Response to commentary by Gutierrez et al.

Gutierrez et al. [1] raise several technical issues concerning our paper [2] to which we will reply later. However, the main thrust of their commentary was that the physiologically based demographic model (PBDM) described by Gutierrez & Ponti [3] would provide a more enlightened, alternative approach ‘that addresses the biology of the invasive species’ [1, p. 1].

For Italy, the Gutierrez & Ponti [3] PBDM predicted that coastal areas of Rome, southern areas of Sardinia and the Italian peninsula, Sicily, and Liguria in northwest Italy are favourable for the medfly [3, p. 2670], but colder regions of the country are unfavourable. Gutierrez & Ponti [3, p. 2671] selectively cite the findings by Israely et al. [4] that these researchers could not document medfly overwintering in the Jordean Hills, but fail to cite research by the same group in Israel that verifies medfly overwintering in another mountainous region [5]. After stating that ‘data on its [medfly] distribution [in Italy] are not available’ [3, p. 2668], they use anecdotal information concerning the medfly distribution in Italy (see quote from Ivo Rigamonti; [3, p. 2669]) as the basis for their statement that ‘The [model's] predictions … for Italy … are in accord with these [Rigamoni] observations’. [3, p. 2670].

The Gutierrez & Ponti [3] PBDM predicts that California's Central Valley is too hot for the medfly, yet populations of this pest prosper in regions of the world that experience temperatures similar to those recorded in most regions of the Central Valley. The average maximum temperatures of 33°C in Sacramento, 34°C in Stockton, 35°C in Modesto, 36°C in Fresno and 37°C in Bakersfield correspond closely to the average maxima in the medfly-infested regions of the Mediterranean Basin and Middle East such as Tel Aviv (32°C), Cairo (37°C) and Tripoli (36°C) (World Meteorological Association; http://www.wmo.int/pages/index_en.html). Indeed, the medfly is a pest in the Tunisian governorate of Tozeur [6], an oasis in the Sahara Desert with average high temperatures exceeding 37°C—a temperature that this pest has been shown to tolerate for up to 8 h in controlled studies [7].

The Gutierrez & Ponti [3] PBDM predicts that cities in California's Central Coast and Bay Area are too cold for medfly populations. Yet the average minimum temperatures of 5–6°C during the winter months in Santa Barbara, Santa Cruz and San Luis Obispo, and 8°C in San Francisco, are warmer than average minima in the more northern and/or colder regions where the medfly is established, including average minimum temperatures of 1°C in Thessaloniki (Greece), 2°C in Girona (Spain) and 6°C in Athens (Greece). A sterile medfly rearing factory was constructed for medfly control in the Nereva River Valley in Croatia [8] at the same latitude and with a similar climate as Medford, Oregon (42.3° N lat)—a city located 40 km north of the northern border of California and 1100 km north of the limits predicted by Gutierrez & Ponti [3].

Gutierrez et al. [1] re-stated much of our narrative about our N statistic and re-affirmed that our statistical test was anti-conservative [2, p. 7]. These authors stated correctly that it is impossible to disprove our hypotheses but, short of detections of all stages over multiple years for any particular species, it is impossible to disprove any hypotheses, including any they might propose. As we pointed out (see Introduction in [2]), the concept of ‘preponderance of evidence’ is used to support hypotheses, but proof is unattainable in both theory and practice. These authors claim our theories of and criteria for population establishment have limitations in [2, p. 8 and electronic supplementary material, table S7], yet provide neither alternative concepts nor operational criteria for classifying the establishment status of tephritids. The claim by Gutierrez et al. [1] that we failed to explain why the medfly did not develop measureable populations is incorrect inasmuch as we noted three relevant concepts: (i) population suppression from intervention programmes [2, p. 2]; (ii) population lags [2, pp. 7–8]; and (iii) naturalization [2, p. 8].

The problems associated with the use of complex, age-structured plant growth models such as PDBM for prediction have been extensively discussed both for plant growth models [9] and for age-structured models [10]. The authors of these papers, who are highly respected modellers themselves, point out the strengths of such models in gaining general understanding of processes and the weaknesses of these same models for predicting particular individual processes. In [8], the example is given of the feeding of the same data into several different wheat models and getting very different results from each one. In [9], an example is given in which an age-structured model does a poor job of predicting data generated from that same model when a small amount of noise is added.

The overarching problem with the author's commentary [1] is that they shift the focus of the analysis to the inappropriate use of simulation models in general and of their faulty PBDM in particular [3]. In doing so they ignore the actual data for 17 tephritid species, 11 386 individuals, 3348 locations and 326 infested cities. Consequently, they do not address the most important set of questions concerning the tephritid invasion of California—Why do the same species continue to reappear year after year, while at the same time they are absent from virtually all other fruitfly-friendly regions of the USA with similar or even much greater propagule pressure? We believe that there is value in the type of modelling proposed by Gutierrez et al. [1]. However, the geographical range of medfly establishment predicted by their model is inconsistent with the observed distribution, thus we conclude that their model is not sufficiently realistic for its specific predictions to be accurate. We stand by the methods we used to conclude that five to nine tephritids are established in California.