1. Ecosystem function modelling
Presented by
Bob Scholes
CSIR Environmentek
Welcome to the 7th chapter in the Conservation for climate change course. This chapter discusses the process of ecosystem function modelling, and the course material is prepared by Bob Scholes of the CSIR.

2. Aspects and levels of biodiversity
Composition: what it contains
Biome envelope models
Species niche models
Ecosystem function
models
Biodiversity can be thought of as having three aspects (composition, structure and function) and three levels (the gene, the population and the ecosystem). Almost all systematic conservation planning tools focus at the species composition level (where the red dot is in this diagram). Some deal with biome or habitat modelling (red ellipse). The subject of this presentation is ecosystem function modelling (orange ellipse), which also deal to a degree with ecosystem structure. Clearly, there are gaps that current modelling processes do not cover, but when the three different approaches are combined, they do give a moderately clear picture of how it all works.
Gene
Population
Ecosystem
Ecosystem
Structure: what it looks like?
Function: how it works?

3. Dynamic Vegetation Models
All the major Global Circulation Models have ‘coupled’ models of the land surface
Simulate carbon uptake/loss, albedo, bulk stomatal conductivity, surface roughness
Have a crude representation of biomes or ‘functional types’
Some of the better ones (LPJ, Sheffield) have fire and mammals in them
An example of an ecosystem function model used in relation to climate change are the ‘dynamic global vegetation models (DGVMs) that link to the Global Circulation Models (GCMs) and provide a changing land surface to them. These models simulate the carbon uptake and loss of the surface features, the albedo, the bulk stomatal conductivity, and the roughness of the surface as it interacts with the atmosphere. Of course, since it is dealing with a GCM (which typically have very broad scales) the best that these models have is a very crude representation of several biomes, or functional types. However, some of the better models, such as the LPJ model or the Sheffield DVGM) also include such processes as fire, and the interactions of mammals.

4. DGVMs continued… Problems:
Very hard to use unless you have a supercomputer
Results are not freely available, unlike the GCM outputs
Mostly not optimised for Africa
Scale is inappropriate for protected areas
Equations are complex and untransparent
Unfortunately, they are very generalised (they have to be, to run everywhere in the world: for example, all savannas are in one category) so they are not very useful for providing advice to local land managers.
In general, the computational complexity means that they are very hard to use unless you happen to have a supercomputer handy. Furthermore, unlike GCM outputs, the results are not typically made available over the internet. In general, DVGMs are optimised for Northern temperate conditions, since the teams that run them are typically from these areas. The scale is inappropriate for conservation planning, and the equations are both extremely complex and unavailable for study and consideration by the end user.

5. A ‘reduced form’ ecosystem model for savannas under climate change
‘Functional types’ are restricted to those occurring in savannas (but are expanded beyond the generic global types)
Includes effects of temperature, rainfall, seasonality, CO2, soil texture, fire and megaherbivores
‘Quasi-mechanistic’ equations
Simple, reduced forms based on emergent properties at ecosystem scale
Timestep of one year (‘implicit seasonality’) and ‘patch’ spatial scale
Ecosystem models can often be very complicated, requiring hundreds of parameters. Can we make a simple one, just for African savannas, that is nevertheless realistic in its main features? This is called a ‘reduced form’ model.
The functional types for this system are obviously restricted to those occurring within the savanna region, but they were significantly expanded beyond the generic global types. This model includes the effects of temperature, rainfall, seasonality, carbon dioxide, soil texture, fire regimes and megaherbivores. The equations used to integrate these are “quasi-mechanistic” in nature. That is, they are simple , reduced forms of the mechanistic processes that work within plants, and describe the emergent properties that are observed at an ecosystem scale. The model was run with a timescale step of a single year (hence seasonal effects were implied within the model but not actually calculated separately), and the spatial scale of the model was a “patch” of land.

6. Basic savanna system model
Fire freq
Tree ht & BA
Fire intens
Elephants
Browsers
CO2
Tree prodn
Mixed
Carnivore
Sour grass
Coarse graz
Here is what the ‘plumbing’ of such a model might look like. Note that plants and animals have both been lumped together into broad functional types (the boxes). The interactions between them are shown as arrows, and factors controlling those interactions are shown as the ‘bowties’.
Temperature
Fine grazers
Sweet grass
Sand %

