2.4 Inference design
2.4.3 Temporal Inference Design
Overview Status Temporal Spatial Results and next steps
Temporal pattern is a general term we use to cover the variety of ways you might be interested in characterizing the change in your indicator(s) over time. You might be interested in the following:
- Net or Gross Change Between Two Points in Time
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- Net change is the difference between the indicator at time 1 and at time 2 at the aggregate level (e.g., the difference in total abundance of spawners in a population between the first and the fifth years of monitoring).
- Gross change refers to the volume of change at the individual site level (e.g. how often the abundance of spawners at individual sites shift from positive to negative or vice versa).
While net change is a very common expression of change, it may only tell you part of the story. For example, you may observe a relatively small net change in overall spawner abundance whereas an analysis of gross change may indicate that the abundance at a number of sites significantly increased while conversely significantly decreasing at other sites. This may give you valuable insights into changes in the spatial structure of your salmon population.
NOTE that estimating net change does not require revisiting sites while estimating gross change does require revisiting sites. - Trend
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By trend we mean a monotonic pattern of change (i.e. a consistent increase or decrease in your indicator through time). Below are some examples of common trend inference approaches.
- Average change per unit time (i.e. linear trend).
- Non-constant rate of change (i.e (. quadratic, exponential).
- Periodic
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By periodic we mean a cyclic pattern of change (e.g. ocean cycles). Quantification of periodic patterns that can be represented with sine waves (e.g. tidal cycles) can be accomplished using the method of Fourier transform. Other periodic patterns where nonlinearity and nonstationarity are the rule rather the exception may be more efficiently described by wavelet analysis. This may often occur in situations that involve population processes driven by large scale environmental forcing such the influence of freshwater and ocean conditions on salmon population dynamics.
- Other Approaches
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Specific trends (at least three visits) you might consider indicators that can be estimated from the distribution of site specific trends and how these indicators might be changing. Some examples of possible indicators are:
- The proportion of sites with a positive linear trend
- The average trend across all sites and its standard deviation
- The trend in proportion of occupied sites
- The trend in proportion of sites exceeding a specific abundance
- Benchmark over time (i.e. comparing the results of periodic monitoring to an established benchmark or goal). For example the objective of your monitoring might be to evaluate whether or not a population equals or exceeds a spawner escapement goal x number of years over a specified number of years.
Evaluating temporal pattern as a site’s metric can be thought of as a version of status: a snapshot of the temporal pattern over the time interval of interest. In this context, all the concerns, caveats, types of assumptions that are covered under the status section are relevant. This is especially the case when you are making inferences to a population for which you have sample based data. Your uncertainty reflects the uncertainty of estimating the temporal patterns in the data set itself AND the uncertainty in making the inferences to your target population. For example, if your spatial design is a census, then your inference uncertainty comes from the set of census data. If your spatial design is a survey, then your inference uncertainty comes from BOTH the data and the specific survey design used. If your spatial design is opportunistic, then, just as with status estimation, your inference uncertainty includes assumptions regarding the sample’s representativeness. If your spatial design is model based, then the model assumptions become relevant.
Whereas the description of status relies primarily on the spatial design chosen, the description of temporal patterns additionally relies on the temporal design you chose. As an absurd example, suppose your spatial-temporal design includes selecting different sites each year of the survey. You will be severely limited in the kinds of temporal patterns you will be able to detect. However, if you incorporate a pattern of revisits to sites across years (considering annual as the time unit of interest), your possibilities for evaluating temporal patterns expands significantly.
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