Post provided by Bethan Hindle

Understanding Population Responses to Environmental Change

Rapid climatic change has increased interest about how populations respond to environmental change. This has broad applications, for example in the management of endangered and economically important species, the control of harmful species, and the spread of disease. At the population level changes in abundance are driven by changes in vital rates, such as survival and fecundity. So studies that track individual survival and reproduction over time can provide useful insights into the drivers of such changes. They allow us to make future population level predictions on things like abundance, extinction risk and evolutionary strategies.

Archbold Biological Station - site of numerous long-term demographic studies, including that of Eryngium cuneifolium used in this paper. ©Reed Bowman
Archbold Biological Station – site of numerous long-term demographic studies, including that of Eryngium cuneifolium used in this paper. ©Reed Bowman

Predicting the future isn’t a simple task though. Anyone whose washing has got soaked through after the weather forecast suggested the day would be dry and sunny will know that (though the accuracy of short term weather forecasts has increased dramatically in recent years). Ideally, if we want to predict what will happen to populations as their environment changes, we would identify the drivers of variation in their survival and reproduction. We do this by asking questions like ‘are years of low survival associated with high rainfall?’ But, this is not a simple task; identifying drivers and the time periods over which they act and accurately estimating their effects requires long-term demographic data.  

It seems unfair to suggest that datasets, such as the eight-year Carduus nutans dataset used in this manuscript, may “not be enough”. A vast amount of work goes into collecting long-term demographic data, from the logistics of the field work to the difficulties of maintaining funding. As a PhD student, a lot of my peers would have bitten my hand off for access to an eight-year dataset. This dataset, like most demographic datasets, may not be long enough to estimate the effects of environmental drivers though. And it’s not possible to rectify this problem quickly (there are fairly obvious limitations to how quickly you can go out and collect a long-term dataset…). So we need efficient statistical methods to make good use of the available data.

Structured Population Models

Rates such as survival and reproduction differ among individuals within a population. For example, juvenile herbivores typically have lower and more variable survival than prime age adults. Larger plants may have higher survival and reproduction than smaller ones. This has led to the widespread use of structured population models. These allow rates such as survival to vary according to either discrete categories, such as age or sex (matrix population models), or continuous variables such as size (integral projection models).

Vital rates are often correlated, as shown for Carduus nutans here.
Vital rates are often correlated, as shown for Carduus nutans here.

Typically, such studies estimate vital rates and attempt to determine the drivers of these separately for each vital rate (and in the case of MPMs for each age/stage class). The same drivers are often important for multiple age classes or multiple vital rates though. Harsh winter weather, for example, may decrease survival across the life cycle. So, the vital rates within a population are rarely independent. A good year for survival tends to be a good year for reproduction. Years of high juvenile survival are often associated with years of high adult survival (although negative relationships, or trade-offs are also possible) 

Using a Factor Analytic Approach

In our paper, ‘Exploring population responses to environmental change when there is never enough data: a factor analytic approach‘, we describe a method for capturing temporal covariation among demographic rates via one or more latent variables. Example code for the approach is provided on GitHub. When the rates are positively correlated, as is often the case, we can think of each latent variable as an axis of ‘environmental quality’. Positive values are associated with years where survival, growth and reproduction were higher than average.

Schematic of the factor analytic approach (more detail in our article).

The advantages of this method are twofold. Firstly, it allows ecological and evolutionary responses to environmental change to be explored even when the specific drivers of this change cannot be identified. Populations can be simulated using different distributions for the latent variable. You could try increasing or decreasing the mean to determine how populations might respond to improving or deteriorating conditions respectively. Unlike most previous approaches this method takes into account that the demographic processes are not independent of each other. We show this by exploring the effects of different environmental conditions on reproductive strategies in the monocarpic perennial Carduus nutans. In our study, we found that selection for earlier flowering and longer times in the seedbank dominated in lower quality environments. On the other hand, selection for a more perennial life history is predicted in higher quality environments.

The other advantage of this method is that it can provide a simpler target for identifying environmental drivers. Instead of treating each vital rate separately we can explore the drivers of the latent variable(s) instead. We illustrate this using a demographic model of the fire dependent herb Eryngium cuneifolium. Using this approach, we can include time since fire as a driver of all four of the vital rates we looked at (survival, growth, flowering and fecundity) with the addition of just a single parameter. Simulating populations under different fire return intervals allowed us to predict optimal management regimes for this rare species.

Eryngium cuneifolium. ©Eric Menges (left) and ©Amarantha Quintana-Morales (right)

Our general approach can be applied in any setting where it’s possible to construct a stochastic, demographic projection model. Where explicit causal drivers cannot be identified, this may represent the best alternative for exploring possible population-level responses to environmental change. Where temporal replication is sufficient for drivers to be identified the method can provide a much simpler target for this complex task.

To find out more about the factor analytic approach, read our Methods in Ecology and Evolution article ‘Exploring population responses to environmental change when there is never enough data: a factor analytic approach

This article was shortlisted for the Robert May Prize 2018. You can find all of the shortlisted articles is this Virtual Issue.