous estimation of both population-growth and dispersal parameters from consistent spatio-temporal data sets. As the simulation model produced stochastic time series and random spatially discrete distributions of individuals we estimated parameters by minimising the expectation of weighted sum of squares. These sums of squares criteria considered population sizes, radial population distributions around the area of origin and distributions of individuals within squares of 25cm×25 cm, the range of density action. Optimal parameter values, together with the precision of the estimates, were obtained from calculating sum of squares in regular grids of parameter values. Our modelling results showed that transport of fractions of seeds by ants over distances of 1-2m was indispensable for explaining the observed population spread that led to distances of at most 8mfrom population origin within 3 years. Projections of population development over four additional years gave a diffusion-like increase of population area without any "outposts". This prediction generated by the simulation model gave a hypothesis which should be revised by additional field observations. Some structural deviations between observations and model output already indicated that for full understanding of population spread the set of dispersal mechanisms assumed in the model may have to be extended by additional features of plant-animal mutualism.

Modelling the competitiveness of clonal plants by complementary analytical and simulation approaches
(1999)

The paper presents a simulation and parameter-estimation approach for evaluating stochastic patterns of population growth and spread of an annual forest herb, Melampyrum pratense (Orobanchaceae). The survival of a species during large-scale changes in land use and climate will depend, to a considerable extent, on its dispersal and colonisation abilities. Predictions on species migration need a combination of field studies and modelling efforts. Our study on the ability of M. pratense to disperse into so far unoccupied areas was based on experiments in secondary woodland in NE Germany. Experiments started in 1997 at three sites where the species was not yet present, with 300 seeds sown within one square meter. Population development was then recorded until 2001 by mapping of individuals with a resolution of 5 cm. Additional observations considered density dependence of seed production. We designed a spatially explicit individual-based computer simulation model to explain the spatial patterns of population development and to predict future population spread. Besides primary drop of seeds (barochory) it assumed secondary seed transport by ants (myrmecochory) with an exponentially decreasing dispersal tail. An important feature of populationpattern explanation was the simultaneous estimation of both population-growth and dispersal parameters from consistent spatio-temporal data sets. As the simulation model produced stochastic time series and random spatially discrete distributions of individuals we estimated parameters by minimising the expectation of weighted sums of squares. These sums-ofsquares criteria considered population sizes, radial population distributions around the area of origin and distributions of individuals within squares of 25*25 cm, the range of density action. Optimal parameter values, together with the precision of the estimates, were obtained from calculating sums of squares in regular grids of parameter values. Our modelling results showed that transport of fractions of seeds by ants over distances of 1…2 m was indispensable for explaining the observed population spread that led to distances of at most 8 m from population origin within 3 years. Projections of population development over 4 additional years gave a diffusion-like increase of population area without any “outposts”. This prediction generated by the simulation model gave a hypothesis which should be revised by additional field observations. Some structural deviations between observations and model output already indicated that for full understanding of population spread the set of dispersal mechanisms assumed in the model may have to be extended by additional features of plant-animal mutualism.

Myrmecochory, i.e. dispersal of seeds by ants towards and around their nests, plays an important role in temperate forests. Yet hardly any study has examined plant population spread over several years and the underlying joint contribution of a hierarchy of dispersal modes and plant demography. We used a seed-sowing approach with three replicates to examine colonization patterns of Melampyrum pratense, an annual myrmecochorous herb, in a mixed Scots pine forest in northeastern Germany. Using a spatially explicit individualbased (SEIB) model population patterns over 4 years were explained by short-distance transport of seeds by small ant species with high nest densities, resulting in random spread. However, plant distributions in the field after another 4 years were clearly deviating from model predictions. Mean annual spread rate increased from 0.9 m to 5.1 m per year, with a clear inhomogeneous component. Obviously, after a lag-phase of several years, non-random seed dispersal by large red wood ants (Formica rufa) was determining the species’ spread, thus resulting in stratified dispersal due to interactions with different-sized ant species. Hypotheses on stratified dispersal, on dispersal lag, and on non-random dispersal were verified using an extended SEIB model, by comparison of model outputs with field patterns (individual numbers, population areas, and maximum distances). Dispersal towards red wood ant nests together with seed loss during transport and redistribution around nests were essential features of the model extension. The observed lag-phase in the initiation of non-random, medium-distance transport was probably due to a change of ant behaviour towards a new food source of increasing importance, being a meaningful example for a lag-phase in local plant species invasion. The results demonstrate that field studies should check model predictions wherever possible. Future research will show whether or not the M. pratense–ant system is representative for migration patterns of similar animal dispersal systems after having crossed range edges by long-distance dispersal events.