7. Water balance modelling
(1) G =  Rain/E0 * daysmonth if Rain<E0, else R/E= 1
months
(2) E0 = open water evaporation
~ 0.8 x {700(T+0.006A)/(100-L) (0.0023A+0.37T*0.53(TxTn)
+0.35Tann-10.9))/(80-Tx)}
T = mean air temperature ( C)
Tx= max air temp
Tn=min air temp
A=altitude (m)
L=latitude (deg) [Linacre 1984]
Water is key to savanna ecosystem modelling, because they are water limited rather than temperature or light limited. Even when they are nutrient limited, the nutrient availability is controlled by when the soil is moist. Here is a very simple way of modelling water balance, using only the information easily available from climate change simulations: monthly rainfall, maximum temperature and minimum temperature. It ends up as an index of the number of days in the year for which plant growth is possible (‘G days’)
Basically, the water balance is the sum for each month of the average daily amount of precipitation, divided by the daily evaporation, multiplied by the number of days in the month. This assumes that the rainfall is greater than the evaporation; if this is not the case, then the rain over evaporation term is given to be 1. The E0, or open water evaporation is calculated using the second equation. We needn’t go into the details of this term, but it is worth noting that it incorporates air temperature (the monthly mean, minimum and maximum) as well as the altitude and latitude of the cell being modelled. This equation was developed by Linacre.

8. Controls on grass growth at the annual timescale
Rainfall in the current growing season
Actually, it is the duration of growth opportunity that matters
This is affected by evaporation as well as rain, and is mediated by soil texture
The fertility of the soil
The amount of tree cover
Daytime temperature
[CO2]
These are the main factors known to control how much grass grows every year. First of these is the rainfall, although it is not so much the quantity of rain that matters, as the duration of growth opportunity (ie: that length of time in which conditions are appropriate for growth). This factor is affected by evaporation as well as rain, and the effects of soil texture on the drainage of water from the soils plays an important role. The soil fertility is important, and the tree cover plays a role because grass typically does not grow well under shade. Daytime temperatures must fall within an optimal range for grass growth, and, as shown in Chapter 4, the levels of CO2 in the air can be a significant factor in controlling plant growth.
In some fertile savanna ecosystems, moderate grazing also has a mildly stimulating effect on grass growth.

9. Linear relation between grass production and rainfall
500
400
300
clay soil
Grass AG NPP (g/m2/y)
sand soil
200
Here is a data-based graph of yearly aboveground grass net primary productivity in the absence of trees. It clearly shows what is called the ‘Inverse texture hypothesis’, first attributed to Emmanuel Noy-Meir: clay soils tend to have a higher response than sandy soils and are more productive at high rainfall intensities. At low rainfall intensities, the formation of a solid clay cap on the soil will limit grass growth to a much greater extent than sandy soil, which is therefore more productive.
100
200
400
600
800
1000
Annual rainfall

10. Slope: Rain Use Efficiency (g/m2/mm)12 10 8 6
Rain use efficiency (kg/ha/mm)
The linear grass production versus rainfall relation has two parameters: a slope and intercept. The slope is called the Rain Use Efficiency. It is approximately inversely linearly related to the sand content of the soil. Mechanistically, it is probably more correct to say that it is directly and linearly related to the (clay+silt) content of the soil, and the relationship shown above follows from the fact that sand+silt+clay=100%. 4 2 50 60 70 80 90
100
Sand %

11. Intercept: dependent on soil water holding capacity; co-varies with the rain use efficiency
2000
1500
1000
500
Intercept of AGGNPP vs Rain
(kg/ha/y)
-500 5 10 15
-1000
It turns out that the intercept of the grass production vs rainfall curve is approximately linearly related to the slope (RUE): in other words, you actually only need one constant to characterise this relation, since you can calculate the other from it.
The higher the rain use efficiency, the lower the intercept value, following an approximately straight line relationship. Higher intercept values mean that more rain is required for a given amount of primary production in comparison to lower values. In other words, the significance of this graph is that the more efficiently water is used, the less rainfall is required, and efficiency of use is covariant with soil water holding capacity.
-1500
-2000
-2500
-3000
Rain use efficiency (kg/ha/mm)

12. Effect of trees on grass
1.00
0.90
0.80
0.70
0.60
0.50
Fraction of treeless grass NPP
0.40
0.30
0.20
In savannas, the presence of trees has a powerful suppressive effect on grass production, due to competition. This effect is almost always non-linear – the first increments of tree biomass have a greater suppressive effect than the last ones. The degree of curvature depends on site conditions. A form for this curve can be derived from first principles regarding the way trees and grass carve up the space in savannas. Here is a simplified solution for a particular set of assumptions regarding tree canopy radius and rooting radius. In this equation, P is the fraction of grass primary productivity in relation to P0, the productivity of an untreed area, and BA is the total basal area of trees in square metres per hectare.
0.10
0.00
0.000
5.000
10.000
15.000
20.000
Tree basal area (m 2
/ha)
P = P0 * e-0.1BA

13. Maximum tree basal area
See Sankaran et al Nature (in press Aug 2005)
So, given that tree cover limits grass growth potential, we might expect to see areas becoming increasingly treed until the grass dies out. This is not the case, however, and so clearly some other factor is guiding the maximum tree basal area.
Considering savanna data from all around the world, there is a clear upper limit to the amount of tree biomass or leaf area that a piece of land can support, given its water balance. This line represents the limit of tree-on-tree competition.

