The Use of Growth Indices in Climate Matching

In the earlier part of the 20th century, time series plots of daily, weekly or monthly temperature and other variables would be used to create graphs (e.g. thermohygographs) that characterized climate favourable to the distribution of species. This empirical approach did not include the physiological responses of species to the climatic factors. Fitzpatrick and Nix (1970) made an important innovation by characterizing the growth rates of temperate and tropical pastures in Australia as normalized hump-shaped physiological response indices to weather and edaphic factors (Fig. 16.1a). A low index value means that the factor was either below or above the optimum (i.e. the peak). The easiest effect to demonstrate is that of temperature on developmental rate (Fig. 16.1b). The derivative of the developmental rate function is also hump-shaped (e.g. Fig. 16.1a), suggesting that development occurs above a lower thermal threshold and stops at an upper one with the maximum at the peak. Temperature sets the baseline for the potential developmental rate of poikilotherms, with other factors altering growth, development and reproduction. The relationship of developmental rate to temperature is shown for three hypothetical species in a food chain (Fig. 16.1c). In this example, the

Temperature (T)

Fig. 16.1. Hypothetical developmental responses of a poikilotherm to temperature: (a) the developmental rate; (b) the temperature derivative of the developmental rate function in (a); (c) the hypothetical developmental rates on temperature of a plant, a herbivore and a predator.

Temperature (T)

Fig. 16.1. Hypothetical developmental responses of a poikilotherm to temperature: (a) the developmental rate; (b) the temperature derivative of the developmental rate function in (a); (c) the hypothetical developmental rates on temperature of a plant, a herbivore and a predator.

plant has a broad response to temperature, the herbivore has an intermediate one, and that of the predator is quite narrow. This means that the plant may develop at lower and higher temperatures than both the herbivore and the predator, and that the herbivore has a broader range than the predator. The studies of Messenger and Force (1963) and Messenger (1964, 1968) on the spotted alfalfa aphid and its parasitoids are excellent examples of such thermal effects on trophic-level developmental and demographic rates, and the consequences on the geographical distribution of these species.

This exposé is a reasonable explanation for the formulation of the temperature index (77) in the Fitzpatrick—Nix system. For factors such as soil nitrogen, a low index value might mean that either there is too little or that it is present in toxic quantities. In general, growth is assumed to be a function of several factors each assumed to have similarly shaped growth indices. In the Fitzpatrick-Nix approach, the final growth index is a product of all growth indices. Assuming indices for temperature (77), nitrogen (AT), soil water (Wl) and other factors and using the Fitzpatrick-Nix model, the growth index Gl(t) at time t at location ij is computed as:

Glij(t) = Tljj(t) ¥ Nlj(t) ¥ Wlj(t) ... (Eqn 16.1)

A factor may be limiting (i.e. equal zero), making Gl(t) = 0, and is a demonstration of von Liebig's Law of the Minimum. Normally, factors exhibit different levels of favourability, and the product of their indices reflect the compounding effects on Gl(t).

To demonstrate the utility of their approach, Fitzpatrick and Nix computed the weekly 30-year average G7 for temperate and tropical pastures for all sites in Australia having the requisite meteorological data. Though not stated, the net flux of factors such as soil water, nitrogen and other essential nutrients have to be updated at each site to characterize their time-varying effects. The areas of favourability of pasture growth across Australia could then be mapped for the different periods of the year using equation 16.1.

Gutierrez et al. (1974) modified this approach and used it to explain the phenology and abundance of several species of aphid trapped weekly at 32 locations over a 2-year period (1969/70) in southeast Australia. Weather in this area is highly variable temporally and spatially, and many of the aphids do not survive year round in much of this area because of winter frost or summer drought. These aphids must recolonize areas when favourable conditions return. Small areas of microclimate may enable small numbers to persist but these are usually insufficient to repopulate the area. Their migration is undirected and winged aphids are blown on the winds to favourable and unfavourable areas alike. A good example of a species with this migratory habit is the cowpea aphid (Aphis craccivora Koch), which breeds on pasture legumes throughout Australia. In most areas, influxes of migrants are required to begin local population growth when conditions are favourable. It is not uncommon for areas with lush pasture to receive few or no aphid migrants and only small populations arise. Large influxes of migrants may arrive in areas with mostly bare ground during extended periods of drought (Gutierrez et al., 1971, 1974). Populations of the cowpea aphid on occasion reach the very high densities reported by Johnson (1957). This may occur when local conditions are favourable for long periods and large influxes of migrants arrive. Normally the season is too short for such outbreaks to occur on a regular basis. Hence, soil moisture limits pasture growth during summer and frost limits the aphid during winter. Natural enemies play a minor role in regulating aphid numbers, hence cowpea dynamics in most areas of southeast Australia are weather-driven.

