Here I give a summary of my talk to EcoTas13. A joint conference of the Ecological Society of Australia and New Zealand Ecological Society, Auckland. A big thanks to my co-authors Chris Dickman and Glenda Wardle.
Determining the factors that influence the spatial dynamics of species’ populations remains a key goal in ecology and is an imperative for managing species that are in decline. Sub-populations across species’ ranges seldom share the same level of resources, and this may lead to different densities and growth rates among them. Dispersal may dampen these differences, but this effect decreases with distance. Nonetheless, local populations can still behave synchronously across large (>1000 km) spatial scales, suggesting that external drivers are operating.
Patrick Moran was born in Sydney in 1917. He was educated at the University of Sydney and Cambridge. At university, he studied chemistry, zoology, mathematics and physics. He was discouraged to continue with mathematics, but persevered anyway. He studied statistics and in the 1950s wrote a series of influential papers on the population dynamics of the Canadian lynx. One of these papers was published in the first volume of Australian Journal of Zoology. This paper described how populations of lynx could be in synchrony across vast areas of Canada, due to climate. This work is now known as the Moran effect or Moran’s theorem. Prof. Moran continued and contributed significantly to the advancement of population biology and statistics. To learn more about Moran see here.
The Moran effect or theorem provides a theoretical basis for population synchrony across large areas, and states that sub-populations with a common density dependent structure can be synchronised by a spatially correlated density independent factor, such as climate.
In this study we tested five hypotheses concerning the spatial population synchrony of five species of small mammals – two rodents and three dasyurids (the carnivorous or insectivorous marsupials). We then use the best fitting spatial models (based on AICc) to incorporate drivers that may regulate these populations. Using Moran’s theorem, we predicted that species with synchronous spatial dynamics are driven by factors that operate at the landscape scale, such as resource-pulses from large-scale rainfall events or wildfires, whereas species with asynchronous sub-populations will be influenced largely by factors operating at local scales.
MARSS framework is hierarchical and allows modelling of different spatial population structures and parameters, such as density dependence, while including both process and observation variability. Process variability represents temporal variability in population size due to environmental stochasticity. Observation variability includes sampling error.The process component is a multivariate first-order autoregressive process and is written in log-space:
where X = matrix of all m sub-populations at time t
B = density dependence
u = mean growth rate of the sub-population
w = process errors, assumed to be independent and to follow a multivariate normal distribution with a mean of 0 and variance-covariance matrix Q.
The observation component, written in log-space:
where Y = a matrix of observations of all sub-populations at time t,
a = the mean bias between sites
Z = a matrix of 0’s and 1’s that assigns observations to a sub-population structure.
v = observation error, assumed to be uncorrelated and follow a multivariate normal. distribution, with a mean of 0 and a variance-covariance matrix R
We used multivariate autoregressive state-space (MARSS) models to investigate the spatial population structures of small mammals using 17 ‑ 22 years of intensive live-trapping data from nine spatially distinct sites in central Australia.
What we found
For rodents and the mulgara, sub-populations were synchronous or had two structures and driven by large-scale processes. Populations of the smaller insectivorous marsupials (S. youngsoni and N. ridei) were asynchronous and driven by local events. Density dependence was detected in all species, but was weakest in insectivorous dasyurid marsupials.
The covariates spinifex seed, spinifex cover and 12 months cumulative rainfall were significant drivers of the population dynamics for both species of rodents. For the mulgara, spinifex cover and rodents were both positively correlated with their population. For the smaller dasyurids: S. youngsoni populations were positively correlated with two month prior mean rainfall event size and negatively correlated with mulgara captures (a predator and/or competitor of this species). For N. ridei population only spinifex cover was positively associated.
Our findings suggest that local environmental stochasticity is more important than intrinsic factors in driving dasyurid population dynamics. In contrast, populations of rodents and a large carnivorous dasyurid were driven by both extrinsic and intrinsic factors that operate at the landscape scale, confirming predictions derived from Moran’s theorem.
Moran, P. (1953) The statistical analysis of the Canadian Lynx cycle. Australian Journal of Zoology, 1, 291-298.
For more on Moran: http://www.science.org.au/fellows/memoirs/moran.html
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