14. What controls the growth rate of trees?
Ptree = e -0.2d * e -3(A/Amax) where A = basal area, d = diameter (cm)
12.00
10.00
y = x R = 2
8.00
6.00
Predicted Relative Annual Increment (%)
Charlie Shackleton’s PhD consisted of measuring tree circumference growth of thousands of stems, in savannas all over South Africa, every year for six years. From this wonderful dataset, some patterns emerge: the two main controllers of tree growth in savannas are the size of the tree (its stem diameter), and how much tree-on-tree competition it experiences. The latter is indexed by the tree basal area, as a fraction of the maximum basal area given that climate. The graph here shows the performance of this model: about 64% of variance is explained.
The interesting thing about this relationship is that a population of small diameter trees is much more productive than one with large diameter trees – this is important, and will be discussed later.
Size of the tree?
Competition with other trees?
4.00
2.00
0.00
0.00
2.00
4.00
6.00
8.00
10.00
Shackleton data
Observed Relative Annual Increment (%)

15. Effect of CO2 on NEP F (CO2) = 1+  ln([CO2]/[CO2ref]
Rising levels of carbon dioxide in the atmosphere have a stimulatory effect on plant growth. This effect saturates above about 1000 parts per million (ppm), and is different for C4 photosynthetic plants (tropical grasses) and C3 plants (trees). A simple ‘phenomenological’ model that fits the empirical data uses a ‘beta function’. [A phenomenological model is one that does not try to explain the underlying process, it just reproduces the result]
Hence, in conditions of increasing carbon dioxide, as currently is occurring through anthropogenic causes, it is likely that the proportion of trees in the savanna ecosystem will increase.
F (CO2) = 1+  ln([CO2]/[CO2ref]
~ 0.4 for trees, 0.2 for grass
[CO2ref] = 360 ppm

16. Effects of temperature on NEP
0.000
0.200
0.400
0.600
0.800
1.000
1.200 10 20 30 40 50
Mean daytime temperature (C)
Relative performance
trees
grass
There is also a difference in the temperature response of grasses and trees. In both cases it is hump-shaped, but C4 plants have a higher temperature optimum. These curves have a big impact on the outcome, because mean summertime daytime temperatures in many savannas are close to the C3 optimum. If they get hotter, production of trees goes down, but production of grasses continues to rise initially, and then declines at a slower rate than trees. The function that is used to model this relationship is shown under the graph.
ƒ[T] = ec*(1-{[(b-T)/(b-a)]^d }/d *(b-T)/(b-a)c
a = position of optimum ~ 28°C for trees, ~33°C for grasses
b =temperature below which no growth occurs ~5C trees, 10C grass
c = steepness of curve below optimum ~3
d = steepness of curve above optimum ~7

17. What controls tree mortality?
Fire
Elephants
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400 50
100
150
200
250
Growth days
Fraction of landscape burned
So, what are the main factors governing tree mortality? For the savanna ecosystem, the first is exceedingly well known, since savannas are one of the globe’s prime examples of a fire-driven landscape. The second factor governing mortality is elephants – elephants are capable of knocking trees over in order to get at the foliage or fruits at the top, and typically do so, particularly in marginal habitats where other (lower) food sources are being consumed rapidly by other herbivores. These smaller trees are then susceptible to burning. An emerging result from work by Brian van Wilgen and others is that the fraction of the landscape that burns is almost independent of fire management policy! In general, up to about 140 days of growth in a year, the amount of burning increases in response to the large amount of burnable foliage. However, over 170 growth days per year, this proportion decreases because of the large amount of rainfall and concomitant dampness of the area. In other words, climate plays a much larger role in the extent of burning than does management policies.

