rate_change: Rate of community change over successive time intervals
In codyn: Community Dynamics Metrics

Description Usage Arguments Details Value References Examples

Calculates the slope of the differences in species composition within a community over increasing time intervals, which provides a measures of the rate of directional change in community composition. Differences in species composition are characterized by Euclidean distances, which are calculated on pair-wise communities across the entire time series. For example, a data set with six time intervals will have distance values for five one-year time lags (year 1 vs year 2, year 2 vs year 3 ...), four two-year time lags (year 1 vs year 3, year 2 vs year 4 ...) and so forth. These distance values are regressed against the time lag interval. The slope of the regression line is reported as an indication of the rate and direction of compositional change in the community.

1	rate_change(df, time.var, species.var, abundance.var, replicate.var = NA)

`df`	A data frame containing time, species and abundance columns and an optional column of replicates
`time.var`	The name of the time column
`species.var`	The name of the species column
`abundance.var`	The name of the abundance column
`replicate.var`	The name of the optional replicate column

The input data frame needs to contain columns for time, species and abundance; time.var, species.var and abundance.var are used to indicate which columns contain those variables. If multiple replicates are included in the data frame, that column should be specified with replicate.var. Each replicate should reflect a single experimental unit - there must be a single abundance value per species within each time point and replicate.

The rate_change function uses linear regression to relate Euclidean distances to time lag intervals. It is recommended that fit of this relationship be verified using rate_change_interval, which returns the full set of community distance values and associated time lag intervals.

The rate_change function returns a numeric rate change value unless a replication column is specified in the input data frame. If replication is specified, the function returns a data frame with the following attributes:

rate_change: A numeric column with the synchrony values.
replicate.var: A column that shares the same name and type as the replicate.var column in the input data frame.

Collins, S. L., Micheli, F. and Hartt, L. 2000. A method to determine rates and patterns of variability in ecological communities. - Oikos 91: 285-293.

data(knz_001d)
rate_change(knz_001d[knz_001d$subplot=="A_1",],
                       time.var = "year", 
                       species.var = "species",
                       abundance.var = "abundance") # for one subplot
                       
rate_change(knz_001d, 
             time.var = "year", 
             species.var = "species",
             abundance.var = "abundance",
             replicate.var = "subplot") # across all subplots

[1] 0.6706902
     subplot rate_change
1        A_1   0.6706902
389      A_2   1.3087934
793      A_3   2.1391173
1264     A_4   1.5587084
1705     A_5   2.3302497
2077     B_1   1.5640603
2564     B_2   2.6077139
2934     B_3   1.3402601
3337     B_4   1.4758986
3771     B_5   1.5537590
4233     C_1   2.2018922
4687     C_2   2.5573852
5067     C_3   1.4992809
5560     C_4   1.3525710
5957     C_5   1.3203894
6459     D_1   2.1336282
6965     D_2   2.1188434
7447     D_3   1.5775734
7935     D_4   1.6354767
8302     D_5   1.3237555