Dynamics in pollen diagrams example

Vegetation series encompassing time spans of thousands of years can only be found in fossil records, for example in pollen diagrams (Lischke 2005).

Year BP

• Abies (1) ■ Pinus (2) ■ Fagus (3) HQuercus (4) «Acer (5) «Fraxinus (6) ■ Ulmus (7) ITilia (8) ■ Betula (9) BAlnus (10) ■ Populus (11)«Salix (12) «Sorbus (13) a Picea (14)

Year BP

• Abies (1) ■ Pinus (2) ■ Fagus (3) HQuercus (4) «Acer (5) «Fraxinus (6) ■ Ulmus (7) ITilia (8) ■ Betula (9) BAlnus (10) ■ Populus (11)«Salix (12) «Sorbus (13) a Picea (14)

Figure 9.14 Tree species in the pollen diagram from Soppensee (Lotter 1999).

Here extreme nonlinearity can be expected because very long time spans increase the chance that changes in the functional role of species within the vegetation cover will occur, caused mainly by invasions and extinctions. I demonstrate typical patterns using pollen of tree species of the Soppensee profile from Lotter (1999) (see also Lischke et al. 2002), documenting the change in tree species on the Swiss Plateau from about 13000 BP until 5700 BP (Figure 9.14, without considering the changes in the technology of 14C dating that have taken place in the meantime).

First we look at the velocity of process, defined as the rate of change in total species composition per time unit:

where d is the Euclidean distance (a measure of dissimilarity) between any two consecutive states in the pollen diagram. This type of calculation allows the derivation of a velocity profile of the change processes over the period of measurement (Figure 9.15). There are different time steps used for this, the shortest of 50 years being given by the temporal resolution of data, whereas a step of 800 years shows the long-term trends. The 50-year time step is also used to interpret the ordination in Figure 9.16. The states in time are the circles and their diameter is proportional to velocity. There are linear phases where velocity is high and others where it is low. Velocity seems to

-13100 -12100 -11100 -10100 -9050 -6050 -7050 -6050

Year BP

Figure 9.15 Velocity profile of the Soppensee pollen diagram. The time-step length in the data is 50 years.

-13100 -12100 -11100 -10100 -9050 -6050 -7050 -6050

Year BP

Figure 9.15 Velocity profile of the Soppensee pollen diagram. The time-step length in the data is 50 years.

10500

Figure 9.16 Time trajectory of the Soppensee pollen diagram. The diameter of the circles is proportional to the velocity of change.

Figure 9.16 Time trajectory of the Soppensee pollen diagram. The diameter of the circles is proportional to the velocity of change.

fluctuate considerably during periods of nonlinearity, when large and small circles alternate.

It is also worth distinguishing the qualitative and the quantitative components in the data. In the analyses shown so far the quantitative view is adopted; that is, the species scores are percentages of total pollen abundance. In these analyses the most abundant types of pollen dominate the result. Rare species, including the invaders in their first years of arrival, do not contribute much to the rate of change. However, species scores can be transformed to presence-absence (or any intermediate scale, see Section 7.2.3) so that the velocity expresses change in species presence. This is shown in Figure 9.17, where the lower lines express change in the quantity of pollen composition while the upper lines are change in quality; that is, the emergence or disappearance of pollen of a specific species. Obviously, these two types of change happen at different points in time. There are phases in which several species emerge (upper lines) but no considerable change in quantity can be observed (lower lines) and vice versa. Numbers 1 through 6 indicate discrete events:

1 Invasion of Alnus, followed by two invasions of Quercus.

2 Invasion of Acer, Fraxinus, Tilia and Ulmus.

3 Fraxinus disappearing.

4 Fraxinus returning.

5 Abies invading.

6 Fagus and Picea arriving.

Figure 9.17 Velocity profiles from quantitative (bottom line) towards qualitative (top line). The peaks in the upper lines stem from species invasions.

Numbers 7 and 8 indicate increased velocities in mass changes:

7 Mass expansion of Pinus.

8 Mass retreat of Pinus.

Even when inspecting the velocity profiles in detail, no evidence is found for velocity being related to nonlinearity, such as that around 12 600 and 10 500 BP. But there is yet another interesting way of looking at similarity, when taking its second derivative, acceleration in the change process, A:

When A is positive, the velocity increases; when it is negative, the velocity decreases. In Figure 9.18 acceleration is used to interpret the same time trajectory as in Figure 9.16: circles are proportional to acceleration. The result is striking: linear phases, whether fast or slow, show very low acceleration. Nonlinear, on the other hand, are characterized by huge positive as well as negative accelerations. Hence, strong fluctuations in the dynamics of the systems distinguish nonlinear from smooth, predictable linear phases.

Figure 9.18 Time trajectory of the Soppensee pollen diagram. The diameter of the circles is proportional to the acceleration of change. Grey are positive, black negative values.

Is this finding a generally valid rule? No, it is not. First of all, the observation is restricted to one profile only and in this there are just two phases of strong nonlinearity. Second, fluctuation manifesting in speed and acceleration can be caused by disturbance of the profile. Sedimentation is dependent on many factors and cannot be expected constant over thousands of years. Hence, investigation of many more profiles would be needed to find evidence for validity of the rule.

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