Understanding how the spatial and temporal dynamics of populations vary across the landscape is fundamentally important to managing and conserving species. For example, populations may fluctuate in synchrony, or exhibit other forms of spatial sub-structuring, due to intrinsic population parameters or to influences from environmental factors. Importantly, synchronous populations may be at greater risk of extinction if all populations are decreasing to zero at the same time, thereby reducing rescue through colonisation. Different species may not have similar dynamics, even if they share the same environment and thus unravelling the spatial dynamics of multiple species provides vital information about what scale to apply management actions.

MARSS models
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

Using long-term data (17‑22 years) across a large-scale study region (8000 km²) in arid central Australia, we test for regional synchrony in a population driver, annual rainfall, across nine sites (>20 km apart). We then draw from examples from small mammal and reptile populations and investigate if each species exhibits synchrony. For species that did not exhibit synchrony, we used multivariate autoregressive state-space (MARSS) models to explore four other sub-population structures. We also use the MARSS models to identify important drivers that may regulate populations of these species.

We show that species exhibited different spatial population structuring and respond to extrinsic factors in different ways. We conclude that investigating how the spatial connections among populations interact with their temporal dynamics and eventual persistence or decline, is important for determining the appropriate scale to implement management actions and that “one size does not fit all”.

More on population dynamics of small mammals, MARSS models and Moran:

EcoTas 2013: Spatial and temporal synchrony in small mammal populations