Modelling & Invasion
- Population models
- Metapopulations & Spatial models
- Metapopulation models
- Spatial Heterogeneity
- Spatially-explicit population models
Population models
In SBI201 Introductory Ecology, you were introduced to tools that describe and model population size and population growth. In particular, you learnt about life tables, deterministic models and stochastic models. If you need to refresh your knowledge on these concepts, please read Stiling (2002) on SBI201 E Reserve, pages 66-88. Please also read Reading 3.6 Lockwood et al 2007 for an overview of ecological process and how they impact on invasive species spread.
Life tables provide a tool for characterising a species' life-history strategies by estimating how the likelihood of mortality and reproduction change with age. Time-specific life tables provide a snapshot of a population's age structure from a sample at a given time. Age-specific life tables follow an entire cohort of individuals from birth to death.
Deterministic models of population growth predict changes in population size based on intrinsic properties of the population such as growth rate, current size and carrying capacity.
Stochastic models of population growth incorporate the effects of genetic variability and extrinsic factors like climate on population dynamics.
See Readings 3.7 (Londsale 1993) and 3.8 (Lonsdale et al 1995) for examples of population modelling of two tropical weeds: Mimosa pigra and Sida acuta.
Metapopulations & Spatial models
The population models (eg. demographic models, regression models, geometrical models) described thus far typically use data collected from a single spatial scale and focus on a single population. These models tend to focus on small-scale dynamics and contain the following assumptions (Gillman & Hails 1997).
- Individuals are in close proximity and mixing well (ie. a single population).
- Environmental heterogeneity is not important.
- Populations are closed (ie. no immigration or emigration).
Clearly these assumptions are unrealistic for populations not confined to a single area and/or where a larger spatial scale introduces environmental heterogeneity.
Higgins and Richardson (1996) argue that the violation of these assumptions, in particular local habitat variation, is one of the reasons that the ability to predict invasions has been limited.
Models incorporating spatial elements (e.g. distribution of habitat patches) are becoming increasingly popular - one reason for this is the development of computer software such as Geographic Information Systems and increased processing power of desktop computers.
A second reason is that, by explicitly incorporating spatial processes, the stability and dynamics that were unpredicted from local population models may be explained (Gillman and Hails 1997).
Metapopulation Models
The metapopulation concept was proposed during the development of models for species distributed across a number of sub-populations.
A metapopulation is defined as a set of local populations that are linked by dispersal, comprising subpopulations or local populations. Metapopulation models take into account interactions between these subpopulations.
Spatial Heterogeneity
Spatial heterogeneity describes the non-uniform distribution or occurrence of environmental variables and events in the landscape. In response to this heterogeneity, populations are not distributed uniformly across a landscape.
If we acknowledge landscape heterogeneity, we can no longer assume that all individuals within a landscape experience the same probability of surviving and reproducing. Therefore we need to find a way to explicitly incorporate landscape heterogeneity into our models. Landscape heterogeneity is important for two reasons:
- It constrains the survival and reproduction of individuals within a population.
- The degree of exchange between local populations within the metapopulation.
For example, Para grass (Urochloa mutica) a pasture species invading floodplains in the Northern Territory cannot survive submersion for extended periods. Water depth on the floodplains can vary from between 1-3m. Combined with other environmental factors, wet season depth produces a metapopulation structure in this invasive species.
Further, Para grass spreads vegetatively in the NT, either by growth from the edge of patches into uninvaded areas or by fragments of the plant being dispersed by floodwaters or by animals. So dispersal, or links between populations, is constrained by both habitat suitability and abiotic factors such as water flow during flood and animal movements. As none of these variables are homogeneously distributed across the floodplains, the patterns of para grass spread will reflect landscape heterogeneity heterogeneity (see reading 3.9 Ferdinands et al 2005).
Spatially-explicit population models
Metapopulation models assume that some parts of the landscape are habitat patches that are, or could potentially be, occupied by the species, and the remainder is unsuitable habitat (Akgakaya et al. 1999).
Advances in remote sensing and Geographic Information Systems (GIS) enable the examination of the spatial structure of habitats, and the relationships of populations to this structure. This can then be incorporated into spatially explicit population models.
We would now like you to start work on the activity below.
Activity 3.1
What contribution can population models make to weed management? We want you to critically consider this question by working through Higgins & Richardson (1996) Reading 3.10.
Reading 3.10 Higgins S.I. and Richardson D.M. (1996). A review of models of alien plant spread. Ecological Modelling 87: 249-265.
There has been limited progress in the development of predictive models of plant spread, despite the long-standing recognition that invasive plants have substantial negative effects on ecosystems worldwide. Higgins and Richardson (1996) argue that the problem is not intractable and that new approaches and new technologies will improve the way we model plant invasions. They review the approaches that have been commonly employed and propose a conceptual model that may progress the way we approach the study of plant invasions.
In reading the article you do not need to understand how each of the modelling approaches works; concentrate your reading on parts 1 & 2 and the Summary (part 4). The intention is that you get an overview of the variety of methods that have been used and the assumptions and limitations of these approaches. Having read the article consider the following questions.
- Is there a 'correct' way to model plant invasions?
- Why is it important to have a conceptual model of the plant invasion you are studying? Refer to the model proposed by Higgins and Richardson in answering.
- If you understand the life history and physiology of an invasive plant species, Can you predict which species will become invasive and their potential impact?
- In light of you answer to question 3, what are the implications for choice of modelling method and subsequent management of the invasive species?
Reading 3.2 Higgins S.I. and Richardson D.M. (1996). A review of models of alien plant spread. Ecological Modelling 87: 249-265.