Temperature indices for the aphid and soil moisture indices for the plant were computed at the 32 trap locations for the period 1968-1970, using observed weather and 30-year average weather. Autumn is an important period for the build-up of cowpea aphid (Gutierrez et al,, 1971). Weekly values for autumn (roughly weeks 6 to 20) for 1969 and 1970 and 30-year average weekly values are shown in Fig. 16.2a, for Bathurst and Trangie, New South Wales. These data demonstrate the large variability of weather that regularly occurs in southeast Australia. The autumn of 1969 was wetter and cooler than the same period in 1970 which was a period of drought. Cowpea aphid populations developed in 1969 but not 1970 at these two locations.

During the years 1969 and 1970, cowpea populations developed at 18 of the 32 sites. The populations developed at different times of the year at the different locations. Average temperature and moisture indices for the periods of aphid activity at these sites are plotted in Fig. 16.2c. The data exhibit a remarkable degree of clustering, with the boundary around the data being the bivariate normal tolerance limits (P <0.05). This figure may be viewed as a physiological thermohygrogram that defines the physiological limit of tolerance of the aphid to the two factors (i.e. an estimate of Shelford's Law of Tolerance for the two factors). This means that local conditions are favourable for cowpea aphid population growth when the indices are within this boundary. Price (1984) illustrated this concept quite nicely and Fig. 16.3 is redrawn from that work. Gutierrez et al. (1974) also examined the regional migration of cowpea aphid, explaining how the patterns of winds characteristic to southeast Australia enable it to bridge areas of favourability. The original papers should be consulted for details.

Other species may respond differently to the same two factors, and of course many other factors (more dimensions) may impinge on them. Similar growth indices computed for two grass aphids (Rhopalosipum padi and R. maidis) yielded similar clustering of the data, but in different areas of the physiological thermohygrogram (Fig.16.2d). The distribution of the growth index data reflects the fact that R. maidis population occurs late in the spring and early summer, when the Mediterranean grasses are drying. Populations of R. padi may develop during wet cool periods of autumn and early spring because they are protected at the base of bunch grasses. Gutierrez and Yaninek (1983) used different methods to examine the thermohygrograms for six other species, and included the size of the populations in computing the tolerance region.

The important point of these analyses is that site favourability determines when outbreaks can occur, but the arrival of migrants is a necessary prerequisite for the build-up of cowpea populations.

Fig. 16.2. Growth indices for cowpea aphid in southeast Australia (Gutierrez et al., 1974) using the Fitzpatrick and Nix (1970) method: the historical 30 year average values (i.e. the margins of the shaded area) and the values for autumn 1969 (—) and 1970 (—) at (a) a highland site (Bathurst, New South Wales) and (b) on the interior plains (Trangie, New South Wales); (c) the average indices at 18 of the 32 locations for the periods when cowpea aphid populations developed (see Gutierrez et al., 1974, and text); (d) the average indices for two grass aphids (the shaded area is that of cowpea aphid in (c).

Temperature index

Fig. 16.2. Growth indices for cowpea aphid in southeast Australia (Gutierrez et al., 1974) using the Fitzpatrick and Nix (1970) method: the historical 30 year average values (i.e. the margins of the shaded area) and the values for autumn 1969 (—) and 1970 (—) at (a) a highland site (Bathurst, New South Wales) and (b) on the interior plains (Trangie, New South Wales); (c) the average indices at 18 of the 32 locations for the periods when cowpea aphid populations developed (see Gutierrez et al., 1974, and text); (d) the average indices for two grass aphids (the shaded area is that of cowpea aphid in (c).

The studies of Fitzpatrick and Nix (1970) and Gutierrez et al. (1974) predate the advent of modern GIS, which can now quickly capture and map regional data. The climate-matching GIS program climex developed by Sutherst et al. (1991 and citations therein) is also based on the Fitzpatrick-Nix approach; it uses 30-year weather averages and includes areas outside of Australia. This algorithm has been used effectively to map the potential range of the Russian grain aphid (Diuraphis noxia) (Hughes and Maywald, 1990), the pathogen Phytophthora cinnamoni on Quercus spp. (Brasier and Scott, 1994) and other pests. Its successful application has occurred because the Fitzpatrick-Nix indices capture the shape of some essential biology. A

Fig. 16.3. Hypothetical physiological growth response of a poikilotherm to two environmental factors (cf. Price, 1984).

shortcoming of climex is that the physiological—mathematical bases have not been published. Below we develop a reasonable mathematical description of this biology.

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