18. Mammal dynamics dN/dt = rN - offtake r = rmax * (f*N)/(c*Prey biomass)
Ln(rmax) = Body mass
f = food requirement (kg/head/d)
The population dynamics of herbivores and carnivores basically follows logistic growth functions: there is a maximum intrinsic population growth rate (which scales with body size), and it is reduced linearly as the population approaches its ‘carrying capacity’, which is in turn determined by the abundance of its food.
Thus the change in mammalian population numbers is equivalent to the current population multiplied by the growth rate, less the offtake (through predation or other mortality).
The growth rate is calculated in this second equation. The value rmax is the maximum growth rate for a population, and is a logarithmic function as described in the third equation. The f value in the second term of the growth rate calculation is the food requirement per head per day, and the C in the same term is the fraction of prey biomass that can be consumed in a year.
C = fraction of prey biomass than can be consumed in a year

19. Keeping it together! Complete competitors cannot coexist
Give each herbivore a partly unique resource
The faster-growing prey must be more preferred by predators
Preference = N2/N2
Predators must grow slower than prey
When you build even a moderately complex food web model, you soon find out that it is very hard to keep all the pieces coexisting. If you have two types of herbivore eating one grass resource, one will soon outcompete the other. So there must be some resource partitioning, although it is possible for each herbivore to share some of its optimal forage with other types.
You can balance this by making one more preferred by a predator. Predators are likely to prefer the faster-growing prey, for the simple reason that it is likely to be more available for consumption. This is included in the model by a preference term for predators, such that its preference for a species is a function of its representivity in the total herbivore population.
Finally, predators in general are much longer-lived than herbivores, and are also proportionally slower growing - if the predators have a fast growth rate, they will go into a ‘boom-and-bust’ cycle with the prey.

20. Test 1: trees, grass and fire10 20 30 40 50 60
2000
2020
2040
2060
2080
2100
Year
Plants (m2/ha),(g/m2),(m)
Basal Area
Grass prod
Tree ht
A simple model of the interactions between grasses and trees for the next 80 years shows us a reasonable pattern – over a century the tree biomass declines somewhat, and grass increases – as would be expected.
This model does not take into account any of the herbivore interactions, and assumes no further change in carbon dioxide levels or temperature – this change is based on the climatic status quo. Fire is included in the model, however.

21. Test 2: +herbivores, carnivores
If herbivores and carnivores are added into the system, the system is still stable, but not yet equilibrated in one century. Initially, coarse grazers (which are currently the dominant animal biomass component of the savanna system), Increase with the grass component of the ecosystem. However, browser numbers initially expand, and then decrease slowly as the proportion of the ecosystem given over to grassland increases. The carnivore population will also likely increase (tracking the growth in browser numbers), and then follow a gradual decrease as it becomes prey limited. It must be noted that all these models assume an unmanaged landscape with little or no human interaction.

22. Plants (m2/ha),(g/m2),(m)10 20 30 40 50 60
2000
2020
2040
2060
2080
2100
Year
Plants (m2/ha),(g/m2),(m)
Basal Area
Grass prod
Tree ht
Test 3: +elephants
5000
4000
Elephants
Coarse
3000
Adding elephants into the system, however, throws things completely out of kilter. Since elephants are known to prefer browsing (although they can survive as grazers as well), their impact on the tree population is considerable. The proportion of grass grows very rapidly, and both tree basal area and tree height drop to a low stable (coppiced point), as the elephants push over the larger trees and coppice the smaller ones. This stable, highly productive coppiced tree population is optimal for supporting elephants, since the level of production is so much higher than fully-grown trees.
The elephant population climbs rapidly from an initially moderate level to a very high one (in excess of 4t/km2). Even more importantly, the browsing pressure from elephants would push the browser population into competitive collapse before 2040, and then a shift in diet to include more graze would cause the coarse grazer population to crash within the next 25 years. The main reason for this is that there are no real predators for elephants, and the question that follows is why has this effect not been observed in nature? It seems the most probable reason is that there is no such thing as an undisturbed wild population, as hypothesized. For tens of thousand of years, the top predator in the African savanna has been the human, and in fact the hunter of our ancestors is the only reason we are not knee-deep in elephants today.
Herbivores (kg/km2)
Browser
2000
1000
2000
2020
2040
2060
2080
2100
Year

23. The experiment design B2 Scenario Hadley model 550 ppm A2 Scenario
Upper estimate
+5C, -6% rain
CCModel
Lower estimate
+2.2C, -1.2%
700 ppm
Now we apply a climate experiment on top of the pattern with no climate change. The ‘minimum experiment’ is a high change and low change scenario (A2 and B2), and two different climate change models, chosen from the about 12 available from the IPCC Data Distribution Centre website because they behave rather differently over southern Africa. For purposes of this experiment, the upper estimate of environmental shift was provided by the Hadley A2 scenario (giving an increase in temperature of about 5 °C, and a reduction in average rainfall of approximately 6%), whilst the lower estimate of climate change was provided by the CCModel B2 scenario (an average increase of 2.2 °C and a decrease of 1.2% in average rainfall). In order to use these estimates, however, the outputs of these models had to be downscaled significantly, since at the scale of GCM outputs, the whole of South Africa falls within about 12 cells.

24. Change in production drivers
2.0
1.5
Water balance
f(CO2)g
Production drivers
1.0
f(CO2)t
f(T)g
0.5
f(T)t
0.0
0.5
1.0
1.5
2.0
2000
2020
2040
2060
2080
2100
Year
Production drivers
Water balance
f(CO2)g
f(CO2)t
f(T)g
f(T)t
0.0
2000
2020
2040
2060
2080
2100
Year
To understand the climate change outputs, it is important to remember the factors that drive change in tree and grass production: water balance (controlled by both rainfall and temperature), CO2, and temperature. The water balance and temperature factors drive production down in the future in this case, while CO2 drives it up. It differs for trees and grass, but note that the climate factors overwhelm the CO2 effect. As you can see, the trends are similar but the extent of the change in drivers differs. For the first scenario, the water balance will drop, and the increasing carbon dioxide will slowly increase the grass production (f(CO2)g), whilst increasing tree production to a greater extent f(CO2)t. The temperature increase will increase grass production f(T)g, and decrease tree production f(T)t. The same drivers are true for the second scenario, but the extent of the drivers is greater.

25. Change in vegetation structure10 20 30 40 50
2000
2020
2040
2060
2080
2100
Year
Plants (m2/ha),(g/m2),(m)
Basal Area
Grass prod
Tree ht
Here are the runs without herbivores, carnivores and elephants. In the first (low impact) scenario, we see an increasing amount of grass primary production, although the rate of increase tapers somewhat by 2080 in response to decreasing rainfall. In the high impact scenario below the grass primary production initially increases very rapidly, but after mid century the rapidly decreasing water balance causes a drop in production. By 2080, the grass primary production is likely to be less than current levels. In both scenarios tree production drops.

26. Change in herbivores 3000 2500 2000 Coarse Herbivores (kg/km2) 1500
Browser
1000
500
2000
2020
2040
2060
2080
2100
Year
These effects carry through into the herbivores, but in neither case are they as dramatic as adding uncontrolled elephant populations, even in the absence of climate change.
In the low impact scenario, the responses are similar to those modelled at current levels – an initially rapid increase in browser population, peaking in 2020, and then steadily decreasing, and a gradually increasing grazer population throughout. However, in the high impact scenario, there is considerable change. The browser population follows a similar trend, although the 2020 peak population is lower than the low impact scenario, and the subsequent rate of population loss is greater. However, grazers do not steadily increase, but rather quickly reach a stable population, which begins to reduce as the amount of available grass decreases in response to reduced rainfall. Clearly the high impact scenario details significant impacts on savanna biodiversity, both in terms of animal and plant life.

27. Preliminary conclusions
Water and temperature effects can overwhelm the CO2 effect
Substantial changes in herbivore stocking rate are possible in the future
Elephants at high density put the tree cover into a stable coppice state
The outcome of climate-change induced habitat change depends on how you manage fires and elephants
So this simple model leads us to the hypothesis (it would need more detailed work to have a more firm conclusion) that contrary to current wisdom, rising CO2 will not necessarily lead to trees taking over from grasses. Just the opposite happens, because the detrimental effects of drying and warming on trees are greater than the benefits of rising CO2. In terms of parks management, grazer and browser numbers could be impacted by climate change towards the second half of the century, under high climate change scenarios, and this would in turn impact carnivores. Elephants are a major factor in the vegetation, and when at a high density, transform the landscape into a stable coppiced state, to the detriment of some other herbivores. Thus, the outcome of climate change induced habitat transformation is to a large extent dependent primarily on management policies and impacts in the arena of fires and elephants. This means that managers can therefore concentrate efforts on these two areas, minimising the required inputs.

28. Chapter 7: test yourself
Check your understanding of Chapter 7
PASS MARK 80%
Please do not proceed further until you have PASSED
Chapter 7: test yourself

29. Links to other chapters
Chapter 1 The evidence for anthropogenic climate change
Chapter 2 Global Climate Models
Chapter 3 Climate change scenarios for Africa
Chapter 4 Biodiversity response to past climates
Chapter 5 Adaptations of biodiversity to climate change
Chapter 6 Approaches to niche-based modelling
Chapter 7 Ecosystem change under climate change
Chapter 8 Implications for strategic conservation planning
Next
Chapter 9 Economic costs of conservation responses
I hope that found chapter 7 informative, and that you enjoy chapter 8.